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Study Guide: How to Solve: Ideal Gas Equation
Source: https://www.fatskills.com/k-12-assessment-tests/chapter/how-to-solve-ideal-gas-equation

How to Solve: Ideal Gas Equation

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~5 min read

How to Solve: Ideal Gas Equation

For Students Who Want to Ace Their Exam & Teachers Who Need a Ready-to-Record Script

Introduction

"Imagine you’re a scuba diver—your oxygen tank’s pressure drops. How long can you stay underwater? The Ideal Gas Equation holds the answer. Master it, and you’ll solve real-world problems AND crush exam questions on gases, pressure, and temperature."

What You Need To Know First

Before tackling the Ideal Gas Equation, you must understand: 1. Pressure (P): Force per unit area (e.g., Pascals, atm). 2. Volume (V): Space a gas occupies (e.g., liters, m³). 3. Temperature (T): Must be in Kelvin (K)—never Celsius for gas laws!

Key Vocabulary

Term Plain-English Definition Quick Example
Ideal Gas A gas that follows all gas laws perfectly (no real gas is 100% ideal, but close enough for exams). Helium in a balloon behaves like an ideal gas.
Moles (n) A count of gas particles (1 mole = 6.022 × 10²³ molecules). 2 moles of O₂ = 12.044 × 10²³ O₂ molecules.
Universal Gas Constant (R) A fixed number that connects P, V, n, and T. R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K).
STP Standard Temperature and Pressure (0°C = 273 K, 1 atm). At STP, 1 mole of any gas occupies 22.4 L.
Boyle’s Law At constant T, P × V = constant. Squeezing a balloon (↓V) increases P.
Charles’s Law At constant P, V/T = constant. Heating a balloon (↑T) makes it expand (↑V).

Formulas To Know

1. Ideal Gas Equation

Formula: PV = nRT

Variable Meaning Unit (MUST match R!)
P Pressure atm, Pa (Pascals), or kPa
V Volume Liters (L) or cubic meters (m³)
n Number of moles mol
R Universal Gas Constant 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K)
T Temperature Kelvin (K) only!

⚠️ MEMORISE THIS: You’ll use PV = nRT in 90% of gas law problems.

2. Combined Gas Law (Given on Exam Sheet)

Formula: (P₁V₁)/T₁ = (P₂V₂)/T₂

Variable Meaning Unit
P₁, V₁, T₁ Initial pressure, volume, temperature atm/L/K or Pa/m³/K
P₂, V₂, T₂ Final pressure, volume, temperature Same as above

✅ Given on exam sheet: Don’t memorise—just know how to use it.

3. Molar Volume at STP (Given on Exam Sheet)

Formula: 1 mole of any gas at STP = 22.4 L

✅ Given on exam sheet: Useful for quick conversions.

Step-by-Step Method

How to Solve ANY Ideal Gas Problem in 5 Steps

  1. Read the question carefully. Underline what’s given and what’s asked.
  2. Convert all units to match R.
  3. Pressure → atm (if using R = 0.0821) or Pa (if using R = 8.314).
  4. Volume → Liters (L) or cubic meters (m³).
  5. Temperature → Kelvin (K) (add 273 to °C).
  6. Write down PV = nRT. Plug in known values.
  7. Solve for the unknown. Rearrange the equation first!
  8. Check units and sig figs. Does your answer make sense?

Worked Example (Using the Steps)

Question: A 2.5 L container holds 0.4 moles of nitrogen gas at 300 K. What is the pressure inside?

Step 1: Given: V = 2.5 L, n = 0.4 mol, T = 300 K. Find P. Step 2: Units already match R = 0.0821 L·atm/(mol·K). Step 3: PV = nRT → P(2.5) = (0.4)(0.0821)(300) Step 4: P = (0.4 × 0.0821 × 300) / 2.5 = 3.94 atm Step 5: Units = atm (correct), sig figs = 2 (matches given data).

Answer: 3.94 atm

Worked Examples

Example 1 - Basic (Find Volume)

Question: What volume does 0.5 moles of helium occupy at 1.2 atm and 25°C?

Solution: 1. Convert T to Kelvin: 25°C + 273 = 298 K. 2. Use PV = nRT → (1.2)V = (0.5)(0.0821)(298). 3. V = (0.5 × 0.0821 × 298) / 1.2 = 10.2 L.

What we did and why: - Converted °C to K (critical step!). - Plugged into PV = nRT and solved for V. - Answer makes sense: ~10 L for 0.5 moles at near-STP.

Example 2 - Medium (Find Moles)

Question: A gas occupies 3.0 L at 740 mmHg and 27°C. How many moles are present?

Solution: 1. Convert P to atm: 740 mmHg ÷ 760 = 0.974 atm. 2. Convert T to K: 27°C + 273 = 300 K. 3. Use PV = nRT → (0.974)(3.0) = n(0.0821)(300). 4. n = (0.974 × 3.0) / (0.0821 × 300) = 0.119 mol.

What we did and why: - Converted mmHg to atm (R requires atm!). - Solved for n (moles). - Answer is reasonable: ~0.12 moles in 3 L.

Example 3 - Exam Style (Disguised Problem)

Question: A scuba tank has a volume of 12 L. When filled, it contains 48 moles of air at 200 atm. What is the temperature inside the tank in °C?

Solution: 1. Given: V = 12 L, n = 48 mol, P = 200 atm. Find T. 2. Use PV = nRT → (200)(12) = (48)(0.0821)T. 3. T = (200 × 12) / (48 × 0.0821) = 609 K. 4. Convert to °C: 609 K – 273 = 336°C.

What we did and why: - Recognized it’s a PV = nRT problem (even though it’s about scuba tanks). - Solved for T, then converted to °C. - Answer is high (336°C) but makes sense for compressed gas.

Common Mistakes

Mistake Why it Happens Correct Approach
Using °C instead of K Forgetting gas laws require Kelvin. Always add 273 to °C to get K.
Wrong R value Mixing up units (e.g., using 0.0821 with Pa). Match R to pressure units (atm → 0.0821, Pa → 8.314).
Ignoring unit conversions Plugging in mmHg or kPa directly. Convert pressure to atm or Pa first.
Rounding too early Rounding intermediate steps (e.g., 0.0821 → 0.08). Keep full precision until the final answer.
Misreading the question Solving for the wrong variable (e.g., finding n when V is asked). Underline what’s given and what’s asked.

Exam Traps

Trap How to Spot it How to Avoid it
Hidden unit conversions Question gives pressure in mmHg or kPa. Convert to atm or Pa before plugging into PV = nRT.
Temperature in °C Question states temperature in Celsius. Always convert to Kelvin (+273).
"At STP" shortcut Question mentions STP but doesn’t give values. Remember: 1 mole = 22.4 L at STP (0°C, 1 atm).

1-Minute Recap

"Okay, let’s lock this in. The Ideal Gas Equation is PV = nRT. Here’s your 60-second cheat sheet:

  1. Units are everything. Pressure in atm? Use R = 0.0821. Pressure in Pa? Use R = 8.314. Temperature must be in Kelvin—add 273 to °C.
  2. Rearrange first. Need volume? Solve for V before plugging numbers in.
  3. STP is your friend. 1 mole = 22.4 L at 0°C and 1 atm. Use this for quick conversions.
  4. Watch for traps. Examiners love hiding mmHg or °C in questions. Convert first!
  5. Check your answer. Does it make sense? 1 mole of gas at room temp is ~24 L. If your answer is 0.001 L, you probably messed up units.

Now go crush that exam. You’ve got this!


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