Given Grams, Convert to Moles

Return to Mole Table of Contents

In chemistry, the mole is the standard measurement of amount. However, balances DO NOT give readings in moles. Balances give readings in grams.

So the problem is that, while we compare amounts of one substance to another using moles, we must also use grams, since this is the information we get from balances.

There are three steps to converting grams of a substance to moles.

- Determine how many grams are given in the problem.
- Calculate the molar mass of the substance.
- Divide step one by step two.

Make sure you have a periodic table and a calculator handy.

The solution technique can also be expressed in the following ratio and proportion:

grams of the

substancemolar mass of the

substance in grams––––––––––– = ––––––––––––––– moles of the

substanceone mol

In this particular lesson, the moles of the substance (lower left) will be the unknown (which will be signified by the letter x). The exact same proportion is used in the moles-to-grams conversion lesson. Then the "x" will reside in the upper left.

This proportion is a symbolic equation. When you solve a particular problem, you insert the proper numbers & units into the proper places of the symbolic equation and then you solve using cross-multiplication and division. Also, do not attach units to the unknown. Let it be simply the letter "x." The proper unit shouldwill evolve naturally from solving the proportion and cancellation of units.

**Example #1:** Convert 25.0 grams of KMnO_{4} to moles.

**Solution:**

1) Step One:

The problem will tell you how many grams are present. Look for the unit of grams. The number immediately preceeding it will be how many grams. Common abbreviations for grams include g (just the letter) and gm.I suppose that a problem can be worded in such a way that the number of grams comes after the unit, but that type of trickery isn't very common in high school.

The problem gives us 25.0 grams.

2) Step Two:

You need to know the molar mass of the substance. Please refer to the lessons about calculating the molecular weight and molar mass of a substance if you are not sure how to calculate a molar mass.The molar mass of KMnO

_{4}is 158.034 grams/mole. Please take a moment and calculate the molar mass of KMnO_{4}, just to be sure.

3) Step Three:

Divide the grams given in the problem by the substance's molar mass:

25.0 g ––––––––– = 0.158 mol 158.034 g/mol The answer of 0.158 mole has been rounded to three significant figures because the 25.0 value had the least number of significant figures in the problem.

4) If this problem were set up like the proportion above, you would have this:

25.0 g 158.034 g –––––– = ––––––– x 1 mol

5) Cross-multiply and divide to solve for the unknown.

(25.0 g) (1 mol) = (x) (158.034 g)x = 0.158 mol

**Example #2:** Calculate how many moles are in 17.0 grams of H_{2}O_{2}

**Solution:**

1) 17.0 grams are given in the text of the problem.

2) The molar mass is 34.0146 grams/mole, which is calculated using the formula and the atomic weights on a periodic table. You may want to calculate this value as a double-check of your mastery of calculating molar masses.

3) Divide the grams given in the problem by the substance's molar mass:

17.0 g –––––––––––– = 0.500 mol 34.0146 g/mol This answer has been rounded to three significant figures based on the 17.0.

4) This problem can also be set up as a proportion:

17.0 g 34.0146 g ––––– = –––––––– x 1 mol

**Example #3:** Calculate the moles present in 2.00 grams of H_{2}O

**Solution:**

2.00 g ––––––––––– = 0.111 mol (to three sig figs) 18.015 g/mol

**Example #4:** Calculate the moles present in 100. grams of KClO_{4} (note the use of an explicit decimal point with 100. This is done so as to indicate that the two zeros are significant, making for three sig figs in 100.)

**Solution:**

Ratio and proportion set-up only.

100. g 138.547 g ––––– = –––––––– x 1 mol (100. g) (1 mol) = (x) (138.547 g)

x = 0.722 mol (to three sig figs)

**Example #5:** Convert 8.76 grams of NaOH to moles.

8.76 g 39.97 g ––––– = –––––––– x 1 mol (8.76 g) (1 mol) = (x) (39.97 g)

x = [(8.76 g) (1 mol)] / 39.97 g

x = 0.219 mol (to three sig figs)

**Example #6:** Determine how many moles are in 5.00 g of cobalt(II) sulfate hexahydrate (CoSO_{4} **⋅** 6H_{2}O).

**Solution:**

1) Notice the presence of water in the formula. This is a hydrate.

The weight of the CoSO_{4}alone is 154.994 g.The weight of six moles of water is 18.015 x 6 = 108.09 g

The molar mass of CoSO

_{4}⋅6H_{2}O is 263.084 g/mol.

2) Convert grams to moles:

5.00 g / 263.084 g/mol = 0.0190 mol

**Example #7:** A sample contains 0.900 g of CaSO_{4} **⋅** ^{1}⁄_{2}H_{2}O. How many moles is this?

**Solution:**

1) The presence of water makes this a hydrate. Remember that the middle dot is not a multiplication sign.

The weight of the CaSO_{4}alone is 136.139 g.The weight of one-half mole of water is 18.015 x 0.5 = 9.0075 g.

The molar mass of CaSO

_{4}⋅^{1}⁄_{2}H_{2}O is 145.1465 g/mol.

2) Convert grams to moles:

0.900 g / 145.1465 g/mol = 0.00620 mol (to three sig figs)

3) Sometimes, you see the formula rendered thusly:

CaSO_{4}⋅0.5H_{2}O

**Bonus Example:** How many oxygen atoms are in 3.78 grams of water? How many hydrogen atoms?

**Solution:**

1) The first step is to convert grams to moles in the usual manner:

3.78 g / 18.015 g/mol = 0.209825 mol

2) The next step is to convert moles to number of molecules, a calculation that uses Avogadro's Number:

(0.209825 mol) (6.022 x 10^{23}mol¯^{1}) = 1.26 x 10^{23}molecules (rounded to three sig figs)

3) In every one molecule of H_{2}O, there is one atom of oxygen. Therefore, there are 1.26 x 10^{23} atoms of O in 3.78 g of water.

4) Because there are two hydrogen atoms for every one water molecule, there are 2.52 x 10^{23} atoms of H in 3.78 g of water.