### 5.5: Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities of reactants and products using masses for solids and volumes in conjunction with the molarity for solutions; now, the gas volumes can also be used to indicate quantities. If the volume, pressure, and temperature of a gas is known, then the ideal gas equation to calculate how many moles of the gas are present, can be used. Conversely, if the amount of moles of gas is known, the volume of a gas at any temperature and pressure can be determined.

As an example, let's calculate the volume of hydrogen at 27 °C and 723 torr prepared by the reaction of 8.88 g of gallium with an excess of hydrochloric acid.

First, convert the provided mass of the limiting reactant, Ga, to moles of hydrogen produced:

Convert the provided temperature and pressure values to appropriate units (K and atm, respectively), and then use the molar amount of hydrogen gas and the ideal gas equation to calculate the volume of gas:

#### Avogadro’s Law Revisited

One can also take advantage of a simple feature of the stoichiometry of gases that solids and solutions do not exhibit: All gases that show ideal behavior contain the same number of molecules in the same volume (at the same temperature and pressure). Thus, the ratios of volumes of gases involved in a chemical reaction are given by the coefficients in the equation for the reaction, provided that the gas volumes are measured at the same temperature and pressure.

Avogadro’s law can be extended (that the volume of a gas is directly proportional to the number of moles of the gas) to chemical reactions with gases: Gases combine, or react, in definite and simple proportions by volume, provided that all gas volumes are measured at the same temperature and pressure.

For example, since nitrogen and hydrogen gases react to produce ammonia gas according to

a given volume of nitrogen gas reacts with three times that volume of hydrogen gas to produce two times that volume of ammonia gas if pressure and temperature remain constant.

According to Avogadro’s law, equal volumes of gaseous N_{2}, H_{2}, and NH_{3}, at the same temperature and pressure, contain the same number of molecules. Because one molecule of N_{2} reacts with three molecules of H_{2} to produce two molecules of NH_{3}, the volume of H_{2} required is three times the volume of N_{2}, and the volume of NH_{3} produced is two times the volume of N_{2}.

*This text is adapted from Openstax, Chemistry 2e, Chapter 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions.*