Article: How To Find Molar Mass From Molarity: Detailed Explanation

You're reading How To Find Molar Mass From Molarity: Detailed Explanation, last updated on 2022-06-01 20:46:51

2022-03-25

how to find molar mass from molarity: There are many ways to find molar mass from molarity, but we are going to work with one equation from which on rearranging it we can obtain the required product.…

In this article we are going to analyze how to find molar mass from molarity.

There are many ways to find molar mass from molarity, but we are going to work with one equation from which on rearranging it we can obtain the required product. For this we should know the other quantities other than the one of our interest.

To understand how to find molar mass from molarity we must first understand the relationship between the two terms.

The below equation is of our interest:

M = w/( mv )  … equation 1

Where in,

M = molarity ( in moles/L )

w = the weight of the solute ( in grams )

m =molar mass of solute ( g/mole)

V = volume of the final solution once the complete dissolution is done ( in litres ).

We can find molar mass from molarity by rearranging the equation 1

m = w/ Mv … equation 2

So we can find the three quantities the weight of the solute ( w ), Molarity ( M ), and Volume of the solution ( V ).

Finding molarity:

There are many ways in which we can find or calculate molarity but the very basic one that we use nowadays is:

Molarity = moles of solute / Liters of solution or Volume of solution.

By using the above relation we can calculate molarity.

Finding Volume:

The provided Volume make sure before substituting it should be in liters.

After knowing the three quantities, we can substitute them in equation 2 and obtain molar mass. So in this way by using the above relationship we can find out molar mass from molarity.

how to find molar mass from molarity
how to find molar mass from molarity

Image credit: Wikimedia

How to find molarity from molar mass and density?

In order to find molarity from molar mass and density, we should have a relation between the three terms.

What I am referring to is if we know the two terms we can find out the third one. We can understand molarity in simple words as the amount of any substance present in a given volume of solution ( the one being considered). Another term used to describe molarity is the molar concentration ( of given solution).

The notation used to denote molarity is M and its standard unit is mol m-3. Density, which is also referred to as specific mass is the mass per unit volume, and the notation used to denote it is rho ( a Greek letter). Its standard unit is kg/m3. A quantity like the pressure is directly proportional to density meaning as the pressure is increased ( keeping the temperature constant ) the density will increase. 

Image credit: Shutterstock

Temperature is inversely proportional to density meaning as the temperature is increased ( keeping the pressure constant) the density will decrease.  The Molar mass of a compound ( chemical) is the mass of the compound ( in consideration) divided by the substance ( amount) in the sample of the compound being referred. 

It’s sometimes also referred to as molecular weight. The standard unit used to describe molar mass is kg/mol. So now we know the perfect meaning of the three terms. So the relation can be given as

Molarity = density/molar mass × 1000

So, if we know density and molar mass of a substance we can easily calculate its molarity.

How to find moles from molar mass ?

We know that 1 mole is equivalent to 6.022 × 1023. We can find moles from the molar mass by using the formula given below:

n = m/M         

n = number of moles

m = given mass

M= molar mass

For better understanding let’s see some examples:

  1. Find out the number of moles in 70g of CH4.

Solution

First, we should calculate molar mass ( by simply adding the weight of the atoms in CH4 formula) and we are provided with mass = 70g (m)

Molar mass = CH4 = 12 4 = 16g/mol.

n = m/M = 70/16 = 4.36 mol

2. Find out number of moles in 10g of NaOH.

Molar mass (M) = NaOH = 23 16 1 = 40g/mol

m = 10g

n = m/M = 10/40 = 0.25 mol

3.Find out number of moles in 35g of glucose

Molar mass (M) = C6H6O12 = 6×12 12×1 6×16 = 180g/mol

m = 35g

n = m/M = 35/180 = 0.194 mol

4.Find out number of moles in 96g of NaCl

Molar mass = NaCl = 23 35 = 58g/mol

m = 96g

n = m/M = 96/58 = 1.65 mol

Read more about: How To Find Molar Mass From Volume: Detailed Explanations

How to find mole fraction from molarity?

Let us now see what is the relation between mole fraction and molarity.

Consider,

XA = mole fraction of solvent

XB = mole fraction of solute

MA = Molecular mass of solvent

MB = Molecular mass of solute

nA = number of moles of solvent

nB = number of moles of solute

WA = mass of solvent

WB = mass of mass of solute

So the mole fraction of the solvent:

XB = nA / nA nB   … equation 1

And the mole fraction of the solvent :

XA = nA / nA nB  … equation 2

After dividing equation 1 by equation 2 we get

XB × 1000 / XA × MA = WB × 1000 / WA × MB = m = Molarity

Therefore Molarity = XB × 1000 / ( 1- XB ) × MA

By rearranging the above equation in an order of our requirements we can calculate mole fraction.

Read more about: Is Hydrogen Bond Stronger Than Covalent: Why, How and Detailed Facts

How to find the mass of a mole fraction?

We can understand the interconversion of the two quantities from the following example:

mass → mole

36   C

16   H

20   O

28   N

Assume a basis 100g

Change mass to moles

36g C / 12g / mole = 3 moles

16g H / 1g / mole = 16 moles

20g O / 16g / mole = 1.25 moles

28g N / 14g / mole = 2 moles

Add all the moles together = 22.25 moles

Find the mole fraction: moles / total moles

So the mole fraction will be

C : 3 / 22.25 = 0.135

H : 16 / 22.25 = 0.719

O : 1.25 / 22.25 = 0.056

N : 2 / 22.25 = 0.090

The total of mole fraction comes up to be 1.0.

Mole to mass fraction

36 C

16 H

20 O

28 N

Assume a basis of 100 moles

Change moles to mass

C : 36 moles × 12g / mole = 432g

H : 16 moles × 1g / mole = 16g

O : 20 moles × 16g mole = 320g

N : 28 moles × 14g / mole = 392g

On addition of all the masses we get 1160g

Find mass fraction: mass / total mass

C : 432 / 1160 = 0.372

H : 16 / 1160 = 0.014

O : 320 / 1160 = 0.276

N : 392 / 1160 = 0.338

So, in this way we can find the mass of a mole fraction.

Read more about: 12 Hydrate Examples: Detailed Explanations

How to calculate molar mass example?

Calculating molar mass is very simple just have to add the weights of the atoms, let’s understand through the below example:

Image credit: Istockphoto

1.Calculate the molar mass of sodium carbonate

Solution :

We know that the chemical formula of sodium carbonate is Na2CO3

Na (sodium) : 23×2 = 46

C : 12×1 = 12

O : 16×3 = 48

After adding all the masses :

46 12 48 = 106g/mol

So the molar mass of sodium bicarbonate is 106g/mol.

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Bending Stress Formula: Several Use Cases And Examples

18-01-2022 · Bending stress formula derivation Let us consider a beam section as shown in the diagram below-. Let us assume a moment, M is applied on the beam. The beam curves by an angle theta and makes a radius of curvature R as... Strain is also given by-. from above equations we can conclude that,. Now,. ...

18-01-2022

This article discusses about bending stress formula for different types of beam configurations. We all know that when an object curves due to application of load then it is said to be subjected under bending.

It is very important to know the amount of bending stress being experienced by the work piece. The work piece will break if the applied bending stress exceeds more than the maximum allowable bending stress. The bending strength of the material is the maximum amount of bending strength that can be applied on the work piece before the work piece starts to fracture.

What is bending stress?

Let us start our discussion with the definition of bending stress. It is simply the stress which is responsible for bending of the work piece.

In further sections we shall see the mathematical forms of bending stress for various beam configurations and cross sectional shapes.

What is a beam?

A beam is a structural element that is mainly used for supporting the primary structure. The beam is not necessarily a support, it can itself be a structure for example bridges and balconies.

Most commonly used beams in industry are cantilever beams, simply supported beams and continuous beams.

Bending stress formula for beam

The bending stress depends on the bending moment moment of inertia of cross section and the distance from the neutral axis where the load is applied.

Mathematically, it can be represented as-

\sigma = \frac{My}

y it he distance from the neutral axis

I is the moment of inertia of cross section

In terms of section modulus-

\sigma = \frac

where,

Z is the section modulus of the beam

M is the bending moment

Bending stress formula units

The formula of bending stress can be given as-

\sigma = \frac{My}

The formula in terms of units of each quantity can be given as-

Units= \frac{N-mm\times mm}{mm^}

From above, we can derive that the units of bending stress is-

Units= \frac{mm^}

Allowable bending stress formula

The allowable stress is the value of stress beyond which stress should not be applied for safety reasons. The allowable bending stress depends on the flexural rigidity of the material.

The allowable bending stress formula can be given as-

\sigma_{allowable} = \frac{\sigma _{max}}{Fs}

where,

Fs is the factor of safety

Bending stress formula derivation

Let us consider a beam section as shown in the diagram below-

bending stress formula
Image: Beam

Let us assume a moment, M is applied on the beam. The beam curves by an angle theta and makes a radius of curvature R as shown in figure below-

Image: Bending moment on beam

The strain in neutral axis is zero. Whereas the strain acting on the line where force is applied experiences strain. Balancing all strain values we get total strain,

\frac{(R y)\Theta -R\Theta }{R\Theta }= \frac{y}

Strain is also given by-

Strain =\frac{\sigma }

from above equations we can conclude that,

\frac{\sigma }{y}= \frac

Now,

M= \sum \frac\times y^

and,

\delta A=\frac\sum y^\delta AM= \frac\times I

From above equations we conclude that,

\frac{\sigma }{y}= \frac= \frac

Hence derived.

Bending stress formula for rectangular beam

Depending upon the cross section of the beam, the moment of inertia changes and hence the bending stress formula.

The moment of inertia of rectangle is given as-

I= \frac{bd^}

From above, bending stress formula for a rectangular beam can be written as-

\sigma = \frac{bd^}

Bending stress formula for hollow rectangular beam

Hollow beams are used to reduce the weight of the beam. These beams can be used in light weight applications.

Let us consider a beam with hollow rectangular cross section with outside length as D and inner length as d, outside breadth as B and inner breadth as b.

The section modulus of this cross section will be-

Z=\frac\times (BD^-bd^)

Hence the bending stress formula for a hollow beam can be given by-

\sigma =\frac{(BD^-bd^)}

Bending stress formula for circular cross section

Let us consider a beam having a circular cross section of diameter D.

The moment of inertia of circular section can be given by-

I=\frac{\pi D^}

From above, we can write the bending stress formula for circular beam as-

\sigma =\frac{bd^}

Bending stress formula for hollow shaft

Let us consider a hollow circular shaft having inner diameter d and outside diameter D.

The moment of inertia of hollow circular section can be given as-

I=\frac{\pi (D^-d^)}

From above, the bending stress can be written as-

\sigma =\frac{\pi (D^-d^)}

Bending stress formula for pipe

A pipe is simply a hollow circular shaft. So the bending stress formula is same as that of hollow circular shaft.

That is,

\sigma =\frac{\pi (D^-d^)}

Maximum bending stress for simply supported beam

The general formula for bending stress remains the same that is-

\sigma =\frac{My}

However, the formula is modified as per the type of loading. The loading can be in the form of point load, uniformly distributed load or uniformly variable load. In further sections we shall see the different formulae for simply supported beams in different forms of loading.

What is bending moment?

The reaction induced in a structural element or the bending effect produced when an external load is applied on the beam (structural element).

Bending moment formula for different beam configurations under different types of loading is discussed in below sections.

Bending moment formula for fixed beam

A fixed beam is a type of beam which is fixed at both the ends. At both the ends the reaction forces are present. The bending moment formula for fixed beam under different types of loading is given below-

  • Bending moment under UDL or Uniformly distributed load

The formula for bending moment of fixed beam under UDL is given as-

M=\frac{wL^}
  • Bending moment under point load

The formula for bending moment of fixed beam under point load is given as-

M=\frac{wL}
  • Bending moment under trapezoidal load or UVL or uniformly variable load

The formula for bending moment of fixed beam under trapezoidal load is given as-

M_=\frac{wL^}

For other side,

M_=\frac{wL^}

Bending moment formula for continuous beam

The bending moment of continuous under different types of loading is shown below-

To find the bending moment of continuous beam under uniformly distributed load, we need to find the reaction forces at the end points. After that we have to apply equilibrium conditions that is sum of all horizontal and vertical forces is zero as well as moments is zero. To solve UDL, we multiply the length with the magnitude of UDL. For example, if 2N/m of UDL is applied till 4m length of work piece then the net load acting will be 2×4= 8N at center that is at 2m.

  • Bending moment under point load

The procedure is same as for UDL. The only difference is that here we know the magnitude of force and the distance at which it is acting so we need not convert it into point load as we did for UDL.

  • Bending moment under UVL or uniformly varied load

To solve UVL, we need to find the area of the triangle formed by UVL. The area is the magnitude of point load that will be acting due to UVL. The distance from vertex will be L/3 at which the point load will act. Rest of the procedure is discussed above.

Bending moment formula for rectangular beam

Bending moment of the beam does not depend on the shape of the beam. The bending moment will change as per the loading conditions and the type of beam (whether continuous, cantilever simply supported etc).

Only the moment of inertia changes with the shape of the cross section of the beam. This way the bending stress formula changes. The bending stress formula for rectangular cross section is discussed in above section.

Bending moment formula for UDL

UDL or uniformly distributed load is the type of load which is applied to a certain length of the work piece and is equal in magnitude wherever applied.

The bending moment formula for UDL of different beam configurations are given below-

  • For simply supported beam-

The formula for bending moment of simply supported beam under UDL is given as-

M=\frac{wL^}

The formula for bending moment of cantilever beam under UDL is given as-

M=\frac{wL^}

Bending moment formula for point load

Point load is the type of load which acts only at a particular point on the surface of the work piece.

The bending moment formulae for point loads for different beam configurations are given below-

  • For simply supported beam: The formula for bending moment of simply supported beam under point load is given as-
M=\frac{wL}
  • For cantilever beam: The formula for bending moment of cantilever beam under point load is given as-
M={wL}

For other beam configurations, the formula for bending moment is discussed in above sections.

Bending moment formula for trapezoidal load

Trapezoidal load is a type of load which is applied to a certain length of the work piece and varies linearly with length. Trapezoidal load is combination of both UDL and UVL. Lets assume magnitude of UDL as zero to ease our calculations.

The bending moment for different beam configurations under trapezoidal load are given below-

  • For simply supported beam– The bending moment of simply supported beam under trapezoidal load is given as-
M=\frac{wL^}
  • For cantilever beam– The bending moment of cantilever beam under trapezoidal load is given as-
M=\frac{wL^}

For other beam configurations, the formula is discussed in above section

Summary of bending moment formula

Table below shows a brief summary of formula for different beam configurations under different types of loading

Type of beamPoint loadUDLUVL
CantileverwL(WL^2)/2(WL^2)/6
Simply supportedwL/4(WL^2)/8(WL^2)/12
FixedwL/8(WL^2)/12(WL^2)/20
Table: Maximum bending moments of different beam configurations under different types of loading

Summary of bending stress formula

Table below shows a brief summary of formula for bending stresses of different beam cross sections

Cross sectionBending stress
Rectangular6M/(bd^2)
Hollow rectangular3M/BD^3-bd^3)
Circular32M/bd^3
Hollow circular32MD/(D^4-d^4)
Table: Summary of bending stress formula
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NH3 Lewis Structure: Drawings, Hybridization, Shape, Charges, Pair …

19-05-2022 · NH3 polar or nonpolar. The difference between electronegativity of the atoms participate in the formation of any compounds is one of the important factor for finding polarity or amount of dipole moment in the compounds. NH3 is a polar compound, which is imposed by the existence of dipole moment in the compound.

19-05-2022

NH3 Lewis structure needs to be described for illustrating the knowledge about the compound. This article would be developed with the facts delivered by the Lewis structure of NH3.

The facts that would be emerged in this article are:

Drawing Lewis structure for NH3

There are few basic steps, which are followed to draw the Lewis structure of several compounds. Those steps determines the structure properly and provides knowledge about step by step formation of internal shape of a compound through electronic changes.

NH3 Lewis structure from Wikipedia

At first, calculating the number valance electron present in the elements of the compound must be done. Then recognising the centre atom is regulatory to develop the initiation of drawing.

The calculation of formal charges and the number of bond pairs and lone pairs in the compound is the next step for completing the drawing of structure of Ammonia. Sketching the structure of Ammonia gives proper shape with the inclusion of these steps.

NH3 Lewis structure shape

The shape of Ammonia can be determined after drawing the NH3 Lewis structure. It denotes the formation internal geometry of the compound.

NH3 hold Trigonal pyramidal or distorted tetrahedral molecular geometry in terms of its shape. This shape is identified from the Lewis structure as it indicates the presence of one lone pair in the Nitrogen atom, which is centre atom in the compound.

NH3 Lewis structure formal charges

A fundamental formula helps to identify the formal charges held by the atoms in any compound. This is a significant characteristic, which is highly considerable in the case of drawing Lewis structure of the any compound.

The formula of finding formal charges is (valance electrons – nonbonding electrons – ½ bonding electrons).

Therefore, formal charge of Nitrogen atom is (5-2 (1/2)6) = 0

Formal charge of each of the Hydrogen atoms (1-0 (1/2)2) = 0

Summing up the individual formal charges of the atoms present in Ammonia the entire charge of the compound is estimated as zero.

NH3 Lewis structure lone pairs

The presence of lone pair is also denoted by Lewis structures of the compounds. As the lone pairs affect the shape of the compounds, it is important to identify the number of lone pairs in those compounds.

Ammonia has two lone pairs held by Nitrogen atom as the hydrogen atoms holds only two electrons, which participate in making bond pairs. Besides, this lone pairs effect on the polarity of the overall compound.

NH3 hybridization

Hybridization of the compounds are also encountered by the Lewis structure, which indicates the internal structure of the compounds, it also influences the shape of the compounds.

nh3 lewis structure
Hybridization of NH3 Lewis structure from Wikipedia

NH3 has sp3 hybridisation in the pyramidal or distorted tetrahedral shape.  The hybridisation of Nitrogen atom denotes the overall hybridisation of Ammonia. The combination of 2s and 2p orbitals are found in the compound.

NH3 Lewis structure resonance

In the case of posing resonance, the compounds must hold one or more than one π bonds. Only sigma bonds cannot show resonating features in the compounds.

NH3 does not possess any π bonds in the molecular structure, which is lacking resonating characteristics in the Ammonia. Without presence of double bonds there is no chance of transitioning the bonds and structure by keeping the formula same.

NH3 Lewis structure octet rule

Octet rule says that the last energy level of the compounds gives extreme stability to the atoms by driving the atoms to precede electron-sharing process. The elements are likely to adopt the similar electronic configuration like the nearest noble gases by fulfilling their last electron shell of octet state.

In order to maintain this octet rule N and H both the atoms undergoes election-sharing method by sharing their valance electrons with each other. Hydrogen needs one electron for filling octet and Nitrogen needs three electrons for the same.

Each Hydrogen atoms partially adopts one electron from the last electronic shell of Nitrogen. Nitrogen shares its electrons with three hydrogen atoms for adopting three electrons from those hydrogen atoms partially as well.

NH3 polar or nonpolar

The difference between electronegativity of the atoms participate in the formation of any compounds is one of the important factor for finding polarity or amount of dipole moment in the compounds.

NH3 is a polar compound, which is imposed by the existence of dipole moment in the compound. Huge difference in electronegativity of Nitrogen and Hydrogen gives rise to this polar nature. Non-symmetrical pyramidal shape with the lone pairs in the compound is responsible for giving high polarity to the Ammonia.

NH3 Lewis structure bond angle

Bond angle can also be found from the Lewis structure. The bond angle of the compounds is quite dependent on the shape of the compounds and the place of the lone pairs.

The bond angle of NH3 is 107o, which is just a little bit lower than the standard bond angles of the compounds. This bond angle is the result of lone pair-bond pair and lone pair-lone pair repulsion, expressed by the molecular geometry.

NH3 Lewis structure electron geometry

Electron geometry refers to the molecular geometry of the compounds, which is fundamentally obtained from the Lewis structure of the compounds.

The molecular geometry of Ammonia denotes its distorted tetrahedral shape or pyramidal shape with slightly lower bond angle than the standard one. This happens due tie presence of lone pairs. The lone-pair-lone pair repulsion gives slightly bent structure to the electron geometry of Ammonia.

NH3 valence electrons

Valance electrons refer to those electrons, which are present in the last electronic shell of the elements. The number of valance electrum defines the capacity of adopting the dividing electrons of the periodic elements to satisfy octet.

In NH3, the number of valance electrons on Nitrogen is five and each of the three Hydrogen atoms holds one valance electron.

NH3 uses

Ammonia is used in several industrial productions. It has high demand in Agriculture as powerful fertiliser for cultivating crops.

The uses are:

Question 1: What is the difference between NH4 and Ammonia?

Answer: NH3 possess zero charges in it. It is completely a neutral compound where NH4 represent Ammonium ion which has one extra Hydrogen atom beyond its capacity.

Question 2:  What is Aqueous Ammonia?

Answer: The dissolved state of Ammonia gas in water is called Aqueous Ammonia or Liquid Ammonia.  

Question 3: Is ammonia Acidic or basic?

Answer: Ammonia is a basic compound with the pH between 11 and 12.

VGA vs HDMI:Exhaustive Comparison and Detailed Facts and FAQs

05-11-2021 · HDMI is recommended over for 1080p as VGA carries analog signal where HDMI carries digital in VGA at 1080p refresh rate is limited to 75 Hz at most, whereas with different versions of HDMI …

05-11-2021

VGA and HDMI are both display interfaces. Nowadays, HDMI is widely in use, where VGA is used in limited applications as VGA is the oldest display interface. 

This article will discuss the comparison between VGA vs HDMI in a detailed manner.

VGA HDMI Comparison:

VGA is the oldest display interface, and HDMI is one of the latest display interfaces, so lets compare these two technologies:

ParametersHDMIVGA
Stands ForHigh Definition Multimedia InterfaceVideo Graphic Array
Founded inHDMI was introduced at the end of 2002VGA is the oldest digital interface introduced in 1987
Designed and Introduced byHitachi, Sony, Toshiba, Philips, Silicon Image, Panasonic, and Thomson.IBM
SignalHDMI uses digital signals for communication. HDMI uses digital data signal and VGA uses analog data signal, then transfer or transmission of data is more efficient in HDMI than VGA. and HDMI is easily completable with digital devicesVGA uses analog signals for communication. New devices use a digital signal, so for using VGA cable digital to analog and  then analog to digital conversion required.
CompatibilityHDMI is compatible with DVI, VGA, etc, with converter.VGA to DVI and VGA to HDMI converter is also available
Resolution and Refresh rateHDMI with different versions, it can attain 8k (7680 X 4320) resolution with 120Hz refresh rate, but HDMI with 2K resolution it can achieve 480Hz refresh rate.The maximum resolution of a standard VGA is 640 X 480 with a 60 Hz refresh rate. Higher resolution can be attained with different versions of VGA.
ConnectorHDMI has 19 or 29 pins in its connector, there are five different types of connectors in HDMI, such as Type A, Type B, Type C, Type D and Type E.VGA only has 15 pins in the D-SUB connector and VGA BNC connector has a separate connector for each color and sync, such as Red, Blue, Green, Horizontal Sync, and Vertical sync.
Noise or InterferenceHDMI cables are less sensitive to crosstalk but can suffer from interference by electromagnetic fields.VGA cables are easily subjected to crosstalk and interference.
CableVGA cable cannot carry audio, and video signal with one cable, for carrying audio and video two different cables is required. HDMI cables carry Consumer Electronics Control (CEC) which enable user to control HDMI devices with a maximum of 15 devices.HDMI cable carries both video and audio signal through one cable simultaneously .
CostVGA is inexpensive, but converters from VGA to any other signal can cost more than that of a VGA cable.HDMI is relatively costlier than that of a VGA, but converters of HDMI to Other signal is cheaper.
LagHDMI apply post processing on the input signal which causes lag.VGA connections generally exhibit less input lag than HDMI connections because VGA does not apply post-processing on the (input) signal.
HDMI
Image Credit: “HDMI” by Sam-Cat is licensed under CC BY-ND 2.0

HDMI vs VGA quality

HDMI can transfer eight channels of uncompressed or compressed digital audio simultaneously

The quality of HDMI is better than that of VGA because HDMI uses an uncompressed or compressed digital signal. In contrast, VGA uses an analog signal, which creates a significant difference in quality.

Since HDMI uses an uncompressed connection, HDMI is independent of the various digital standards used by individual devices. It can carry high-quality multi-channel audio data and can carry all standard videos. HDMI is capable of carrying control and Status information in both directions, and as modern devices use digital signals, HDMI is easily compatible with them. HDMI allows managing pixel by pixel the native resolution of the screen with whatever the source devices.

VGA vs HDMI gaming

High-resolution and high refresh rates, all frame rates are required for a quality gaming experience for modern gaming.

The standard VGA is limited to 640 X 480 resolution and refresh rate of 60 Hz, which is not very much suitable with modern gaming standards. In contrast, the maximum resolution HDMI can attain 8K with a 120 Hz refresh rate which is very much ideal for every modern gaming experience.

Although the cables do not limit the refresh rate or resolution, they can be restricted by the source or connectors used. As HDMI is comfortable with digital devices, it is preferred over VGA because VGA Uses an analog interface which seems outdated nowadays. Only limited devices use an analog signal, so if it is not necessary to use VGA, always go for HDMI for gaming.

VGA vs HDMI resolution

HDMI was introduced in 2002 to improve existing connectivity standards by creating more miniature and better connectors which can summon tenuously transmit digital video and audio signals.

The standard VGA 640 X 480 resolution with 60 Hz refresh rate, whereas with a different version of HDMI, it can go up to 8K resolution with 240 refresh rate.

VGA’s maximum resolution can attend up to 2048 X 1536, but VGA does not prefer HDMI for high-resolution.

VGA vs HDMI
Image Credit: “Monitor” by davispuh is licensed under CC BY 2.0

VGA vs HDMI cable

Resolution and refresh rates are not limited to the cable but are determined by the source or device.

The quality of HDMI cables is much better than that of VGA cables, as VGA requires separate cables for audio and video, where HDMI can transfer audio and video simultaneously. HDMI cable is capable of up to 8 compressed or uncompressed digital audio channels, along with Consumer Electronic Control (CEC). 

13w3 to VGA cable
Image Credit: “13w3 to VGA cable” by gctwnl is licensed under CC BY-SA 2.0

The data in the VGA signal is analogous, so loss in data or interference in this type of signal is easy. With an increase in the length of the wire, the quality of the signal decreases. VGA Analogue data signal is also prone to noise and interference. HDMI uses transmission minimized differential signaling (TMPS), which can convert A picture automatically into the most appropriate format such as 16:9 or 4:3.

HDMI cable has16 wires that are wrapped in a single cable and carry a bandwidth of 5gbps. HDMI carries high-quality multi-channel audio data and can carry all standard formate of video. HDMI has three different channels for communication such as Display Data Channel (DDC), Transition-minimized differential signaling (TMDS) and Consumer Electronics Control (CEC).

Does VGA to HDMI reduce quality

VGA to HDMI converter is more expensive than the price of the VGA cable.

As the signal in VGA is analog and signal in HDMI Digital, when the conversion of the signal takes place, some loss of Signal quality happens, which can also introduce noise in the Signal.

During the conversion from VGA to HDMI, the analog signal is converted into a digital signal (using analog to digital converter), and running the VGA signal directly into an HDMI connector can cause damage. The connector as an analog signal has a higher voltage level, so a scaler or converter is required, which will take the VGA analog signal and audio signal to convert them into a digital signal (using digital to analog converter), which can be sent out to HDMI cable for connection.

Why does VGA to HDMI not work

Convert the signal between VGA and HDMI using a converter chip, where the converter chip is either designed to convert a VGA signal to HDMI or HDMI signal to VGA signal.

VGA to HDMI converter is not working causes can be:

  • The problem with the connector or port.
  • The malfunctioning signal from VGA to HDMI.
  • Check the power supply of the converter as VGA to HDMI converter requires external power for processing.
  • Check connection or lose connections.
  • Bad quality display can be caused by incorrect interference with the cable or faulty connector.
  • Restart the device after connecting as VGA is required to restart for better compatibility with the device.
  • New cables can be covered with a plastic cap so remove the plastic cap before using it.

Can VGA do 1080p 144Hz

Nowadays, only the older version of devices uses VGA port; otherwise, the newer ones use DisplayPort or HDMI.

VGA is not recommended for 1080p 144Hz, as it can adequately work till 1080p with a 60 Hz refresh rate, when the refresh rate increases beyond 60 Hz resolution decreases.

Original VGA cable can have a maximum resolution of 640 X 480 with a refresh rate of 60Hz; nowadays, 1080p is possible with VGA. The maximum resolution of VGA can be limited by signal source refresh rate also depends upon the signal source and display different modern connectors can easily achieve 1080p with 144 Hz.

Is HDMI better than VGA for 1080p

HDMI carries a digital signal where VGA has an analog signal that causes a significant difference between both the signals.

HDMI is recommended over for 1080p as VGA carries analog signal where HDMI carries digital in VGA at 1080p refresh rate is limited to 75 Hz at most, whereas with different versions of HDMI 240hz frequency rate can be achieved with 1080p resolution.

Standard VGA has a maximum resolution of up to 640 X 480, but with the latest technology, it is capable of 1080p. Still, the resolution and frequency rate can be limited due to the signal source or display.

Is HDMI sharper than VGA

Currently, HDMI is used with most devices as devices are compatible with digital signals, where is the use of VGA is very much limited.

HDMI has sharp images or videos, then VGA for higher resolution.

HDMI uses a digital interface that is able to carry video and audio 17 easily as HDMI uses digital signal which has many advantages over analog signal practically the difference in image quality is unnoticeable between HDMI and VGA. As VGA uses an analog signal, which can decrease image quality during transmission or conversion of the signal, noise or interference may occur incorrect translation of level may happen, as the length increases, the quality of signal decreases. The difference in quality VGA and HDMI is noticeable for higher resolution.

Can a VGA cable affect screen resolution

Connectors have 15 pins for VGA cable and VGA cables require separate cables for video and audio transmission. The source and quality of the cable can control the resolution of VGA.

Analog signal is not much immune to external noise, flickering, interference, etc. And with an increase in the distance, the quality of the signal degraded, which affects the overall resolution. Using a better quality VGA cable with a covering minimum length as possible may reduce noise and interference.

Do I need both VGA and HDMI?

VGA uses analog interference, whereas HDMI uses digital interference.

Display devices cannot use VGA and HDMI simultaneously, but display devices can change or switch between the cables if required.

Generally, VGA and HDMI are not required simultaneously. VGA is the oldest interface with display. The devices which still use the VGA port are very much limited, where the HDMI port is widely in use.

How can I increase my VGA resolution?

The standard VGA resolution is very much limited; it doesn’t support high-definition images or video.

HDMI to VGA converter or adaptor can be used to get better resolution from the source for a better and sharper image or video for VGA connector.

HDMI uses digital signal and can carry both audio and video conversion of HDMI to VGA converter will not improve the quality of the original signal, but for better transmission HDMI cable can be used instead of VGA cables. If Required but with HDMI converter will be needed, which will increase the overall expenditure.

Do monitors need a VGA cable

VGA is the oldest display interface, introduced by IBM in 1987.

Only an older version of monitors or devices have a VGA connector so the VGA cable can only be used for only older monitors or devices.

As VGA cable is much more intensive than other cables, it can be used when the budget is limited but not recommended with converters as the converter is more expensive than that of the VGA cable. If any device has an HDMI port, use an HDMI cable. If any device has a VGA port, then only use a VGA cable because using a converter also reduces the quality of the signal and using a converter increases the overall expenditure.

Does VGA to HDMI adapter work

HDMI adapter is used to convert the analog VGA signal into a digital HDMI signal.

If all the connections are correctly connected to the eye doctor and from the adapter, then the adaptor should work properly if their adapter is not faulty.

Does VGA affect gaming

VGA uses separate cables for audio and video. It cannot transfer video and audio simultaneously through a single cable.

The slandered version of VGA is limited to 640 X 480 resolution with a 60 Hz refresh rate, which is not suitable for modern gaming standards. With many different versions of VGA, it can extend up to 1080p with a 60 Hz to 75 HZ refresh rate, which can limit the use of VGA in gaming.

VGA can affect the quality and can get interference, on lower quality of VGA cables and the image quality also may get affected. Several devices that produce or use analog signals had different refresh rates with different resolutions, the processor of the device must be able to process it as VGA cable does not limit the resolution or reference rate these are mainly limited by the source, but with higher refresh rate then limit can degrade the image quality.

Does VGA cause lag

More components or converters are connected in the path of the signal, and more lag is added to the signal as every component causes some degree of delay.

VGA has a relatively lower leg than HDMI because the VGA signal does not apply post-processing on the input.

XeF2 Lewis Structure: Drawing, Hybridization, Shape, Charges, Pair, …

29-04-2022 · XeF2 lewis structure is the abbreviation of xenon difluoride. It is one of those rare compounds which involve noble gases despite their strong stability. XeF2 lewis structure and its properties are illustrated in this article. XeF2 lewis structure involves 1 atom of xenon and 2 atoms of fluorine. Xenon has 8 valence electrons and fluorine has 7 ...

29-04-2022

XeF2 lewis structure is the abbreviation of xenon difluoride. It is one of those rare compounds which involve noble gases despite their strong stability. XeF2 lewis structure and its properties are illustrated in this article.

XeF2 lewis structure involves 1 atom of xenon and 2 atoms of fluorine. Xenon has 8 valence electrons and fluorine has 7 valence electrons. So to form a reliable lewis structure xenon will share its 2 electrons with fluorine forming a single covalent Xe-F bond. This completes the octet stability of fluorine atoms.

XeF2 lewis structure

XeF2 is in itself a strong fluorinating and oxidizing agent. Xenon is the only noble gas that despite its strong stability reacts and forms various compounds like XeF4 (Xenon tetrafluoride), and XeF6 (Xenon hexafluoride), etc. But out of these XeF2 lewis structure is the most stable one.

Like all the fluorinating compounds it is moisture sensitive. When comes in contact with water vapor, it immediately shows decomposition. So its storage is really important. Except for that it is easy to store and is not in the category of cautious compounds

XeF2 is a dense, colorless, crystalline solid and has a nauseating odor. Being a crystalline solid structure its bond length is 200 pm. Its packing arrangement is very rigid and strong where fluorine atoms of adjacent XeF2 molecules avoid the equatorial region of each other. It is a very important constituent of coordination chemistry. Its bonding type is a three-center four-electron bond. It acts as a potential strong ligand in various metal coordination complexes. Some of the examples where XeF2 has acted as a ligand and coordinated with metals are: [Mg(XeF2)4](AsF6)2 and Ca2(XeF2)9(AsF6)4.

XeF2 lewis structure has a sizeable contribution in the field of crystallographic analysis and supramolecular chemistry. Its major application is in laboratory setups and electrochemical procedures as a fluorinating agent in various organic synthetic reactions where direct fluorine usage is prohibited due to its explosive nature.

To analyze and understand the chemical and physical properties of XeF2 it is important to know its lewis structure and the properties associated with it. The properties and the structural formation are discussed below:

XeF2 lewis structure lone pair

Lone pairs of electrons are those which do not participate in chemical bond formation. Whenever lone pair of electrons is discussed then it is usually about the central atom as that affects the geometry of lewis’s structure.

In the XeF2 lewis structure, the lone pair around Xe are given importance. The terminal fluorine atoms are not included. Coming back to it then there are 2 bonding pairs formed between Xe and F. Xenon can form an expanded octet and can accommodate more than 8 electrons, thereby having 3 lone pairs of electrons surrounding it.

XeF2 lewis structure hybridization

Hybridization is a vital concept for determining the geometry of the molecule. It is the mixing of 2 or more orbitals during bond formation to make a new hybrid orbital. The electronic configuration of Xenon is [Kr]4d105s25p6 and this is in the ground state.

During bond formation, the XeF2 lewis structure will be in an excited state which will change the arrangement of electrons around xenon to s2p5d1 giving 2 unpaired electrons. So the hybridization of XeF2 will be sp3d.

XeF2 lewis structure shape

Lewis structure usually helps in predicting the shape of the molecule, but the XeF2 lewis structure is an exceptional case. Its shape and geometry can be understood using the VSEPR theory.

XeF2 lewis structure has 5 electron pairs. Out of these 2 electron pairs are bonding pairs as they form a single covalent bond with 2 fluorine atoms and the rest 3 are lone pairs. So according to the rule, its shape and geometry should be trigonal bipyramidal but it is not. XeF2 lewis structure is a linear shape molecule because the 3 lone pairs are in an equatorial arrangement with fluorine atoms giving it a symmetrical form. Hence it is of trigonal bipyramidal geometry and linear shape.

XeF2 lewis structure formal charge

As mentioned above in XeF2 lewis structure hybridization, there is sharing of electrons among atoms so it becomes crucial to know the formal charge.

The least possible formal charge of each combining atom gives us the perfect diagrammatic representation of a molecule.

Formal charge = Valence electrons – ½ Bonding electrons – Non-bonding electrons

For Xenon

              FC = 8 – 1/2* 4 – 6 = 0

For Fluorine

             FC = 7 – 1/2* 2 – 6 = 0

As they both have 0 formal charges so XeF2 is the most authentic and best reliable lewis structure.

After going through all the properties, it has become easy to draw 2 dimensional XeF2 lewis structure which is described below schematically:

How to draw XeF2 lewis structure

Xenon (Atomic number = 54 and electronic configuration = 2,8,18,18,8) is a noble gas with 8 valence electrons. Fluorine (Atomic number = 9 and electronic configuration = 2,7) has 7 valence electrons. So the total number of valence electrons are 8 7×2 = 22.

Xenon being a noble gas is less electronegative than fluorine. So it will acquire the position of the central atom. Now fluorine atoms will fulfill their octet stability criteria by sharing each of their electrons with the central xenon atom. This leads to the formation of 2 Xe-F single covalent bonds

Xenon on the other hand has more valence electrons around itself after the chemical bond formation. Xenon being a hypervalent species can adjust more than 8 valence electrons due to the availability of empty d orbitals and can form an expanded octet.

The stability and existence of the XeF2 lewis structure can be calculated through formal charge (which comes out to be 0 for both xenon and fluorine) which confirms the existence and authenticity of the structure.

XeF2 lewis structure (Related FAQs)

Explain the polarity of the XeF2 lewis structure.

As explained above xenon difluoride is a symmetrical molecule with a linear shape and trigonal bipyramidal geometry. There is an uneven distribution of electrons in the structure and many anomalies as well. But due to its symmetrical shape, the individual bonds are evenly distributed thereby nullifying each other charges. This leads to zero net dipole moment and hence XeF2 lewis structure is a non-polar molecule.

Why xenon can form compounds despite being a noble gas?

Xenon is the only element amongst the noble gas family that can form compounds. This is because Xenon is a very large molecule with the atomic number 54. This implies that it has more shells and orbitals. Due to this the electron attraction to the nucleus becomes weak and the interaction with the last shell is the weakest. Due to these weak attractions, it can react with small highly electronegative atoms like fluorine thereby participating in reactions and chemical bond formation.

Why Xenon is considered an important element?

Xenon can produce blue glowing light when excited by an electric charge and can be used as a special light source. The xenon lamps have sizeable applications as high-speed electronic flashbulbs, bactericidal lamps, and sunbed lambs which are used in the photography and food processing industries respectively.

XeF4 Lewis Structure: Drawings, Hybridization, Shape, Charges, …

10-05-2022 · XeF4 lewis structure involves one atom of xenon and four fluorine atoms. Xenon (Atomic number = 54 and electronic configuration = 2,8,18,18,8) belongs to group 18 of the periodic table and has 8 valence electrons.

10-05-2022

XeF4 lewis structure comprises noble gas xenon and the halogen atom named fluorine. Though noble gases remain in their elemental state, Xe is an anomaly. XeF4 lewis structure and various properties associated with it are discussed in this article.

In the XeF4 lewis structure, xenon is a noble gas that has 8 valence electrons. Similarly, fluorine belongs to group 17 of the periodic table and has 7 valence electrons. To achieve octet stability 4 fluorine atoms will share their 1 electron each with a Xenon atom thereby providing the desired XeF4 lewis structure.

XeF4 lewis structure

Elaborating on XeF4 lewis structure then it is one of those handful compounds where noble gases participate in chemical bond formation. Usually. History and many academic research papers confirm that the first compound of xenon was not XeF4 lewis structure but Xe PtF6- as reported by scientist Bartlett. But now it has been confirmed that xenon and fluorine both can form stable XeF4 lewis structure under room temperature conditions.

Elaborating on XeF4 lewis structure properties and characteristics then it is a colorless solid. At -78 degrees celsius XeF4, lewis structure vapor pressure is negligible and at room temperature, it is approximately 3 mm. XeF4 lewis structure exhibits the property of sublimation at room temperature. Due to this easy sublimation character XeF4, the lewis structure is sealed under vacuum in glass tubes.

As such XeF4 lewis structure does not have major applications. XeF4 lewis structure are used as ligands and coordinate with metal ions forming various fluorescent complexes. Another useful property of the XeF4 lewis structure is in space exploration where xenon is the main propellant. Another common use is in the xenon discharge tubes and flashbulbs used in cameras

XeF4 lewis structure formation is the electron symbolism of the compound and confirms its stability and reliability. Certain steps can be used to draw a perfect XeF4 Lewis structure.

How to draw the XeF4 lewis structure?

XeF4 lewis structure involves one atom of xenon and four fluorine atoms. Xenon (Atomic number = 54 and electronic configuration = 2,8,18,18,8) belongs to group 18 of the periodic table and has 8 valence electrons. Similarly, fluorine (atomic number = 9 and electronic configuration = 2,7) belongs to group 7 of the periodic table and has 7 valence electrons. So the total number of valence electrons are 8 7×4 = 36.

After finding the number of valence electrons participating in the XeF4 lewis structure, it is important to look out for the central atom. Between Xenon and fluorine, xenon is the least electronegative element and fluorine is the one with the highest electronegativity. So xenon will be the central atom surrounded by 4 fluorine atoms. This will make sure that the electron cloud is bent towards fluorine atoms thereby making sharing of electrons easier.

As both xenon and fluorine in the XeF4 lewis structure are non-metals so there will be sharing of electrons. To complete its octet stability criteria each fluorine atom will share its 1 electron with the central xenon atom. Xenon being a hypervalent species on the other hand can accommodate more than 8 electrons in its valence shell in its excited state and can form an expanded octet.

To confirm the structural composition and reliability of the XeF4 lewis structure formal charge of both xenon and each fluorine atom is calculated individually which comes out to be 0. So this confirms the uniform electric charge distribution and the existence of the XeF4 lewis structure.

There are many properties and characteristics associated with a XeF4 lewis structure that cannot be ignored and sidelined. Some of the important properties are discussed below in detail. 

XeF4 lewis structure lone pairs

A lone pair of nonbonding electrons or unshared pair of electrons are those which do not participate in chemical bond formation. They are shown as pointed electron dots around the atom. But lone pairs of electrons are significant in deciding many other properties like the shape of the molecule. The presence of lone pair especially on the central atom is the reason for repulsion which in turn can modify the shape of the molecule.

In the context of the XeF4 lewis structure, the central atom xenon has 4 electrons left after sharing one electron with 4 fluorine atoms. This means that there are 2 lone pairs of electrons on the xenon atom.

XeF4 lewis structure octet rule

The octet rule is a very important rule in chemistry which says that all main-group elements of a periodic table should bond in such a way that there are 8 electrons in its valence shell. It is one of the most important stability criteria required for chemical bond formation.

In the XeF4 lewis structure, there is the presence of fluorine atoms which belong to the halogen family and have 7 valence electrons. They can easily complete their octet by sharing their one electron with the central xenon atom.

Xenon on the other hand belongs to the noble gas family and already has 8 valence electrons. According to the rule, it should be inert but it reacts under certain conditions and is an anomaly to the octet rule. It is a hypervalent species and can form an expanded octet. In the XeF4 lewis structure, there are more than 8 valence electrons which include 2 lone pairs and the bonding electrons. 

XeF4 lewis structure formal charges

The formal charge is an important indicator that confirms the existence and identifies the credibility of lewis structure.  It can be defined as the charge which resides on the atoms in the molecule if the bonding is done equally. In simple and mathematical words if the formal charge of each atom in the molecule is 0 then the molecule is identified according to the criteria of the lewis structure. Its formula is 

FC = V – N – B/2

Where V = no. of valence electrons

               N = no. of non – bonding electrons

               B = no. of bonding electrons 

The formal charge of the XeF4 lewis structure

FC of Xe in XeF4 lewis structure = 8 – 4 -8/2 = 0

FC of F in XeF4 lewis structure = 7 – 6 – 2/2 = 0

XeF4 lewis structure hybridization

Hybridization is a process where orbitals of the atoms involved in molecule formation intermix and form new hybrid orbitals with distinguished properties. Quantum mechanics prove that the hybridized orbitals are the deciding factor in the geometry of the molecule.

In the XeF4 lewis structure, two orbitals namely fluorine and xenon are involved.  According to the electronic configuration of xenon, there are 6 electrons present in the 5p subshell and the d and f orbitals are empty. So during the XeF4 lewis structure formation when the central xenon is excited the 2 electrons jump from 5p to vacant 5d orbitals. So now in the XeF4 lewis structure, there are 2 unpaired electrons in 5p and 5d orbitals. 

Hence XeF4 lewis structure has sp3d2 hybridization. Also, there is the presence of a single covalent bond between Xe and F which is also called the sigma bond.

XeF4 lewis structure shape

XeF4 lewis structure shape is a 3-D representation of how the atoms are arranged and what kind of geometry is suitable for them to maintain stability. The molecular geometry and shape are very important in analyzing reactivity, polarity, color, and the other associated properties.

Coming back to the XeF4 lewis structure then there are 4 lone pairs or nonbonding electrons present on the central xenon atom. The lone pair of electrons generates electronic repulsion which needs to be minimized for stability according to the VSEPR theory. The stable XeF4 lewis structure can only be obtained if the lone pair on xenon are in perpendicular alignment in an octahedral geometry. This will lead to opposite faces with 180 degrees of bond angle. Hence XeF4 lewis structure exhibits a square planar shape and octahedral geometry.

XeF4 lewis structure resonance

Resonance is a phenomenon where a single structure is not able to explain all the properties of a compound. There are various canonical or resonance structures. The resonance structures are formed by the delocalization of electrons and the movements of bonds.

Talking about the XeF4 lewis structure then it does not show the resonance phenomenon because it is an asymmetrical structure and does not have double bonds for the movement. So XeF4 all properties are explained by a single structure that has a square planar shape.

Frequently Asked Questions

Is XeF4 lewis structure polar or nonpolar?

If we look according to the Pauli scale of electronegativity then the Xe-F bond is polar due to the huge electronegativity difference. The electronegativity difference is 1.4. But the XeF4 lewis structure is square planar which is symmetrical. Hence there is no net dipole moment making the XeF4 lewis structure a nonpolar compound.

 Why xenon can form compounds like XeF4 lewis structure despite being a noble gas?

Xenon can form compounds like the XeF4 lewis structure because its inner electrons screen the outer electrons from the nucleus. So they become an easy target for the electronegative elements.

How To Find Velocity With Height:Different Approaches ...

08-01-2022 · How to calculate velocity with height and time? In vertical motion, the distance traveled by the body is equal to the height where the body begins to move. The velocity can be calculated using height and time. The distance moved by the body with time always describes the body’s velocity. The physical entities such as acceleration and height also contribute to the finding …

08-01-2022

When an object is dropped from a certain height, the force of gravity largely influences the object to attain more velocity. So it is clear that height is an entity that influences motion.

A freely falling object initially attains zero velocity, and as it begins to move downward, it gains velocity. Suppose we know the only height of the falling object, how to find velocity with height, and also along with the height, how the other entities influence over velocity are explained in this post.

how to find velocity with height
Free body diagram to show How to find velocity with height

How to find velocity with Height?

Consider a book kept on a table at the height of h from the ground. When the book falls from the table, then how fast the book falls on the ground is given by velocity. Since the book is at the height of h, how to find the velocity with height?

Book falling from certain height to show how to find velocity with height

We know that velocity can be calculated from knowing the distance traveled by the body, and the time taken by it to reach that distance. Mathematically it can be written as,

In the example given above, we are provided with the height h. The height of the body is associated with potential energy. So the basic equation is not valid.

Considering the potential energy possessed by the book before it falls, expression can be written as,

PE = mgh.

But the book is under motion; hence the potential energy is now turned into kinetic energy as

Thus, the potential energy and kinetic energy are equal by the conservation of energy. Hence the equation can be written as

By rearranging the equation, we get velocity as

v2 = 2gh

In the above equation, g is the acceleration due to gravity. Any object falling from a certain height is influenced by gravity and is constantly accelerating more due to gravity.

How to find velocity with acceleration and height?

We know how to find velocity with acceleration and distance from the previous article. But we have given with acceleration and height then how to find velocity with acceleration and height instead of distance?

Acceleration and velocity are the proportional entities as the time derivative of velocity is acceleration. If we have acceleration means, on integrating the acceleration, we can have velocity. But in this case, we have acceleration and height. Let us discuss how to find velocity with height if acceleration is given.

Consider a ball is at a certain height above the ground. The ball is dropped from the height ‘h,’ and it begins to accelerate at ‘a’ is in the direction of acceleration due to gravity; this means that the ball is falling from the height h in the direction of gravitational pull.

Since both acceleration and acceleration due to gravity are in the same direction, the total acceleration of the body is equal to the sum of both accelerations of the body and acceleration due to gravity A = g a. Now the ball’s velocity can be calculated using the equation of motion.

We know from the kinematic equation of motion, distance traveled by the body can be written in terms of the mathematical equation as,

But, we have the height of the ball and the acceleration. The distance can be written in terms of height as,

The ball’s initial position when it begins to move and the final position of the ball gives the distance.

Therefore x = h – 0, i.e., x=h, we can say vertical distance as height. Now substituting the x = h, we have the equation as

Rearranging the above equation, we have

The equation obtained above gives the velocity of the ball given acceleration and height.

Let us set another example if a projectile moving towards the ground from the height h, and its acceleration is more than the acceleration due to gravity because the projectile is overcome from the air friction, then the equation of the velocity will be calculated as,

In the kinematics equations, the velocity is given by

v2 = 2Ax

Where x is the distance. But here x = h, then

v2 = 2Ah

Consider another case; if you throw a ball in the air, after reaching the height h, the ball begins to accelerate downward due to gravity; the motion is called projectile motion; in this situation, how to find velocity with acceleration and height? The ball’s motion in the air is given in the below figure.

how to find velocity with acceleration and height
Diagram showing how find velocity with acceleration and height using projectile motion

From the above figure, the object’s height is h, and distance is not the height, but we have height in terms of distance by using the equation of projectile motion. The relation between distance and height can be written as,

Substituting the value of distance in the equation of motion, we get

Rearranging the equation, we get velocity as

How to find initial velocity with acceleration and height?

The initial velocity can be derived from the acceleration and height, considering the equation of motion.

A body is accelerating means there must be a change in the velocity of the body with a given instance, which also tells that initially, the body has some velocity that keeps on changing with time. So to find the initial velocity, we need to know the final velocity of the body.

When we throw a ball in the air, it reaches a certain height h with a certain velocity and attains acceleration a. Initially; the ball moves with velocity vi. Finally, the velocity will be vf. The equation of initial velocity will be written using the equation of motion of the ball can be calculated as follow.

The velocity can be

The final velocity of the ball is given as vf, hence from the average velocity.

But at the height h, the ball acquires zero final velocity as it falls back to the ground due to gravity.

But we don’t know the time taken by the ball to reach the height h., so we can use the acceleration. Initially, the ball is accelerating against gravity; its acceleration will become negative.

We know the final velocity is zero, then

Therefore we get the time factor as

Substituting in the equation of average initial velocity, we get

Rearranging the equation, we get

We can calculate the initial velocity when the final velocity is not zero. Consider the equation,

To above equation the substituting the value of t as

t=\frac{v_f v_i}{a}

We get the equation as

(vf vi) (vf-vi) = 2ah

The above equation can be written as

vf2-vi2 = 2ah

Rearranging the terms to get initial velocity as

vi2 = vf2– 2ah

How to calculate velocity with height and time?

In vertical motion, the distance traveled by the body is equal to the height where the body begins to move.

The velocity can be calculated using height and time. The distance moved by the body with time always describes the body’s velocity. The physical entities such as acceleration and height also contribute to the finding the velocity.

We can calculate the velocity with height and time in three ways

By vertical motion of the body

If the basketball is falling from the basket at height h, and is accelerating in the direction of gravity, then the velocity can be given as

But the acceleration is given by

Substituting the value of a and replacing distance term as height h, we get

On rearranging the terms, the velocity with height and time is

By Projectile motion

Consider another example; a basketball player shoots the ball to the basket standing at a distance d away from the basket. The ball makes the projectile motion to reach the basket; then we can calculate the velocity as follows:

The general expression of velocity is given by

The ball travels a distance of d along with the height h; if we neglect the friction, distance can be written as

Substituting the value of x in the general equation of velocity, we get

By height vs. time graph

If we plot a graph with height in the y axis and time in the x-axis, the plot is called a height-time graph.

We can calculate the velocity from the height-time graph. The slope of the height-time graph gives the velocity of the body.

Height Vs. Time graph to find velocity

From the above graph, the slope is given by

From the graph, AB is parallel to height h, and BC is parallel to time t; hence we can say that

AB = h and BC = t;

From the definition of velocity, we can say the slope is nothing but velocity. Thus the slope is equal to velocity.

How to find velocity with height and mass?

Though mass does not affect the velocity, it contributes the energy and force required to the body to attain a certain velocity.

The height and the mass are the entities associated with the object’s potential energy. Mass also contributes to the kinetic energy acquired by the object while moving. By knowing mass, let us understand how to find velocity with height.

The object at a certain height possesses potential, which makes the body move, and it is equal to the kinetic energy of the body while moving.

Since both potential energy and kinetic energy are equal, we can equate them.

Ep= Ek

The kinetic energy of the body is

Rearranging the equation, we get

In the beginning, we have told that potential energy = kinetic energy,

Therefore the equation can be rewritten as

Generally, the potential energy is Ep= mgh.

The answer we got from potential energy can be substituted in the above equation to get the velocity of the body.

How to find velocity with height and gravity?

When you throw a stone in the air, it will fall back to the ground due to gravity. It is a general process. But have you observed that the speed of the ball? The speed of the stone while moving down is a little less than the speed of the same stone while it is falling back.

The above statement clarifies that velocity can vary due to gravity also. Gravity comes into action when a body is placed at a certain height; as gravity is an attractive force, it tries to bring the body at height towards the ground—so based on this data, how to find velocity with height and distance?

The earlier section discusses one way of finding the velocity with height and gravity. Let us discuss how to find velocity with height and distance by considering the kinematic equation of motion.

The height is always equal to the distance from the kinematic equation of distance. Hence we can consider the distance as height. So the equation will be

If the motion of the stone is in the direction of gravity, then the acceleration is only due to gravity; hence the equation can be rewritten as

Rearranging the terms, the equation will be

The above equation gives the velocity with height and gravity with the time factor. If the body is accelerating against gravity, then

g = -g

How to find velocity with height and angle?

When a body begins to fall from a certain height towards the surface, it makes some angle θ with the point of dropping. The angle made by the object helps us to find the answer for how to find velocity with height.

The displacement of the body in the vertical position is the height. The vertical component of velocity can be written as

v = v sinθ

If the body is making some horizontal displacement, then velocity is

v = v cosθ

From the equation of motion, the vertical and horizontal velocities can be written as

vx = v cosθ

vy = v sinθ-gt; where g is acceleration due to gravity

At maximum height, vy= 0 = v sinθ –gt

v sinθ = gt

When a body is dropped at an angle θ and travels with velocity v, its range is given by

Therefore, using the value of R,

Therefore, the velocity can be rewritten as

Solved problems on how to calculate velocity with height

Problem 1) A ball is dropped from the height of 15m, and it reaches the ground with a certain velocity. Calculate the velocity of the ball.

Solution:

We are provided with only height h = 15m.

Since the ball moves towards the ground, the motion is due to acceleration due to gravity g. The value of acceleration due to gravity is g = 9.8 m/s2. The velocity of the ball is

Substituting the values of h and g;

v = 17.14 m/s.

Problem 2) Calculate the initial velocity of the stone, which is falling from the height of 3m, and its acceleration is 2 m/s2, and hence find the time taken by the stone to reach the ground.

Solution:

Given data: Height h = 3m

Acceleration of the stone a = 2 m/s2.

The velocity of the stone is given by

v = 3.46 m/s.

The time taken by the stone to reach the ground is given by the equation,

t = 1.79 s.

Problem 3) An object of mass 3 kg is dropped from the height of 7 m, accelerating due to gravity. Calculate the velocity of the object.

Solution:

The data are given –the mass of the object m = 3kg.

Height at which the object has dropped h = 7 m.

Acceleration due to gravity g = 9.8 m/s2.

Since the object’s motion is due to mass, height, and gravity, so the work done is equal to potential energy. it is given by

Ep = mgh

The object is moving, so the object possesses kinetic energy; it is represented by the formula,

From the conservation of energy, when an object begins to move, its potential energy is now termed kinetic energy.

Therefore Ep = Ek

The potential energy is Ep = 3×9.8×7

Ep = 205.8 J

Substituting Ep = Ek = 205.8 J.

v2 = 137.2

v = 11.71 m/s.

Problem 4) An athlete shoots a shot put in the air in the vertical direction, and it takes a time of 3 seconds to fall on the ground vertically from the height of 7 m from the ground. Calculate the velocity while the shot put is returning to earth.

Solution:

Given data – the height from the ground h = 7 m.

Time is taken to reach the ground = 3 seconds.

The velocity is given by

v = 2.33 m/s.

Problem 5) A body of mass 4 kg is dropped at the height of 11 meters above the ground by making an angle of 20°. Calculate the velocity of the body. (Take acceleration due to gravity as 10 m/s2)

Solution:

The data are given –the mass of the body m = 4 kg.

Height h = 11 m.

Angle θ = 20°.

Acceleration due to gravity g = 10 m/s2.

The velocity is given by

v = 43.45 m/s.

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