Partial Pressure Practice- AP Chemistry Problems and Solutions

Partial Pressure Problems: What You Actually Need to Know

Partial pressure shows up constantly on the AP Chemistry exam. Students lose easy points here because they memorize formulas without understanding what they mean. This guide fixes that.

What Partial Pressure Actually Is

Partial pressure is the pressure a single gas in a mixture would exert if it occupied the container alone. That's it. Don't overthink it.

When you have multiple gases in one container, each gas contributes to the total pressure. The amount each gas contributes depends on how many moles of that gas are present.

Dalton's Law of Partial Pressures

The core equation you'll use:

P_total = P₁ + P₂ + P₃ + ...

Total pressure equals the sum of all individual partial pressures. This seems obvious, but it's the foundation for every problem you'll see.

The partial pressure of any gas equals its mole fraction times the total pressure:

P_gas = X_gas × P_total

Mole fraction is just the moles of that gas divided by total moles of all gases:

X_gas = n_gas / n_total

The Gas Collection Problem

Most partial pressure problems involve collecting gas over water. When gas bubbles through water, it becomes saturated with water vapor.

The measured pressure is gas pressure plus water vapor pressure:

P_measured = P_gas + P_{water vapor}

You must subtract the water vapor pressure to get the actual gas pressure. This value comes from a table at a given temperature.

Key Formulas Summary

• P_total = Σ P_i — sum of all partial pressures
• P_i = X_i × P_total — partial pressure from mole fraction
• X_i = n_i / n_total — mole fraction definition
• P_gas = P_measured - P_{water vapor} — for gas collected over water
• PV = nRT — ideal gas law, often combined with partial pressure concepts

Practice Problems

Problem 1: Mole Fraction Calculation

A container holds 2.0 mol of N₂ and 3.0 mol of O₂ at a total pressure of 5.0 atm. What is the partial pressure of N₂?

Solution:

First, find the mole fraction of N₂:

X_N2 = 2.0 mol / (2.0 + 3.0) mol = 2.0 / 5.0 = 0.40

Then calculate partial pressure:

P_N2 = 0.40 × 5.0 atm = 2.0 atm

Problem 2: Gas Collected Over Water

Hydrogen gas is collected over water at 25°C. The total pressure is 755 mmHg and the water vapor pressure at 25°C is 24 mmHg. What is the partial pressure of H₂?

Solution:

P_H2 = P_total - P_{water vapor}

P_H2 = 755 mmHg - 24 mmHg = 731 mmHg

This is the pressure you'd use in PV = nRT calculations for the hydrogen gas.

Problem 3: Finding Total Pressure

A mixture contains 4.0 g of He and 8.0 g of Ne in a 10.0 L container at 300 K. What is the total pressure?

Solution:

Calculate moles of each gas:

n_He = 4.0 g / 4.00 g/mol = 1.0 mol

n_Ne = 8.0 g / 20.2 g/mol = 0.396 mol

n_total = 1.0 + 0.396 = 1.396 mol

Use ideal gas law:

P = nRT / V = (1.396 mol)(0.0821 L·atm/mol·K)(300 K) / 10.0 L

P = 34.4 / 10.0 = 3.44 atm

Problem 4: Partial Pressure with Ideal Gas Law

Using the mixture from Problem 3, what is the partial pressure of He?

Solution:

Method 1 — Use mole fraction:

X_He = 1.0 / 1.396 = 0.716

P_He = 0.716 × 3.44 atm = 2.46 atm

Method 2 — Calculate directly with He moles only:

P_He = nRT / V = (1.0)(0.0821)(300) / 10.0 = 2.46 atm

Both methods give the same answer. Method 1 is faster when you already know total pressure.

Problem 5: Finding Mass from Partial Pressure

A 5.0 L container holds a gas mixture at 2.0 atm and 298 K. The mixture contains CO₂ with a partial pressure of 0.50 atm. How many grams of CO₂ are present?

Solution:

Use ideal gas law with the partial pressure:

n = PV / RT = (0.50 atm)(5.0 L) / (0.0821 × 298 K)

n = 2.5 / 24.5 = 0.102 mol

Mass = 0.102 mol × 44.0 g/mol = 4.5 g

Quick Reference Table

How to Solve Any Partial Pressure Problem

Follow this sequence:

1. Identify what you're solving for. Partial pressure, total pressure, moles, or mass?
2. Check if gas was collected over water. If yes, subtract water vapor pressure first.
3. Decide which formula applies. Mole fraction approach or ideal gas law?
4. Calculate mole fraction if needed. Moles of one gas divided by total moles.
5. Plug in and solve. Watch your units.

Common Mistakes That Cost Points

• Forgetting to subtract water vapor pressure when gas was collected over water
• Using total pressure instead of partial pressure in PV = nRT
• Messing up mole fraction calculations — make sure you have total moles correct
• Forgetting to convert temperature to Kelvin
• Using the wrong units — stick with atm, L, mol, K unless the problem specifies otherwise

Water Vapor Pressure Values

You'll need these for gas collection problems:

The exam usually provides this table or gives you the value. If they don't, the problem is unsolvable as stated.

What to Memorize

• R = 0.0821 L·atm/mol·K — use this unless given different units
• The mole fraction equation and how to rearrange it
• Water vapor correction: always subtract it
• Partial pressure of a gas = (moles of that gas / total moles) × total pressure

That's everything you need. Practice the problems above until you can work through them without checking the solutions.