6.5 Mole-Mass and Mass-Mass Problems

We have established that a balanced chemical equation is balanced in terms of moles as well as atoms or molecules. We have used balanced equations to set up ratios, now in terms of moles of materials, that we can use as conversion factors to answer stoichiometric questions, such as how many moles of substance A react with so many moles of reactant B. We can extend this technique even further. Recall that we can relate a molar amount to a mass amount using molar mass. We can use that ability to answer stoichiometry questions in terms of the masses of a particular substance, in addition to moles. We do this using the following sequence:

Collectively, these conversions are called mole-mass calculationsA stoichiometry calculation converting between masses and moles of different substances in a chemical reaction..

As an example, consider the balanced chemical equation

Fe₂O₃ + 3SO₃ → Fe₂(SO₄)₃

If we have 3.59 mol of Fe₂O₃, how many grams of SO₃ can react with it? Using the mole-mass calculation sequence, we can determine the required mass of SO₃ in two steps. First, we construct the appropriate molar ratio, determined from the balanced chemical equation, to calculate the number of moles of SO₃ needed. Then using the molar mass of SO₃ as a conversion factor, we determine the mass that this number of moles of SO₃ has.

The first step resembles the exercises we did in Section 6.4 "Mole-Mole Relationships in Chemical Reactions". As usual, we start with the quantity we were given:

$$3.59\cancel{{\text{ mol Fe}}_{\text{2}}{\text{O}}_{\text{3}}}\times \frac{{\text{3 mol SO}}_{\text{3}}}{\text{1}\cancel{{\text{ mol Fe}}_{\text{2}}{\text{O}}_{\text{3}}}}=10.77{\text{ mol SO}}_{\text{3}}$$

The mol Fe₂O₃ units cancel, leaving mol SO₃ unit. Now, we take this answer and convert it to grams of SO₃, using the molar mass of SO₃ as the conversion factor:

$$10.77\cancel{{\text{ mol SO}}_{\text{3}}}\times \frac{\text{80}{\text{.06 g SO}}_{\text{3}}}{\text{1}\cancel{{\text{ mol SO}}_{\text{3}}}}=862{\text{ g SO}}_{\text{3}}$$

Our final answer is expressed to three significant figures. Thus, in a two-step process, we find that 862 g of SO₃ will react with 3.59 mol of Fe₂O₃. Many problems of this type can be answered in this manner.

The same two-step problem can also be worked out in a single line, rather than as two separate steps, as follows:

We get exactly the same answer when combining all the math steps together as we do when we calculate one step at a time.

It is a small step from mole-mass calculations to mass-mass calculationsA stoichiometry calculation converting between the mass of one substance and the mass of a different substance in a chemical reaction.. If we start with a known mass of one substance in a chemical reaction (instead of a known number of moles), we can calculate the corresponding masses of other substances in the reaction. The first step in this case is to convert the known mass into moles, using the substance’s molar mass as the conversion factor. Then—and only then—we use the balanced chemical equation to construct a conversion factor to convert that quantity to moles of another substance, which in turn can be converted to a corresponding mass. Sequentially, the process is as follows:

This three-part process can be carried out in three discrete steps or combined into a single calculation that contains three conversion factors. The following example illustrates both techniques.