Gram-Mole Conversions (Section 6.2)

Goals for Education
  • Finding the equivalent in moles of mass

As we've seen, 1 mole of a substance (or Avogadro's number of molecules or formula units) is equal to the mass (in grams) of 1 gram of that substance.

A mole-gram conversion (or the opposite, a gram-mole conversion) is the simplest manipulation involving molar mass as a conversion factor.

Moreover, we determined that 1 mol of Al has a mass of 26 98 g (PageIndex:1 Sample) Putting it mathematically,

1 mol Al = 26 98 g Al

Both sides of this expression can be divided by either one to yield one of two conversion factors:

mol: Al26 [mathrmdfrac1: mol] It's a 98: g: Alquad and quad dfrac26 98: g: Al1: mol: Al] nonnumber

You can use the first conversion factor to go from kilograms to moles, and the second to go back the other way. Both can be used to accomplish what is otherwise difficult to do "by eye." ”

As an illustration, consider the following (PageIndex1):

The mass of 3 what? In terms of mass, 987 mol of Al

To solve a conversion problem, one must first determine the appropriate conversion factor. Since mole units serve as our baseline, we need a conversion factor that subsitutes the mass unit for moles in the denominator. For this reason, we must employ the (mathrmdfrac26 Al2O3 to Al2O3 (g/mol) conversion factor After establishing the base value, we multiply it by the conversion factor:


\(\mathrm{3 The value of 987 on the mole scale is expressed as Altimesdfrac26 Al2O3 (98g: Al, 1mmol: Al)

The mol units are nullified algebraically. (The value 3 Unspoken agreement suggests that the denominator of the fraction whose numerator is 987 mol is 1. Avoiding problems and then fixing them yields

\(\mathrm{3 There are 987 molecules in a cubic inch. 1.98 g Al = 107 mol Al 6\: g\: Al}\)

Our final result is given to four digits of precision.

Try out PageIndex 1

In a hundred, how many moles would you expect to find? 0 g of Al Hint: you need the other conversion factor we found for aluminum. )

The solution to (mathrm100 "0" for "g": "Al" * "dfrac1" for "mol": "Al" * "26" 98\: g\: Al}=3 706\: mol\: Al}\)

You can do this for any substance whose atomic mass, formula mass, or molar mass is known (or can be determined) and is expressed in grams per mole. Figure (PageIndex1) is a chart for determining what conversion factor is needed, and Figure (PageIndex2) is a flow diagram for the steps required to carry out a conversion.

6.2.jpg Figure (PageIndex1): A Convenient Flowchart for Determining the Number of Molecules in a Given Mass From moles to mass or back again, the conversion is a simple mathematical operation. 6.3.jpg (PageIndex 2) Flowchart Showing How Unit Conversions Are Done The same reasoning can be applied to multiple unit conversions.
Instance (PageIndex2)

All that's required of a biochemist is a A bilirubin (C33H36N4O6) molecule (.00655 mol) is needed for a lab experiment. Just how many grams of bilirubin is that?

We can calculate the molar mass of bilirubin from its chemical formula, which gives us the mass per mole we need:

Molar mass of carbon at 33: 33 × 12 01 g = 396.33 g Molar mass of 36 H: 36 × 1 01 g = 36.36 g Mass at the molecular level, 4 N: 4 × 14 01 g = 56.04 g Weight in moles, 6 O: 6 × 16 00 g = 96.00 g Total:   584.73 g

Bilirubin has a molar mass of 584. 73 g With the help of the connection

To convert between moles, use: 1 mol bilirubin = 584 73 g of bilirubin

Understanding how many milligrams are in 0 milligrams is a simple matter of constructing the proper conversion factor. 00655 mol Figure (PageIndex2) details the procedures to be followed.

\(\mathrm{0 Calculating Bilirubin Concentration (in Molecular Units) (00655 x dfrac584) 73 g bilirubin mol bilirubin = 3 (Bilirubin, molar mass 83 g)

For bilirubin, the mol bilirubin unit is null. A biochemist requires 3 level of bilirubin (in grams): 83

Here's a PageIndex 2 exercise

As a chemist, you need 457 Make a solution using 8 grams of KMnO4 Amount in moles of KMnO4

Find the solution to problem (mathrm)457 Eight grams of KMnO4 equals one mole of KMnO4-158 04\: g\: KMnO_4}=2 mol: KMnO_4 = 897

A healthy diet is essential because it provides the building blocks our bodies need to function. Minerals are essential components of a balanced diet because our bodies rely on them for a wide range of processes, from bone and nerve development to muscle function. Mineral Recommended Daily Intakes (RDIs) have been established by the United States Department of Agriculture. The Recommended Dietary Allowances (RDAs) for minerals are shown in the table below in mass and moles, based on a 2,000 calorie diet.

Table (PageIndex 1): Human Composition of Essential Minerals Mineral Human male, ages 19-30 A woman (aged 19-30) Ca 1,000 mg 0.025 mol 1,000 mg 0.025 mol Cr 35 µg 6.7 × 10−7 mol 25 µg 4.8 × 10−7 mol Cu 900 µg 1.4 × 10−5 mol 900 µg 1.4 × 10−5 mol F 4 mg 2.1 × 10−4 mol 3 mg 1.5 × 10−4 mol I 150 µg 1.2 × 10−6 m ol 150 µg 1.2 × 10−6 mol Fe 8 mg 1.4 × 10−4 mol 18 mg 3.2 × 10−4 mol K 3,500 mg 9.0 × 10−2 mol 3,500 mg 9.0 × 10−2 mol Mg 400 mg 1.6 × 10−2 mol 310 mg 1.3 × 10−2 mol Mn 2.3 mg 4.2 × 10−5 mol 1.8 mg 3.3 × 10−5 mol Mo 45 mg 4.7 × 10−7 mol 45 mg 4.7 × 10−7 mol Na 2,400 mg 1.0 × 10−1 mol 2,400 mg 1.0 × 10−1 mol P 700 mg 2.3 × 10−2 mol 700 mg 2.3 × 10−2 mol Se 55 µg 7.0 × 10−7 mol 55 µg 7.0 × 10−7 mol Zn 11 mg 1.7 × 10−4 mol 8 mg 1.2 × 10−4 mol

Several examples are shown in table (PageIndex1). To begin, men and women have different mineral requirements. The iron situation is extreme; females have a much higher requirement than males. When the RDI is different, men require more than women.

Second, there is a wide range, in terms of both mass and molar volume, in the daily mineral requirements of different organisms. The typical human being has zero 2 grams of Na per day, or 1 mol per day. 5 g The amount of Cr a human body requires daily is negligible, at just 25–35 femtograms (femtog), or less than one millionth of a mole. A deficiency in dietary chromium, even at this low level, has been linked to diabetes-like symptoms and neurological issues, particularly in the hands and feet. Some minerals are essential for proper body function, while others are not.

However, some people choose to take supplements even though a healthy, well-rounded diet can supply all the minerals they need. However, excess of anything is bad for you, and that includes minerals. Some forms of chromium are known to cause cancer (as depicted in the film Erin Brockovich), and exposure to even small amounts can cause a skin irritation.


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