5.5:
Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles
Recall that for a balanced chemical reaction, calculations involving the mass of the reactants and products and the number of moles are performed by following a general conceptual plan.
Here, the stoichiometric coefficients are used as conversion factors between the moles of the reactant and the moles of the product.
In chemical reactions involving gaseous substances, the amount of gas is typically specified in terms of its volume at a given temperature and pressure. This is because gases are fluid and expand to fill any available volume.
In gaseous reactions, the mole amount and volume of a gas are interrelated through the ideal gas law. In this way, the number of moles can be determined from the volume of the gas and vice versa.
Combining concepts of the ideal gas law, molar mass, and stoichiometry allows for calculations related to the volume, the number of moles, and the mass of gaseous reactants and products.
As an example, consider the reaction between lithium and water to produce hydrogen gas. Assuming that the reaction occurs at 291 K and 0.977 atm, what amount of lithium will produce 35.25 liters of hydrogen?
First, by applying the ideal gas law and substituting the given values of pressure, volume, temperature, and the ideal gas constant, the moles of hydrogen gas are calculated.
Then, using the stoichiometric ratio, the number of moles of hydrogen gas is converted to moles of lithium. Finally, multiplying by the molar mass of lithium results in a mass of 20.0 grams. Thus, 20.0 grams of lithium will produce 35.25 liters of hydrogen.
For gaseous chemical reactions that occur at STP — standard temperature and pressure — the molar volume, 22.4 liters, is a constant. The conversion factor is used in stoichiometric calculations involving gases at STP.
Take, for example, the formation of water at STP. What volume of hydrogen is required to produce 2 grams of water?
Following the general conceptual plan, first, the mass of water is divided by its molar mass, to give the moles of water. Then the stoichiometric ratio is used to determine the moles of hydrogen. Finally, the mole to volume conversion factor at STP is used to get 2.5 liters of hydrogen gas.
Thus, 2.5 liters of hydrogen will produce 2 grams of water at STP.
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 N2, H2, and NH3, at the same temperature and pressure, contain the same number of molecules. Because one molecule of N2 reacts with three molecules of H2 to produce two molecules of NH3, the volume of H2 required is three times the volume of N2, and the volume of NH3 produced is two times the volume of N2.
This text is adapted from Openstax, Chemistry 2e, Chapter 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions.