Can I use fractions as coefficients?

During your scratch-work, fractions can be a helpful intermediate step (like using $1/2$ $O_2$). However, a properly balanced equation should be written using the lowest whole-number ratio. If you end up with a fraction, simply multiply the entire equation by the denominator to clear it.

What if an element appears in multiple molecules on one side?

You must add them all together to get the total count for that side. For example, if you have $CO_2$ and $H_2O$ on the product side, your total oxygen count is the oxygens from $CO_2$ plus the oxygens from $H_2O$. Keep track of them carefully when recounting.

Which element should I try to balance first?

A good rule of thumb is to balance metals first, then non-metals, saving hydrogen and oxygen for last. Oxygen is often found in multiple compounds in a single reaction, making it the hardest to balance early on.

How do you balance a chemical equation?

Balancing a chemical equation means adding whole numbers, called coefficients, in front of the chemical formulas so that the number of atoms for each element is exactly the same on both sides.

You can think of it like following a recipe where you cannot make ingredients disappear or appear out of nowhere. If you start with two atoms of hydrogen, you must end up with two atoms of hydrogen. This rule is called the Law of Conservation of Mass. By balancing the equation, you show exactly how the reactants rearrange to form the products without losing any pieces.

What is a coefficient?

A coefficient is the large number written in front of a chemical formula. It tells you how many molecules of that substance are involved in the reaction. For example, in $2H_2O$ , the $2$ is the coefficient. It means there are two water molecules.

Think of a bicycle. A bicycle has two wheels. If you have 3 bicycles, you have 6 wheels in total. The "3" is like the coefficient, and the "2" wheels per bike is like the subscript in a chemical formula. You multiply the coefficient by the subscript to find the total number of atoms.

Why do we balance equations?

We balance equations because of the Law of Conservation of Mass. This law states that matter cannot be created or destroyed in an ordinary chemical reaction. The mass of the reactants (starting materials) must equal the mass of the products (ending materials).

Because every atom has mass, we must have the exact same number of each type of atom before and after the reaction takes place. If an equation is unbalanced, it is like saying a brick wall was built out of thin air.

How to recognize an unbalanced equation

To see if an equation needs balancing, you simply tally up the atoms on the left side (reactants) and compare them to the right side (products). Draw a line down the middle of the reaction arrow to keep things organized.

If any element has a different count on the left compared to the right, the equation is unbalanced. You will need to systematically add coefficients until both sides match perfectly.

Where students slip up

The most common mistake students make is changing the small subscript numbers instead of the coefficients. You can never change a subscript to balance an equation!

If you change $H_2O$ (water) to $H_2O_2$ (hydrogen peroxide) just to get an extra oxygen atom, you have completely changed the chemical involved. Water is safe to drink, but hydrogen peroxide is toxic. Always use coefficients (the big numbers in front) to balance.

Worked through

Balance the following equation for the combustion of methane: $CH_4 + O_2 \rightarrow CO_2 + H_2O$

First, tally the atoms on each side.

Reactants (left): C = 1, H = 4, O = 2.

Products (right): C = 1, H = 2, O = 3 (2 from $CO_2$ and 1 from $H_2O$ ).

The carbon atoms are balanced, but hydrogen and oxygen are not. Start by balancing the hydrogen. We have 4 on the left and 2 on the right. Place a coefficient of 2 in front of $H_2O$ .

Equation becomes: $CH_4 + O_2 \rightarrow CO_2 + 2H_2O$

Now recount. Reactants: C = 1, H = 4, O = 2. Products: C = 1, H = 4, O = 4 (2 from $CO_2$ and 2 from $2H_2O$ ).

Finally, balance the oxygen. We have 4 on the right and 2 on the left. Place a 2 in front of $O_2$ .

Balanced Equation: $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$

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Where this comes from: OpenStax Chemistry 2e, Chapter 4: Stoichiometry of Chemical Reactions · Khan Academy: Chemical reactions and stoichiometry unit