Combine the ideal gas law with stoichiometry to solve gas-related problems
Ideal Gas Law: PV = nRT
Combine gas laws with stoichiometry to calculate volume, mass, or moles
At STP (0°C, 1 atm): 1 mol gas = 22.4 L
atm
K (Kelvin)
From balanced equation (e.g., 2 in 2H₂ + O₂ → 2H₂O)
mol - OR enter mass + molar mass below
grams (g)
g/mol
Gas stoichiometry combines the ideal gas law (PV = nRT) with stoichiometric principles from balanced chemical equations. This allows us to relate the volume of gases to the amounts (moles, mass) of reactants and products in chemical reactions.
PV = nRT
This is the IUPAC standard reference point
Common laboratory conditions
Problem: What volume of CO₂ gas is produced when 8.8 g of CO₂ is formed at STP?
Given: mass = 8.8 g, M(CO₂) = 44.01 g/mol
Step 1: n = mass / M = 8.8 / 44.01 = 0.200 mol
Step 2: At STP, V = n × 22.4 L/mol = 0.200 × 22.4 = 4.48 L
Answer: 4.48 L of CO₂
Problem: How many liters of O₂ at STP are needed to react with 2.5 L of H₂?
Reaction: 2H₂ + O₂ → 2H₂O
From equation: 2 mol H₂ requires 1 mol O₂
At same T and P: Volume ratio = Mole ratio
V(O₂) = V(H₂) × (1 mol O₂ / 2 mol H₂) = 2.5 × (1/2) = 1.25 L
Answer: 1.25 L of O₂
Problem: Calculate the volume of 0.5 mol of N₂ at 25°C and 2 atm.
Given: n = 0.5 mol, T = 298 K, P = 2 atm, R = 0.0821 L·atm/(mol·K)
PV = nRT
V = nRT/P = (0.5 × 0.0821 × 298) / 2 = 6.13 L
Answer: 6.13 L of N₂
Avogadro's Law states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules (or moles).
V₁/n₁ = V₂/n₂ (at constant T and P)
This means volume ratios equal mole ratios for gases under the same conditions
This is extremely useful in stoichiometry because you can directly use volume ratios from balanced equations when working with gases at the same temperature and pressure.
| Conditions | Temperature (K) | Pressure (atm) | Molar Volume (L/mol) |
|---|---|---|---|
| STP (IUPAC) | 273.15 | 1.000 | 22.414 |
| Room Temperature | 298.15 | 1.000 | 24.465 |
| High Pressure | 298.15 | 2.000 | 12.232 |
| High Temperature | 373.15 | 1.000 | 30.620 |
The ideal gas law assumes:
Real gases deviate from ideal behavior at high pressures and low temperatures. Use the Van der Waals equation for more accurate calculations under these conditions.
Always balance your chemical equation first! The mole ratios from the balanced equation are critical for accurate stoichiometric calculations. For gases at the same T and P, volume ratios equal mole ratios.