Write and balance chemical equations, and use them to show that atoms and mass are conserved in a reaction (MA STE HS-PS1-7(MA), conservation of mass).

What this topic is asking

Standard HS-PS1-7(MA) asks you to use the formula of an equation to show that the mass of the reactants equals the mass of the products. The skill underneath it is balancing equations: adjusting coefficients until every kind of atom appears in equal numbers on both sides. Once an equation is balanced, it becomes a model of the conservation of mass and the starting point for every calculation in this module.

Reading a chemical equation

A chemical equation shows reactants on the left, products on the right, and an arrow meaning "produces". For example:

Two pieces of notation matter:

• A subscript (the small number, as in $\text{O}_2$) tells you how many atoms are in one molecule. It is fixed by the substance: $\text{O}_2$ is oxygen gas, $\text{O}_3$ is ozone.
• A coefficient (the big number in front, as in $2\text{O}_2$) tells you how many of that whole unit take part. Coefficients are what you adjust to balance.

The golden rule: balance with coefficients, never by editing subscripts. Changing $\text{H}_2\text{O}$ to $\text{H}_2\text{O}_2$ to "get more oxygen" turns water into hydrogen peroxide, a different substance.

The law of conservation of mass

This is why an equation must balance. Antoine Lavoisier established it in the 1700s by reacting substances in sealed vessels and weighing them: the mass never changed. If a reaction appears to lose mass (wood burning to a small pile of ash) or gain mass (steel wool rusting), it is because a gas has left or joined the system. Carry the reaction out in a closed system and the balance holds exactly.

How to balance an equation

A reliable routine for a first chemistry course:

1. Write the correct formula for every reactant and product. Do not change these afterwards.
2. Count the atoms of each element on each side.
3. Add coefficients to equalise the counts, one element at a time, leaving hydrogen and oxygen until last because they appear in many compounds.
4. Recount every element to check, then reduce the coefficients to the smallest whole-number ratio.

Balancing tells you the conservation of mass

Once balanced, the equation is a statement that mass is conserved. In $2\text{C}_2\text{H}_6 + 7\text{O}_2 \rightarrow 4\text{CO}_2 + 6\text{H}_2\text{O}$, the same 4 carbon, 12 hydrogen, and 14 oxygen atoms exist on both sides. Because each atom keeps its mass, the total mass of reactants equals the total mass of products. This is the bridge to stoichiometry: the coefficients give the exact ratio in which substances react, developed in stoichiometric calculations.

Try this

Q1. Balance $\text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3$. [1]

• Cue. $4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3$ (4 aluminum, 6 oxygen each side).

Q2. A candle loses mass as it burns in open air. Does this break the law of conservation of mass? Explain. [2]

• Cue. No; the products carbon dioxide and water vapor escape as gases, so they are not weighed. In a closed system the total mass would be unchanged.