Ideal Gas Law- Free Response Problem

Ideal Gas Law Free Response Problems: What You Actually Need to Know

Free response problems involving the Ideal Gas Law show up on the AP Chemistry exam almost every year. Students either nail them or lose easy points because they skip steps, mix up units, or forget the basics. This guide cuts through the fluff and gives you exactly what you need to solve these problems correctly.

The Equation You Must Memorize

PV = nRT

That's it. Commit this to memory right now if you haven't already. Every ideal gas problem is just this equation rearranged in different ways.

Where:

• P = Pressure (atm, Pa, kPa, mmHg — watch your units)
• V = Volume (L or m³)
• n = Number of moles
• R = Gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K)
• T = Temperature (MUST be in Kelvin)

The R Values You Need

Temperature: The Mistake Everyone Makes

Temperature must be in Kelvin. Not Celsius. Not Fahrenheit.

To convert Celsius to Kelvin:

K = °C + 273

Or for more precision:

K = °C + 273.15

For most AP problems, adding 273 works fine. But if you're mixing this with other calculations that use 273.15, stay consistent throughout the problem.

How to Solve Ideal Gas Law Problems

Step 1: Identify What You're Given

Write down P, V, n, and T for the initial state and the final state (if there is one). Circle what's missing — that's what you're solving for.

Step 2: Pick the Right R Constant

If pressure is in atm, use 0.0821. If it's in kPa, convert to atm or find a different approach. Don't force a round peg into a square hole.

Step 3: Convert Units

Everything must match. If P is in atm and V is in mL, convert mL to L first. If T is in Celsius, convert to Kelvin. Skipping this step loses you points.

Step 4: Plug In and Solve

Use algebra to isolate the unknown. If you have two states (before and after), you might need the combined gas law or Boyle's/Charles's law.

Common Problem Types

1. Finding Molar Mass

If you know the mass of a gas and can find its moles, you can get molar mass:

Molar Mass = mass / moles

Use PV = nRT to find n, then divide the given mass by n.

2. Density Problems

Density (d) = mass / volume

You can derive: d = (P × M) / (R × T)

Where M is molar mass. This shows that gas density depends on pressure, molar mass, and temperature.

3. Stoichiometry with Gases

Use the mole ratio from a balanced equation, then apply PV = nRT to find volume of gas produced or consumed. At STP (0°C, 1 atm), 1 mole of any gas occupies 22.4 L.

4. Partial Pressures

For gas mixtures:

P_total = P₁ + P₂ + P₃...

And P_individual = X_i × P_total

Where X_i is the mole fraction.

Example Problem Walkthrough

Problem: A 2.5 L container holds 0.85 mol of Ne gas at 25°C. What is the pressure inside the container in atm?

Step 1: List known values

• V = 2.5 L
• n = 0.85 mol
• T = 25°C = 298 K
• R = 0.0821 L·atm/mol·K

Step 2: Solve for P

P = nRT / V

P = (0.85 × 0.0821 × 298) / 2.5

P = 20.79 / 2.5

P = 8.3 atm

Mistakes That Cost You Points

• Forgetting to convert Celsius to Kelvin
• Using the wrong R constant
• Mixing up units (mL vs L, atm vs kPa)
• Not showing your work in free response
• Rounding too early in calculations
• Forgetting that 1 atm = 760 mmHg = 101.325 kPa

The Combined Gas Law

When you have a gas going from one state to another (changing P, V, and/or T), use:

(P₁V₁)/T₁ = (P₂V₂)/T₂

This assumes n stays constant. If the number of moles changes, you need to use the full Ideal Gas Law for each state and connect them through n.

What the graders actually look for

AP Chemistry free response graders aren't looking for fancy explanations. They want:

• Correct setup of the equation
• Proper unit conversions shown
• Correct numerical substitution
• Final answer with correct sig figs and units

Write out each step. If your final answer is wrong but your setup is right, you still get partial credit. If your setup is wrong, you get nothing.

Quick Reference Before the Exam

Know your units. Know your R constant. Convert temperature. Show your work.