## Mole-to-Mole Conversions

#### Learning Objective

• Calculate how many moles of a product are produced given quantitative information about the reactants.

#### Key Points

• The law of conservation of mass dictates that the quantity of an element does not change over the course of a reaction. Therefore, a chemical equation is balanced when all elements have equal values on both the left and right sides.
• The balanced equation for the reaction of interest contains the stoichiometric ratios of the reactants and products; these ratios can be used as conversion factors for mole-to-mole conversions.
• Stoichiometric ratios are unique for each chemical reaction.

#### Terms

• moleIn the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 12 g of carbon-12.
• conversion factorA ratio of coefficients found in a balanced reaction, which can be used to inter-convert the amount of products and reactants.

## Stoichiometric Values in a Chemical Reaction

A chemical equation is a visual representation of a chemical reaction. In a typical chemical equation, an arrow separates the reactants on the left and the products on the right. The coefficients next to the reactants and products are the stoichiometric values. They represent the number of moles of each compound that needs to react so that the reaction can go to completion.

On some occasions, it may be necessary to calculate the number of moles of a reagent or product under certain reaction conditions. To do this correctly, the reaction needs to be balanced. The law of conservation of matter states that the quantity of each element does not change in a chemical reaction. Therefore, a chemical equation is balanced when the number of each element in the equation is the same on both the left and right sides of the equation.

## Using Stoichiometry to Calculate Moles

The next step is to inspect the coefficients of each element of the equation. The coefficients can be thought of as the amount of moles used in the reaction. The key is reaction stoichoimetry, which describes the quantitative relationship among the substances as they participate in the chemical reaction. The relationship between two of the reaction’s participants (reactant or product) can be viewed as conversion factors and can be used to facilitate mole-to-mole conversions within the reaction.

## Example 1

For example, to determine the number of moles of water produced from 2 mol O2, the balanced chemical reaction should be written out:

$2\:H_{2(g)} + O_{2(g)} \rightarrow 2\:H_{2}O_{(g)}$

There is a clear relationship between O2 and H2O: for every one mole of O2, two moles of H2O are produced. Therefore, the ratio is one mole of O2 to two moles of H2O, or $\frac{1\:mol\:O_2}{2\:moles\:H_2O}$. Assume abundant hydrogen and two moles of O2, then one can calculate:

$2\:moles\: O_2 \cdot \frac{2\:mol\:H_2O}{1\:mol\:O_2} = 4 \:moles \:H_2O$

Therefore, 4 moles of H2O were produced by reacting 2 moles of O2 in excess hydrogen.

Each stoichiometric conversion factor is reaction-specific and requires that the reaction be balanced. Therefore, each reaction must be balanced before starting calculations.

## Example 2

If 4.44 mol of O2 react with excess hydrogen, how many moles of water are produced?

The chemical equation is $O_2 + 2\:H_2 \rightarrow 2\:H_2O$. Therefore, to calculate the number of moles of water produced: $4.44 \:mol \:O_2 \cdot \frac{2 \:moles\: H_2O}{1 \:mole \:O_2} = 8.88 \:moles\: H_2O$.