AP Chemistry Partial Pressure

Mole fraction, Dalton's law, gases collected over water, and partial pressures during a reaction, in four worked examples.

Gas mixtures show up on the exam as a table of moles or masses, a total pressure, and a request for one component's pressure. The method is short: find the moles of each gas, turn them into mole fractions, and multiply by the total pressure. The Unit 3 review gives one example; this page adds the mass-based version, the correction for water vapor, and what happens to partial pressures when a reaction changes the moles of gas. It builds directly on the ideal gas law.

Dalton's Law and Mole Fraction Formulas

Dalton's law: P_total = P_A + P_B + P_C + …
Mole fraction: X_A = n_A / n_total, and the mole fractions of all the gases add to 1.
Partial pressure: P_A = X_A × P_total, which is the same as P_A = n_ART/V.

Ideal gas particles do not interact, so each gas fills the container and exerts pressure as though it were alone. That is why partial pressure depends only on how many moles of that gas are present, not on what the gas is. The chart shows how two different total pressures split into their parts.

Worked Example 1: Finding Partial Pressures From Moles and Total Pressure

A 10.0 L container holds 0.80 mol N₂, 0.15 mol O₂, and 0.05 mol Ar, and the total pressure is 4.00 atm. Find the partial pressure of each gas.

Total moles: 0.80 + 0.15 + 0.05 = 1.00 mol.
Mole fractions: X(N₂) = 0.80, X(O₂) = 0.15, X(Ar) = 0.05.
Partial pressures: N₂ = 0.80 × 4.00 = 3.20 atm; O₂ = 0.15 × 4.00 = 0.60 atm; Ar = 0.05 × 4.00 = 0.20 atm.
Check: 3.20 + 0.60 + 0.20 = 4.00 atm.

The volume of the container was not needed, because the total pressure was already given. Always finish with the sum check; if the partial pressures do not add to the total, a mole fraction is wrong.

Worked Example 2: Finding Partial Pressures From Equal Masses of Two Gases

A container holds 4.00 g of He and 4.00 g of CH₄ at a total pressure of 2.50 atm. Find the partial pressure of each, and decide which gas has the greater partial pressure.

Moles: He = 4.00 g ÷ 4.00 g/mol = 1.00 mol; CH₄ = 4.00 g ÷ 16.0 g/mol = 0.250 mol.
Mole fractions: total = 1.25 mol, so X(He) = 1.00/1.25 = 0.800 and X(CH₄) = 0.250/1.25 = 0.200.
Partial pressures: He = 0.800 × 2.50 = 2.00 atm; CH₄ = 0.200 × 2.50 = 0.500 atm.

Equal masses do not mean equal pressures. The lighter gas has more moles, so helium has four times the partial pressure of methane. Converting grams to moles first uses the same steps as any mole conversion.

Worked Example 3: Correcting for Water Vapor When a Gas Is Collected Over Water

Zinc reacts with hydrochloric acid to make hydrogen, which is collected over water at 25°C. The gas volume is 125 mL and the barometric pressure is 755.0 torr. The vapor pressure of water at 25°C is 23.8 torr. Find the moles of H₂ and the mass of zinc that reacted.

Pressure of dry H₂: 755.0 − 23.8 = 731.2 torr, and 731.2 ÷ 760 = 0.9621 atm.
Moles: n = PV/RT = (0.9621 atm)(0.125 L) ÷ [(0.08206 L·atm/mol·K)(298 K)] = 4.92 × 10⁻³ mol H₂.
Zinc: Zn + 2HCl → ZnCl₂ + H₂ is 1:1, so 4.92 × 10⁻³ mol × 65.4 g/mol = 0.322 g Zn.

Skipping the subtraction would use 755.0 torr and give 5.08 × 10⁻³ mol, about 3% too high. The water vapor pressure depends only on temperature; the question supplies it, and the idea behind it is in vapor pressure. The mole-to-mass step is ordinary stoichiometry.

Worked Example 4: Tracking Partial Pressures as a Reaction Runs in a Rigid Container

A rigid vessel at constant temperature contains NO at 0.60 atm and O₂ at 0.50 atm. The gases react completely: 2NO(g) + O₂(g) → 2NO₂(g). Find the final partial pressures and the final total pressure.

At constant volume and temperature, partial pressure is proportional to moles, so the coefficients apply to pressures directly.
Limiting reactant: 0.60 atm of NO needs only 0.30 atm of O₂, and 0.50 atm is available, so NO is limiting.
Final: NO = 0; O₂ = 0.50 − 0.30 = 0.20 atm; NO₂ = 0.60 atm.
Total: 0.20 + 0.60 = 0.80 atm, down from 1.10 atm, because three moles of gas became two.

Treating pressures like moles in a table is a quick route through a gas-phase equilibrium or limiting-reactant problem. When the reaction reaches equilibrium instead of completion, the same partial pressures go into the expression for K_p described in equilibrium constant Kc and Kp.

Five Partial Pressure Practice Questions With Answers

A mixture has 2.0 mol CO₂ and 6.0 mol N₂ at a total pressure of 3.0 atm. What is the partial pressure of CO₂?
Show answer
X(CO₂) = 2.0/8.0 = 0.25, so P = 0.25 × 3.0 = 0.75 atm.
A rigid container holds equal masses of H₂ and O₂. Which has the greater partial pressure, and roughly how many times greater?
Show answer
H₂. It has about 32.0/2.02 ≈ 16 times as many moles, so about 16 times the partial pressure.
Air is 21% O₂ by moles. At a mountain location where the total pressure is 0.50 atm, what is the partial pressure of O₂?
Show answer
The mole fraction stays 0.21, so P(O₂) = 0.21 × 0.50 = 0.105 ≈ 0.11 atm.
A student collects a gas over water but uses the barometric pressure directly as the gas pressure. Is the calculated number of moles too high or too low?
Show answer
Too high. The barometric pressure includes the water vapor, so the pressure used for the gas is too large.
A rigid container holds gases A and B. Gas B is removed completely at constant temperature. What happens to the partial pressure of A and to the total pressure?
Show answer
The partial pressure of A is unchanged, because it depends only on the moles of A. The total pressure decreases by the former partial pressure of B.

Common Partial Pressure Mistakes

Using mass instead of moles for the mole fraction. Convert grams to moles first.
Thinking a heavier gas exerts more pressure. Only the number of moles matters.
Forgetting to subtract water vapor when a gas is collected over water.
Mixing pressure units with R. With R = 0.08206 L·atm/(mol·K) the pressure must be in atm, so convert torr by dividing by 760.
Using Celsius. Convert to kelvins before using PV = nRT.
Letting the other gases affect a partial pressure. Adding or removing a different gas at constant volume does not change it.

Gas questions are a dependable source of points because the steps are so mechanical. To see how a strong Unit 3 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

What is Dalton's law of partial pressures?

The total pressure of a mixture of ideal gases equals the sum of the pressures each gas would exert alone: P_total = P_A + P_B + P_C + …. Each gas behaves as if the others were not there.

How do you calculate the partial pressure of a gas?

Multiply the total pressure by the gas's mole fraction: P_A = X_A × P_total, where X_A is the moles of A divided by the total moles of gas. You can also use P_A = n_A RT / V.

Does a heavier gas exert more partial pressure?

No. In an ideal gas mixture, partial pressure depends only on the number of moles of that gas, not on its molar mass. Equal masses of H₂ and O₂ give H₂ about sixteen times the partial pressure because it has about sixteen times as many moles.

Why subtract water vapor pressure when a gas is collected over water?

The collected gas is saturated with water vapor, so the measured total pressure is the sum of the dry gas and the water vapor. Subtract the water vapor pressure at that temperature to get the pressure of the dry gas alone.

What happens to the other partial pressures if one gas is added to a rigid container?

The other partial pressures do not change, because ideal gases do not interact. Only the total pressure increases, by the partial pressure of the added gas.

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