Stoichiometric Calculations

By the end of this lesson, you will be able to run any mass-to-mass calculation through the mole ratio, handle gas volumes and solution volumes, and check an answer for size before trusting it.

Everything Goes Through Moles

$$\textbf{grams A} \rightarrow \textbf{moles A} \rightarrow \textbf{moles B} \rightarrow \textbf{grams B}$$

Three steps, in that order, every single time. There is no shortcut and no variation.

Step 1: divide by A's molar mass.

Step 2: multiply by the mole ratio from the BALANCED equation. This is the only step that uses the chemistry, and it is the only step where the equation matters.

Step 3: multiply by B's molar mass.

$$2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$$

The ratio of hydrogen to water is $2:2$, so one mole of hydrogen gives one mole of water.

Balance the equation first. An unbalanced equation gives a wrong mole ratio, and a wrong mole ratio gives a wrong answer that looks entirely reasonable. Nothing downstream will catch it.

Coefficients are moles, not grams. Converting to moles before applying the ratio is the entire reason the middle step exists.

The Mole Ratio Is a Conversion Factor

Take it straight from the coefficients, and write it so the unit you have cancels.

$$2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$$

$$\frac{2 \text{ mol } \mathrm{H_2O}}{2 \text{ mol } \mathrm{H_2}} \qquad \text{or} \qquad \frac{1 \text{ mol } \mathrm{O_2}}{2 \text{ mol } \mathrm{H_2}}$$

Which way up depends on what you are converting from, exactly as with any other conversion factor. Moles of hydrogen on the bottom cancels moles of hydrogen on the top.

Label the moles with the substance. Writing "$0.5$ mol" without saying of what is how mole ratios get applied backwards, and the units then cannot warn you.

Sort It: Which Ratio

For $\mathrm{N_2} + 3\mathrm{H_2} \rightarrow 2\mathrm{NH_3}$.

Example 1: A Mass-to-Mass Calculation

Here is every step, worked all the way through.

How many grams of water are produced from $4.00$ g of hydrogen? $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$

• What is the molar mass of H2, in g/mol? 2.02 g/mol
• How many moles is 4.00 g of hydrogen? Give it to two decimal places 1.98 mol
• The ratio of H2 to H2O is 2 to 2. What number do the moles get multiplied by? 1
• What is the molar mass of water, in g/mol? 18.02 g/mol
• Multiply. How many grams of water, to the nearest gram? 36 g

<!-- SLATE_IF_STRONG: science.chemistry.stoichiometry --> <!-- END_SLATE_IF_STRONG -->