How to Calculate the Ideal Gas Law Step by Step

What You'll Need to Calculate the Ideal Gas Law by Hand

Before you start, gather these items:

• Known values for three of the four variables: pressure (P), volume (V), moles (n), or temperature (T).
• The gas constant (R) – choose the appropriate value for your units (see step 3).
• A calculator (for arithmetic).
• Paper and pen to write down the equation and your work.

Step-by-Step Guide to Solving PV = nRT

1. Identify the known and unknown variables. Write down the values you have and the one you need to find. For example, if you know pressure, volume, and temperature, you are solving for moles (n).
2. Rearrange the equation. The ideal gas law is PV = nRT. Solve for your unknown:
   • If unknown is P: P = nRT / V
   • If unknown is V: V = nRT / P
   • If unknown is n: n = PV / (RT)
   • If unknown is T: T = PV / (nR)
3. Check unit consistency. The ideal gas law requires consistent units. Temperature must be in Kelvin (K). If your temperature is in Celsius or Fahrenheit, convert first:
   • From Celsius to Kelvin: T(K) = T(°C) + 273.15
   • From Fahrenheit to Kelvin: T(K) = (T(°F) − 32) × 5/9 + 273.15
   Volume should be in liters (L) when using R = 0.08206 L·atm/(mol·K). Pressure should be in atmospheres (atm). If your values are in different units, convert them to match your R value. (See the Ideal Gas Law Formula page for a full list of unit conversions.)
4. Select the correct gas constant (R). The value of R depends on the units you use. Common choices:
   • 0.08206 L·atm/(mol·K) – use when pressure is in atm, volume in L, temperature in K, and moles in mol.
   • 8.314 J/(mol·K) – use when pressure is in Pa, volume in m³.
   • 62.364 L·mmHg/(mol·K) – use when pressure is in mmHg (torr).
   • 10.731 psi·ft³/(mol·°R) – use for imperial units (pressure in psi, volume in ft³, temperature in Rankine).
   For most chemistry problems, R = 0.08206 L·atm/(mol·K) is the standard.
5. Plug in the numbers. Insert your known values into the rearranged equation. Make sure all units match your chosen R. Multiply and divide as needed.
6. Check your answer. Look at the result and see if it makes sense. For example, at STP (0°C, 1 atm), one mole of an ideal gas occupies about 22.4 L. If your calculated volume is far from that, double-check your units and conversions.

Worked Example 1: Finding Pressure

Problem: A 22.4 L container holds 1.00 mol of an ideal gas at 273 K. What is the pressure in atm?

1. Unknown: P. Known: V = 22.4 L, n = 1.00 mol, T = 273 K.
2. Equation: P = nRT / V
3. Use R = 0.08206 L·atm/(mol·K).
4. Plug in: P = (1.00 mol × 0.08206 L·atm/(mol·K) × 273 K) / 22.4 L
5. Calculate numerator: 1.00 × 0.08206 × 273 = 22.4 (approx). Then divide by 22.4: P = 1.00 atm.

Result: The pressure is 1.00 atm. This matches STP conditions. If you need help understanding the meaning of this result, read our guide on Interpreting Ideal Gas Law Results.

Worked Example 2: Finding Moles

Problem: A gas occupies 10.0 L at 2.50 atm and 300 K. How many moles are present?

1. Unknown: n. Known: P = 2.50 atm, V = 10.0 L, T = 300 K.
2. Equation: n = PV / (RT)
3. Use R = 0.08206 L·atm/(mol·K).
4. Plug in: n = (2.50 atm × 10.0 L) / (0.08206 L·atm/(mol·K) × 300 K)
5. Numerator: 2.50 × 10.0 = 25.0. Denominator: 0.08206 × 300 = 24.618. Then n = 25.0 / 24.618 ≈ 1.015 mol.

Result: Approximately 1.02 moles (rounded to three significant figures). This makes sense because at slightly above STP conditions a 10 L container holds about 1 mol.

Common Pitfalls to Avoid

• Forgetting to convert temperature to Kelvin. This is the most common mistake. Always add 273.15 to Celsius degrees.
• Using the wrong gas constant. Match R to your pressure and volume units. If you use atm and L, use 0.08206. Using 8.314 with liters will give incorrect values.
• Not converting units. If pressure is given in psi or kPa, convert to atm (or use the corresponding R). See the What Is the Ideal Gas Law? page for common conversions.
• Forgetting significant figures. Report your answer with the same number of significant figures as the least precise measurement.
• Misrearranging the equation. Write down the formula and solve for the unknown step by step to avoid algebra errors.

Once you understand the manual process, you can save time by using the Ideal Gas Law Calculator for quick results. It handles unit conversions and shows you the steps.