## Molar Ratios

#### Learning Objective

• Calculate the molar ratio between two substances given their balanced reaction

#### Key Points

• Molar ratios state the proportions of reactants and products that are used and formed in a chemical reaction.
• Molar ratios can be derived from the coefficients of a balanced chemical equation.
• Stoichiometric coefficients of a balanced equation and molar ratios do not tell the actual amounts of reactants consumed and products formed.

#### Term

• stoichiometric ratioThe ratio of the coefficients of the products and reactants in a balanced reaction. This ratio can be used to calculate the amount of products or reactants produced or used in a reaction.

Chemical equations are symbolic representations of chemical reactions. In a chemical equation, the reacting materials are written on the left, and the products are written on the right; the two sides are usually separated by an arrow showing the direction of the reaction. The numerical coefficient next to each entity denotes the absolute stoichiometric amount used in the reaction. Because the law of conservation of mass dictates that the quantity of each element must remain unchanged over the course of a chemical reaction, each side of a balanced chemical equation must have the same quantity of each particular element.

In a balanced chemical equation, the coefficients can be used to determine the relative amount of molecules, formula units, or moles of compounds that participate in the reaction. The coefficients in a balanced equation can be used as molar ratios, which can act as conversion factors to relate the reactants to the products. These conversion factors state the ratio of reactants that react but do not tell exactly how much of each substance is actually involved in the reaction.

## Determining Molar Ratios

The molar ratios identify how many moles of product are formed from a certain amount of reactant, as well as the number of moles of a reactant needed to completely react with a certain amount of another reactant. For example, look at this equation:

$CH_{4} + 2O_{2} \rightarrow CO_{2} + 2H_{2}O$

From this reaction equation, it is possible to deduce the following molar ratios:

• 1 mol CH4: 1 mol CO2
• 1 mol CH4: 2 mol H2O
• 1 mol CH4: 2 mol O2
• 2 mol O2: 1 mol CO2
• 2 mol O2: 2 mol H2O

In other words, 1 mol of methane will produced 1 mole of carbon dioxide (as long as the reaction goes to completion and there is plenty of oxygen present). These molar ratios can also be expressed as fractions. For example, 1 mol CH4: 1 mol CO2 can be expressed as $\frac{1 \ mol \ CH_4}{1 \ mol \ CO_2}$. These molar ratios will be very important for quantitative chemistry calculations that will be discussed in later concepts.