Given Moles, Convert to Grams

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In chemistry, the mole is the standard measurement of amount. When substances react, they do so in simple ratios of moles. However, balances give readings in grams. Balances DO NOT give readings in moles.

So the problem is that, in chemistry, we compare amounts of one substance to another using moles. That means we must convert from grams, since this is the information we get from balances.

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

- Determine how many moles are given in the problem.
- Calculate the molar mass of the substance.
- Multiply 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 grams of the substance (upper left) will be the unknown (signified by the letter x). The exact same proportion is used in the grams-to-moles conversion lesson. Then the "x" will reside in the lower 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 will evolve naturally from soving the proportion and cancellation of units.

The bonus example has a twist in it.

**Example #1:** Calculate how many grams are in 0.700 moles of H_{2}O_{2}

**Solution:**

1) Step One:

The problem will tell you how many moles are present. Look for the word "mole" or the unit "mol." The number immediately preceeding it will be how many moles.I suppose that a problem can be worded in such a way that the number of moles comes after the unit, but that type of trickery isn't very common in high school.

0.700 moles are given in the problem.

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 H

_{2}O_{2}is 34.0146 grams/mole. You may wish to pause and calculate this value, if you desire the practice.

3) Step Three:

Multiply the moles given by the substance's molar mass:0.700 mole x 34.0146 grams/mole = 23.8 grams

The answer of 23.8 g has been rounded to three significant figures because the 0.700 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:

x 34.0146 g –––––––– = –––––––– 0.700 mol 1 mol

5) Then, cross-multiply and divide to solve for the unknown.

(x) (1 mol) = (0.700 mol) (34.0146 g)x = 23.8 g (to three significant figures)

**Example #2:** Convert 2.50 moles of KClO_{3} to grams.

**Solution:**

1) Get the moles:

2.50 moles is given in the problem.

2) Get the molar mass:

The molar mass for KClO_{3}is 122.550 g/mole. Please note the unit of 'g/mole.' It is important for proper cancelling of units that you remember to write this unit down when using a molar mass.

3) Following step three, we obtain:

2.50 moles x 122.550 g/mole = 306.375 gramsThe answer should be rounded off to three significant figures, resulting in 306 g. as the correct answer. Note how the mole in the numerator and the mole in the denominator cancel.

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

x 122.550 g ––––––– = –––––––– 2.50 mol 1 mol

5) Then, cross-multiply and divide to solve for the unknown.

(x) (1 mol) = (2.50 mol) (122.550 g)x = 306 g (to three significant figures)

**Example #3:** Calculate the grams present in 0.200 moles of H_{2}S

**Solution:**

(0.200 mol) (34.0808 g/mol) = 6.82 g

**Example #4:** Calculate the grams present in 0.200 moles of KI

**Solution:**

1) Set it up as a ratio and proportion:

x 165.998 g ––––––– = –––––––– 0.200 mol 1 mol

2) Then, cross-multiply and divide to solve for the unknown.

(x) (1 mol) = (0.200 mol) (165.998 g)x = 33.2 g (to three significant figures)

**Example #5:** Calculate the grams present in 1.500 moles of KClO

**Solution:**

(1.500 mol) (90.5504 g/mol) = 135.8 g (to four sig figs)I calculated the molar mass of KClO here.

**Bonus Example:** What is the mass of silver contained in 0.119 moles of Ag_{2}S?

**Solution:**

1) Determine moles of silver present:

For every one mole of Ag_{2}S, 2 moles of silver are present.(0.119 mol) (2) = 0.238 mol of Ag

2) Determine mass of silver present:

(0.238 mol) (107.868 g/mol) = 25.7 g (to three sig figs)