Gas Stoichiometry

Recall the general stoichiometry road map: convert the given quantity to moles, use the mole ratio from the balanced equation to convert to moles of the desired substance, then convert those moles to whatever unit is requested. Gas volume slots into this exactly like mass did — you just choose the correct conversion tool depending on the conditions given.

1. Write and balance the chemical equation (if not already given).
2. Convert the given quantity to moles: use molar mass for a mass in grams, or use molar volume ($V_m$ = 22.4 or 24.8 L/mol) if the gas is AT STP or SATP, or use the ideal gas law ($n=PV/RT$) if the gas is at non-standard conditions.
3. Use the mole ratio from the balanced equation to convert moles of the given substance to moles of the desired substance.
4. Convert moles of the desired substance to whatever final unit is requested: grams (molar mass), volume at STP/SATP (molar volume), or volume at other conditions (ideal gas law, solved for $V$).

One more subtlety worth noting: when a balanced equation involves TWO gases (for example, both a reactant and a product are gases at the same conditions), the coefficients in the balanced equation directly give you a volume ratio too — by Avogadro's law, equal moles of gas at the same $T$ and $P$ occupy volumes in the same ratio as their mole ratio. This can occasionally save you a step, though solving through moles always works and is the safer default. Joseph Louis Gay-Lussac noticed this pattern in 1808, long before anyone could count molecules: reacting gases always combine in small whole-number volume ratios (his law of combining volumes). For the Haber process that makes ammonia for fertilizer, 10.0 L of nitrogen reacts with exactly 30.0 L of hydrogen to give 20.0 L of ammonia, all measured at the same temperature and pressure. Notice that volume is NOT conserved (40.0 L of reactants make 20.0 L of product), even though mass is: the number of gas particles drops, so the volume drops. The shortcut only applies to gases; a solid or liquid in the equation still needs its own mole conversion.

Many real gas samples are mixtures: air, the gas in a scuba tank, or a gas collected in a lab. The kinetic molecular theory says ideal gas particles ignore each other except when they collide, so in a mixture each gas behaves as if it were alone in the container. Each gas's collisions with the walls produce its own partial pressure, and the total pressure is just the sum. This is Dalton's law of partial pressures. Because pressure depends only on the number of particles, each gas's share of the total pressure equals its share of the moles (its mole fraction). Air is 20.95% oxygen by volume, so at sea level (101.3 kPa) the partial pressure of oxygen is $0.2095\times 101.3\approx 21.2$ kPa. On the summit of Mount Everest the total pressure is only about 33.7 kPa, so the oxygen partial pressure falls to about 7.1 kPa. The air is still 21% oxygen, but each breath delivers only about one-third as many oxygen molecules, which is why most climbers carry bottled oxygen.

A common way to collect a gas made in a reaction (such as hydrogen from zinc and hydrochloric acid, or oxygen from decomposing hydrogen peroxide) is to bubble it into an upside-down bottle or graduated cylinder filled with water. The gas pushes the water out, and the volume can be read directly. Before reading, the cylinder is raised or lowered until the water level inside matches the level outside; then the gas inside is at the same pressure as the atmosphere. But the collected gas is not pure: water evaporates into it, so the cylinder holds a mixture of the gas and water vapour. By Dalton's law, the pressure of the dry gas is the atmospheric pressure minus the vapour pressure of water, which depends only on the temperature.