# 11: The Chemical Equation

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A chemical equation is a concise description of a chemical reaction. Proper chemical equations are balanced.

##### Learning Objectives
• Define chemical equation.
• Identify the parts of a chemical equation.

A chemical reaction expresses a chemical change. For example, one chemical property of hydrogen is that it will react with oxygen to make water. We can write that as follows:

$\text{hydrogen reacts with oxygen to make water}\nonumber$

We can represent this chemical change more succinctly as:

$\text{hydrogen} + \text{oxygen} → \text{water}\nonumber$

where the + sign means that the two substances interact chemically with each other and the → symbol implies that a chemical reaction takes place. But substances can also be represented by chemical formulas. Remembering that hydrogen and oxygen both exist as diatomic molecules, we can rewrite our chemical change as:

$\ce{H_2 + O_2 → H_2O}\nonumber$

This is an example of a chemical equation, which is a concise way of representing a chemical reaction. The initial substances are called reactants and the final substances are called products.

Unfortunately, it is also an incomplete chemical equation. The law of conservation of matter says that matter cannot be created or destroyed. In chemical equations, the number of atoms of each element in the reactants must be the same as the number of atoms of each element in the products. If we count the number of hydrogen atoms in the reactants and products, we find two hydrogen atoms. But if we count the number of oxygen atoms in the reactants and products, we find that there are two oxygen atoms in the reactants, but only one oxygen atom in the products.

What can we do? Can we change the subscripts in the formula for water so that it has two oxygen atoms in it? No—you cannot change the formulas of individual substances, because the chemical formula for a given substance is characteristic of that substance. What you can do, however, is to change the number of molecules that react or are produced. We do this one element at a time, going from one side of the reaction to the other, changing the number of molecules of a substance until all elements have the same number of atoms on each side.

To accommodate the two oxygen atoms as reactants, let us assume that we have two water molecules as products:

$\ce{H_2 + O_2 → 2H_2O}\nonumber$

The 2 in front of the formula for water is called a coefficient. Now there are the same number of oxygen atoms in the reactants as there are in the product. But in satisfying the need for the same number of oxygen atoms on both sides of the reaction, we have also changed the number of hydrogen atoms on the product side, so the number of hydrogen atoms is no longer equal. No problem, simply go back to the reactant side of the equation, and add a coefficient in front of the H2. The coefficient that works is 2:

$\ce{2H_2 + O_2 → 2H_2O}\nonumber$

There are now four hydrogen atoms in the reactants and also four atoms of hydrogen in the product. There are two oxygen atoms in the reactants and two atoms of oxygen in the product. The law of conservation of matter has been satisfied. When the reactants and products of a chemical equation have the same number of atoms of all elements present, we say that an equation is balanced. All proper chemical equations are balanced. If a substance does not have a coefficient written in front of it, it is assumed to be 1. Also, the convention is to use all whole numbers when balancing chemical equations. This sometimes makes us do a bit more "back and forth" work when balancing a chemical equation.

##### Example $$\PageIndex{1}$$

Write and balance the chemical equation for each given chemical reaction.

1. Hydrogen and chlorine react to make $$\ce{HCl}$$
2. Ethane, $$\ce{C2H6}$$, reacts with oxygen to make carbon dioxide and water.
###### Solution
1. Let us start by simply writing a chemical equation in terms of the formulas of the substances, remembering that both elemental hydrogen and chlorine are diatomic: $\ce{H2 + Cl2 → HCl} \nonumber \nonumber$

There are two hydrogen atoms and two chlorine atoms in the reactants and one of each atom in the product. We can fix this by including the coefficient 2 on the product side:

$\ce{H2 + Cl2 → 2HCl} \nonumber \nonumber$

Now there are two hydrogen atoms and two chlorine atoms on both sides of the chemical equation, so it is balanced.

2. Start by writing the chemical equation in terms of the substances involved: $\ce{C2H6 + O2 → CO2 + H2O} \nonumber \nonumber$

We have two carbon atoms on the left, so we need two carbon dioxide molecules on the product side, so that each side has two carbon atoms; that element is balanced. We have six hydrogen atoms in the reactants, so we need six hydrogen atoms in the products. We can get this by having three water molecules:

$\ce{C2H6 + O2 → 2CO2 + 3H2O} \nonumber \nonumber$

Now we have seven oxygen atoms in the products (four from the CO2 and three from the H2O). This means we need seven oxygen atoms in the reactants. However, because oxygen is a diatomic molecule, we can only get an even number of oxygen atoms at a time. We can achieve this by multiplying the other coefficients by 2:

$\ce{2C2H6 + O2 → 4CO2 + 6H2O} \nonumber \nonumber$

By multiplying everything else by 2, we do not unbalance the other elements, and we now get an even number of oxygen atoms in the product—14. We can get 14 oxygen atoms on the reactant side by having 7 oxygen molecules:

$\ce{2C2H6 + 7O2 → 4CO2 + 6H2O} \nonumber \nonumber$

As a check, recount everything to determine that each side has the same number of atoms of each element. This chemical equation is now balanced.

##### Exercise $$\PageIndex{1}$$

Write and balance the chemical equation that represents nitrogen and hydrogen reacting to produce ammonia, NH3.

$\ce{N2 + 3H2 → 2NH3 \nonumber \nonumber$

Many chemical equations also include phase labels for the substances: (s) for solid, (ℓ) for liquid, (g) for gas, and (aq) for aqueous (i.e., dissolved in water). Special conditions, such as temperature, may also be listed above the arrow. For example,

$\ce{ 2NaHCO3 (s)} \overset{200^{\circ}C}{\rightarrow} \ce{Na2CO3 (s) + CO2(g) + H2O(l) }\nonumber$

## Key Takeaways

• A chemical equation is a concise description of a chemical reaction.
• Proper chemical equations are balanced.
• 11.1: Introduction
An introduction to the concept of proportion.
• 11.2: Types of Chemical Reactions - Single and Double Displacement Reactions
A single-replacement reaction replaces one element for another in a compound. The periodic table or an activity series can help predict whether single-replacement reactions occur. A double-replacement reaction exchanges the cations (or the anions) of two ionic compounds. A precipitation reaction is a double-replacement reaction in which one product is a solid precipitate. Solubility rules are used to predict whether some double-replacement reactions will occur.
• 11.3: Types of Chemical Reactions - Single and Double Displacement Reactions
A single-replacement reaction replaces one element for another in a compound. The periodic table or an activity series can help predict whether single-replacement reactions occur. A double-replacement reaction exchanges the cations (or the anions) of two ionic compounds. A precipitation reaction is a double-replacement reaction in which one product is a solid precipitate. Solubility rules are used to predict whether some double-replacement reactions will occur.
• 11.4: Ionic Equations - A Closer Look
Ionic compounds that dissolve separate into individual ions. Complete ionic equations show dissolved ionic solids as separated ions. Net ionic equations show only the ions and other substances that change in a chemical reaction.
• 11.5: Composition, Decomposition, and Combustion Reactions
A composition reaction produces a single substance from multiple reactants. A decomposition reaction produces multiple products from a single reactant. Combustion reactions are the combination of some compound with oxygen to make oxides of the other elements as products (although nitrogen atoms react to make $$N_2$$).
• 11.6: Stoichiometry
Quantities of substances can be related to each other using balanced chemical equations.
• 11.7: The Mole
The mole is a key unit in chemistry. The molar mass of a substance, in grams, is numerically equal to one atom's or molecule's mass in atomic mass units.

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