## Writing Chemical Equations

A chemical equation expresses a chemical reaction by showing how certain reactants yield certain products.

### Learning Objectives

Identify the symbols used to represent the states of matter in a chemical equation.

### Key Takeaways

#### Key Points

• In a chemical equation, the reactants are written on the left, and the products are written on the right.
• The coefficients next to the symbols of entities indicate the number of moles of a substance produced or used in the chemical reaction.
• The reactants and products are separated by an arrow, usually read aloud as “yields.”
• Chemical equations should contain information about the state properties of products and reactants, whether aqueous (dissolved in water — aq), solid (s), liquid (l), or gas (g).

#### Key Terms

• chemical equation: A symbolic representation of a chemical reaction; reactants are represented on the left and products on the right.
• reactant: The starting materials in a chemical reaction.
• product: The compounds produced by a chemical reaction.

A chemical equation is the symbolic representation of a chemical reaction. The reactants (the starting substances) are written on the left, and the products (the substances found in the chemical reaction) are written on the right. The coefficients next to the symbols of entities indicate the number of moles of a substance produced or used in the chemical reaction.

### Notation for a Chemical Equation

A chemical equation consists of the chemical formulas of the reactants (on the left) and the products (on the right). The two are separated by an arrow symbol (“→” usually read aloud as “yields”). Each individual substance’s chemical formula is separated from others by a plus sign. The state of matter of each compound or molecule is indicated in subscript next to the compound by an abbreviation in parentheses. For example, a compound in the gas state would be indicated by (g), solid (s), liquid (l), and aqueous (aq). Aqueous means dissolved in water; it is a common state of matter for acids, bases, and dissolved ionic compounds.

As an example, the formula for the burning of methane can be written as follows:

$\text{CH}_{4\:(g)} + 2\text{O}_{2\:(g)} \rightarrow \text{CO}_{2\:(g)} + 2\text{H}_{2}\text{O}_{(g)}$

This equation would be read as “CH four plus two O two yields CO two and two H two O.” For equations involving complex chemicals, read the chemical formulas using IUPAC nomenclature, rather than reading the letter and its subscript. Using IUPAC nomenclature, this equation would be read as “methane plus oxygen yields carbon dioxide and water.”

This equation indicates that oxygen and CH4 react to form H2O and CO2. It also indicates that two oxygen molecules are required for every methane molecule, and that the reaction will form two water molecules and one carbon dioxide molecule for every methane and two oxygen molecules that react. The equation also identifies that all the compounds are in the gaseous state. The stoichiometric coefficients (the numbers in front of the chemical formulas) result from the law of conservation of mass and the law of conservation of charge (see the “Balancing Chemical Equations” section for more information). Also, please note that, as in the mathematical commutative property of addition, chemical equations are commutative. Reactants and products can be written in any order, provided they are on the appropriate side of the reaction arrow.

### Common Symbols

Symbols are used to differentiate among different types of reactions. Sometimes, different arrows are used to indicate something about the reaction. For example:

$\rightarrow$ indicates where the forward reaction is favored: in other words, more of the product is being produced.

$\leftarrow$ indicates where the reverse reaction is favored: in other words, more of the reactant is being produced.

$\leftrightharpoons$ or $\leftrightarrow$ is used to denote a system in equilibrium.

If the reaction requires energy, it is often indicated above the arrow. A capital Greek letter delta (Δ) is written on top of the reaction arrow to show that energy in the form of heat is added to the reaction; hv is written if the energy is added in the form of light.

When a baking soda volcano is made by mixing vinegar (dilute aqueous acetic acid) and baking soda (sodium bicarbonate), the resulting evolution of gas occurs via the following reaction:

$\text{HCH}_3\text{CO}_{2(aq)} + \text{NaHCO}_{3(s)} \rightarrow \text{CH}_3\text{CO}_2\text{Na}_{(aq)} + \text{H}_2\text{O}_{(l)} + \text{CO}_{2(g)}$

## Balancing Chemical Equations

Matter cannot be created or destroyed, so there must be the same number of atoms of each element on each side of a chemical equation.

### Learning Objectives

Formulate a balanced chemical equation for a given reaction

### Key Takeaways

#### Key Points

• Every chemical equation adheres to the law of conservation of mass, which states that matter cannot be created or destroyed. Therefore, there must be the same number of atoms of each element on each side of a chemical equation.
• Use coefficients of products and reactants to balance the number of atoms of an element on both sides of a chemical equation.
• When an equal number of atoms of an element is present on both sides of a chemical equation, the equation is balanced.

#### Key Terms

• law of conservation of mass: Matter cannot be created or destroyed. Therefore, in a closed system, the mass of the reactants must equal the mass of the products.
• coefficient: A constant by which an algebraic term is multiplied.

A chemical equation is an expression of the net composition change associated with a chemical reaction. It shows how a certain amount of reactants yields a certain amount of products. Both of these amounts are measured in moles. Chemical equations often contain information about the state of the reactants: solid, liquid, gas, or aqueous. In addition, they always adhere to the law of conservation of mass, which holds that matter can change form, but cannot be created or destroyed.

This means that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. In other words, for any chemical equation in a closed system, the mass of the reactants must equal the mass of the products. Therefore, there must be the same number of atoms of each element on each side of a chemical equation. A properly balanced chemical equation shows this.

### How to Balance Reactions

Take a look at the equation for the chemical reaction that yields table salt (NaCl, sodium chloride) from sodium metal and chlorine gas:

$\text{Na}_{(s)} + \text{Cl}_{2(g)} \rightarrow \text{NaCl}_{(s)}$

There are two chlorine atoms on the reactant’s side, which is indicated by the subscript 2 next to chlorine. However, there is only one Cl atom on the product’s side because the ratio of Na to Cl is one to one. Therefore, to balance this reaction, a coefficient will have to be added to the NaCl on the product’s side.

Never attempt to balance a reaction by changing the subscripts on a molecule. The subscripts indicate a very specific molecule; changing the subscripts would indicate a new molecule (not the desired product).

To balance this reaction, add a 2 in front of the NaCl.

$\text{Na}_{(s)} + \text{Cl}_{2(g)} \rightarrow 2\text{NaCl}_{(s)}$

Now, there are two chlorine atoms on each side of the reaction. However, now there is one sodium atom on the reactant’s side and two sodium atoms on the product’s side. Therefore, add a 2 in front of the sodium on the reactant’s side.

$2\text{Na}_{(s)} + \text{Cl}_{2(g)} \rightarrow 2\text{NaCl}_{(s)}$

Now, there are two sodium atoms on both sides and two chlorine atoms on both sides. Therefore, the reaction is balanced.

The law of conservation of mass applies in all chemical equations. This means that the number of atoms of products present is conserved in the number of atoms of reactants.

Interactive: Stoichiometry and Balancing Reactions: To make hydrogen chloride or any other chemical there is only one ratio of reactants that works so that all of the hydrogen and chlorine are used to make hydrogen chloride. Try several different ratios to see which ones form a complete reaction with nothing left over. What is the simplest ratio of hydrogen to chlorine for forming hydrogen chloride?

Balancing Chemical Equations – YouTube: This video shows simple steps to balance chemical equations.