# 8.3: Making Molecules- Mole to Mass (or vice versa) and Mass-to-Mass Conversions

- Page ID
- 47503

## Mole to Mass Conversions

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 calculations.*

As an example, consider the balanced chemical equation

\[Fe_2O_3 + 3SO_3 \rightarrow Fe_2(SO_4)_3 \label{Eq1}\]

If we have 3.59 mol of Fe_{2}O_{3}, how many grams of SO_{3} can react with it? Using the mole-mass calculation sequence, we can determine the required mass of SO_{3} in two steps. First, we construct the appropriate molar ratio, determined from the balanced chemical equation, to calculate the number of moles of SO_{3} needed. Then using the molar mass of SO_{3} as a conversion factor, we determine the mass that this number of moles of SO_{3} has.

As usual, we start with the quantity we were given:

\[\mathrm{3.59\: \cancel{ mol\: Fe_2O_3 } \times \left( \dfrac{3\: mol\: SO_3}{1\: \cancel{ mol\: Fe_2O_3}} \right) =10.77\: mol\: SO_3} \label{Eq2}\]

The mol Fe_{2}O_{3} units cancel, leaving mol SO_{3} unit. Now, we take this answer and convert it to grams of SO_{3}, using the molar mass of SO_{3} as the conversion factor:

\[\mathrm{10.77\: \bcancel{mol\: SO_3} \times \left( \dfrac{80.06\: g\: SO_3}{1\: \bcancel{ mol\: SO_3}} \right) =862\: g\: SO_3} \label{Eq3}\]

Our final answer is expressed to three significant figures. Thus, in a two-step process, we find that 862 g of SO_{3} will react with 3.59 mol of Fe_{2}O_{3}. Many problems of this type can be answered in this manner.

## Mass to Mass Conversions

It is a small step from mole-mass calculations to mass-mass calculations. 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.

## Summary

- Calculations involving conversions between moles of a substance and the mass of that substance are described.
- The balanced chemical reaction can be used to determine molar and mass relationships between substances.

## Contributions & Attributions

This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:

Henry Agnew (UC Davis)