Exam skill: balance fast and check by counting

Marks that are easy to win

A question says: "Balance this equation." It takes one minute. The marks are easy, if you have a method and you check.

The method

Take $\text{Fe} + \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + \text{H}_2$.

1. List the atoms of each side.

2. Balance one atom at a time. Start with the atom that is in the fewest formulas on each side, which is often a metal. Leave hydrogen and oxygen for last, because they are in many formulas.

• Iron: put $3$ in front of Fe. Now Fe is $3$ and $3$.
• Oxygen: the right has $4$. Put $4$ in front of $\text{H}_2\text{O}$. Now O is $4$ and $4$, and H on the left is $8$.
• Hydrogen: the left has $8$. Put $4$ in front of $\text{H}_2$ on the right. Now H is $8$ and $8$.

3. Count again. Fe: $3 = 3$. H: $8 = 8$. O: $4 = 4$. ✓

Three rules to keep

• Change only the coefficients, the numbers in front. Never change a subscript, the small number in a formula. A different subscript is a different substance: $\text{H}_2\text{O}_2$ is not water.
• A group such as $\text{SO}_4$ or $\text{OH}$ that stays together on both sides can be counted as one unit.
• If a fraction helps, such as $\tfrac{7}{2}\,\text{O}_2$, multiply the whole equation by $2$ to remove it.

You should find that $b = 3.5$ balances the oxygen, and that multiplying by $2$ gives $2, 7, 4, 6$.

Where marks are lost

• Counting one side and not the other.
• Forgetting that a coefficient multiplies every atom in the formula, so $2\,\text{H}_2\text{SO}_4$ has $4$ H, $2$ S and $8$ O.
• Writing $\text{O}$ and not $\text{O}_2$ for oxygen gas.

Practise with new numbers

Try it in Python

This program counts the atoms for you and tells you if an equation is balanced.

Remember these

• List the atoms, balance one at a time, hydrogen and oxygen last, and count again.
• Change only coefficients. Never change a subscript.
• A coefficient multiplies every atom of the formula.

Check yourself

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

1. How many hydrogen atoms are there in $3\,\text{H}_2\text{SO}_4$?

2. Why must you never change a subscript when you balance?

3. Balance $\text{P} + \text{O}_2 \rightarrow \text{P}_2\text{O}_5$.

4. A student gets $\text{C}_2\text{H}_2 + \tfrac{5}{2}\,\text{O}_2 \rightarrow 2\text{CO}_2 + \text{H}_2\text{O}$. How does she remove the fraction?