Worked example 1
For 2 H₂(g) + O₂(g) → 2 H₂O(g) at constant temperature and pressure, what volume of O₂ reacts completely with 6.0 L of H₂?
Try it first: Check whether every species involved is a gas at shared conditions.
0 of 3 steps revealed.
Gases, Solutions & SpectroscopyGas StoichiometryContent level: Core 22 min
Gas Stoichiometry
What you'll be able to do: Combine the ideal gas law with mole ratios to relate gas volumes, masses and pressures in a reaction.
Introduction
Stoichiometry always runs through moles. With gases, the ideal gas law is simply the tool that gets you into and out of moles at either end of the calculation.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Convert between gas volume and moles under stated conditions
- Apply mole ratios to reactions that involve gases
- Use the coefficients as a volume ratio when T and P are constant
- Identify the limiting reactant in a gas-phase reaction
Lesson
The route through moles
Every stoichiometry problem has the same skeleton: given quantity, then moles of the given, then moles of the wanted, then the wanted quantity. Only the first and last conversions change when a gas is involved, and for those you use PV = nRT or the molar volume at STP.
Never apply a mole ratio to a volume, a mass or a pressure. Ratios only ever act on moles.
Volume ratios shortcut
When all gases in a reaction are at the same temperature and pressure, volume is directly proportional to moles. That means the coefficients can be used as a volume ratio directly, which turns many questions into one line of arithmetic. This works only for gases and only when T and P are shared.
Mixing gases with solids and liquids
Many reactions have a solid or aqueous reactant and a gaseous product. Convert the non-gas quantity to moles with molar mass or molarity, apply the ratio, and then convert the moles of gas to a volume with PV = nRT at the stated conditions.
Limiting reactant with gases
If two gases are given, convert each to moles and compare them against the balanced ratio just as you would with masses. Because pressure at fixed T and V is proportional to moles, you can often compare pressures directly to find which reactant runs out first.
Find the limiting gas from volume ratios
At a common temperature and pressure, gas volumes are proportional to moles, so reaction coefficients can compare volumes directly. Apply the coefficient ratio to each reactant before predicting product volume. The shortcut does not remove the limiting-reactant check; a gas in excess is not fully consumed.
Use gas-volume ratios only when the compared gases share T and P.
Key ideas
Rule
Moles first
Mole ratios act only on moles, so every gas quantity must be converted before the ratio is applied.
Key concept
Volume ratio
At shared T and P, gas volumes are in the same ratio as the coefficients.
Definition
Molar volume
22.4 L/mol, valid only at STP of 273.15 K and 1 atm.
Key concept
Mixed-phase problems
Non-gas species use molar mass or molarity; gases use PV = nRT.
Equation
Ideal gas law
PV = nRT
- n = moles of gas
- R = 0.08206 L*atm/(mol*K)
Equation
Volume ratio at fixed T and P
VA / VB = coefficientA / coefficientB
- V = gas volume at shared conditions
Worked examples
Worked example 2
What volume of CO₂, measured at 1.00 atm and 300 K, forms when 25.0 g of CaCO₃ decomposes completely by CaCO₃(s) → CaO(s) + CO₂(g)?
Try it first: Notice that the reactant is a solid, so molar mass rather than PV = nRT starts the problem.
0 of 4 steps revealed.
Worked example 3
At common T and P, 4.0 L H₂ reacts with 1.0 L O₂ in 2 H₂ + O₂ → 2 H₂O(g). Find product volume and excess H₂.
Try it first: The reaction uses two volumes of H₂ per one of O₂.
0 of 3 steps revealed.
Common mistakes
Applying a mole ratio directly to a mass in grams.
Why it's wrong: Coefficients count particles, not mass, so the ratio is only valid in moles.
Check instead: Divide by molar mass first, every time.
Using 22.4 L/mol when the problem states a non-standard temperature or pressure.
Why it's wrong: Molar volume is condition dependent and changes markedly away from STP.
Check instead: Default to PV = nRT unless STP is stated explicitly.
Using the volume ratio shortcut for a solid or aqueous species.
Why it's wrong: Only gases have volumes proportional to moles.
Check instead: Confirm the (g) state symbol on both species before using the shortcut.
After the lesson · Question bank
Independent practice
Work through new problems on this topic on your own. The lesson's quick checks and worked examples stay above if you need to review a step.
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What you should now know
Gas stoichiometry uses the familiar three-step route: convert the given quantity to moles, apply the mole ratio from the balanced equation, then convert to the requested quantity. For gases, PV = nRT provides the conversion, and at constant temperature and pressure the coefficients may be used directly as a volume ratio.
- Route every gas stoichiometry problem through moles
- PV = nRT converts between gas volume and moles
- At shared T and P, coefficients are also a volume ratio
- Solids and solutions use molar mass or molarity instead
- Compare moles of each reactant to find the limiting one
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.