### 3.10: Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right) sides of the equation. The relative numbers of reactant and product species are represented by numerical coefficients, placed immediately to the left of each formula. A coefficient of 1 is typically not usually shown. The smallest possible whole-number coefficients are commonly used in a chemical equation, and they are interpreted as ratios. For example, methane and oxygen react to yield carbon dioxide and water in a 1:2:1:2 ratio.

The ratio indicates that the smallest possible coefficients of methane, oxygen, carbon dioxide, and water are 1, 2, 1, and 2, respectively. The coefficients may be interpreted with regard to any amount (number) unit, and so this equation may be correctly read in many ways, including:

i. One methane molecule and two oxygen molecules react to yield one carbon dioxide molecule and two water molecules.

ii. One mole of methane molecules and 2 moles of oxygen molecules react to yield 1 mole of carbon dioxide molecules and 2 moles of water molecules.

The physical states of reactants and products in chemical equations very often are indicated with a parenthetical abbreviation following the formulas. Standard abbreviations include ‘*s*’ for solids, ‘*l*’ for liquids, ‘*g*’ for gases, and ‘*aq*’ for substances dissolved in water.

#### Balancing equations

In a balanced equation, the numbers of atoms for each element involved in the reaction are the same on the reactant and product sides, thereby satisfying the law of conservation of matter. A balanced equation can be confirmed by adding the numbers of atoms on either side of the arrow and comparing these sums to ensure they are equal. Note that the number of atoms for a given element is calculated by multiplying the coefficient of any formula containing that element by the element’s subscript in the formula. If an element appears in more than one formula on a given side of the equation, the number of atoms represented in each must be computed and then added together.

To balance the equation, the coefficients of the equation may be changed as needed. It is sometimes convenient to use fractions instead of integers as intermediate coefficients in the process of balancing a chemical equation. When balance is achieved, all the equation’s coefficients may then be multiplied by a whole number to convert the fractional coefficients to integers without upsetting the atom balance.

For example, the reaction of ethane (C_{2}H_{6}) with oxygen yields water and carbon dioxide, which can be represented by the following unbalanced equation:

The unbalanced equation contains:

Atoms |
Reactant |
Product |
Balanced? |

C | 2 | 1 | No |

H | 6 | 2 | No |

O | 2 | 3 | No |

To balance the number of carbon atoms and hydrogen atoms, multiply CO_{2} by the coefficient 2 and multiply H_{2}O by the coefficient 3, respectively. This changes the total number of oxygen atoms on the product to 7. To balance the number of oxygen atoms, multiply oxygen by the fractional coefficient 7/2. This initial balancing of the carbon, hydrogen, and oxygen atoms by changing the coefficients for reactants and products, gives the provisionally balanced equation:

A conventional balanced equation with integer-only coefficients is derived by multiplying each coefficient by 2, to generate the equation:

*This text is adapted from Openstax, Chemistry 2e, Section 4.1: Writing and Balancing Chemical Equations.*