Stoichiometry and the limiting reagent in code

An equation as data

Natural gas is mostly methane. It burns like this:

• $\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}$

In Python, the coefficients fit into two dictionaries:

The keys are the formulas, and the values are the coefficients. The same code then works for any reaction: only the dictionaries change.

Rounds of the equation

Think of the equation as a recipe. One round uses one $\text{CH}_4$ and two $\text{O}_2$. If you have $0.5\ \text{mol}$ of methane, it is enough for $0.5$ rounds. If you have $1.25\ \text{mol}$ of oxygen, it is enough for $\dfrac{1.25}{2} = 0.625$ rounds.

• rounds for a reactant $= \dfrac{\text{its moles}}{\text{its coefficient}}$

The reactant with the fewest rounds runs out first: it is the limiting reagent. The number of rounds that really happen, the extent, is that smallest value. Then:

• moles of a product $=$ extent $\times$ its coefficient;
• moles of a reactant left $=$ its moles $-$ extent $\times$ its coefficient.

The function

In Python, the limiting reagent is one line:

min with key=rounds.get compares the values but returns the key, here the formula CH4.

Grams in, grams out

A chemist weighs grams, so the function changes grams to moles first and moles back to grams at the end. For gases at STP, one mole fills $22.7\ \text{L}$, so a volume is moles times $22.7$.

The percent yield compares what you really collected with what the equation predicts:

• percent yield $= \dfrac{\text{actual mass}}{\text{theoretical mass}} \times 100$

Test your function

A function that runs is not yet a function that is right. Test it on a case you can work by hand. For $8.0\ \text{g}$ of methane in $40.0\ \text{g}$ of oxygen, methane gives $0.499$ rounds and oxygen $0.625$. Methane is limiting, so the program must say so:

assert stops the program with an AssertionError if the test fails, and does nothing if it passes.

Practise with new numbers

Try it in Python

The program burns $8.0\ \text{g}$ of methane in $40.0\ \text{g}$ of oxygen. It prints the limiting reagent, the products and what is left.

Common mistakes

• Comparing moles, not rounds. Divide each reactant's moles by its coefficient before you compare.
• Using max instead of min. The reactant with the most rounds is in excess, not limiting.
• Mixing grams and moles. Change every mass to moles before using the coefficients.
• A formula spelled differently in two places. molar_mass["co2"] stops with KeyError: 'co2' when the key is "CO2".
• Trusting code without a test. Check it against one example worked by hand.

Remember these

• Keep an equation as two dictionaries of coefficients.
• Rounds $=$ moles $\div$ coefficient; the smallest is the extent, and its reactant is limiting.
• Product moles $=$ extent $\times$ coefficient; excess left $=$ moles $-$ extent $\times$ coefficient.
• Percent yield $= \dfrac{\text{actual}}{\text{theoretical}} \times 100$; a gas at STP fills $22.7\ \text{L}$ per mole.
• Test a function with assert on a case you know.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. For $2\text{SO}_2 + \text{O}_2 \rightarrow 2\text{SO}_3$, write the two dictionaries.

2. With $3\ \text{mol}$ of $\text{SO}_2$ and $2\ \text{mol}$ of $\text{O}_2$, which reactant is limiting?

3. What does min({"A": 4, "B": 2}, key={"A": 4, "B": 2}.get) return?

4. A reaction should give $20\ \text{g}$ of product, and you collect $17\ \text{g}$. What is the percent yield?

5. Why test a function with assert before you trust it?