What if the gas is not ideal?

For gases at high pressures or low temperatures, use the van der Waals equation or another real gas equation of state, which account for molecular volume and intermolecular forces.

How do I handle a changing state?

If the gas undergoes a change in conditions but the number of moles remains constant, use the combined gas law, $(P_1V_1)/T_1 = (P_2V_2)/T_2$.

Which value of R should I use if pressure is in Torr?

Use $R = 62.36$ L Torr mol$^{-1}$ K$^{-1}$, or convert Torr to atm by dividing by $760$ and use $R = 0.08206$ L atm mol$^{-1}$ K$^{-1}.

How to solve an ideal gas law problem

The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas via the equation $PV = nRT$ . This method applies to gases operating under conditions of relatively low pressure and high temperature, where intermolecular forces and molecular volume are negligible.

The setup

Identify the known and unknown variables from the problem statement. Select the universal gas constant, $R$ , whose units match your given pressure and volume. The most common value used in chemistry is $R = 0.08206$ L atm mol $^{-1}$ K $^{-1}$ .

The steps

Step 1: Convert all temperatures to Kelvin ( $K = ^\circ ext{C} + 273.15$ ). Step 2: Convert pressure and volume to match the units of your chosen $R$ . Step 3: Rearrange $PV = nRT$ to solve algebraically for the unknown variable. Step 4: Substitute the known values with units and calculate the result.

Checking the result

Verify that all units cancel correctly to leave the desired unit of the unknown variable. Ensure the magnitude of the answer is physically reasonable; for instance, absolute temperature and volume must be strictly positive.

Common errors

Failing to convert Celsius to Kelvin is the most frequent mistake. Another common error is using an $R$ value with units that do not match the pressure and volume units, resulting in an answer off by orders of magnitude.

Worked example

A 5.00 L cylinder contains 2.50 mol of nitrogen gas at 25.0 $^\circ$ C. Calculate the pressure inside the cylinder in atmospheres.

Known: $V = 5.00$ L, $n = 2.50$ mol, $T = 25.0 ^\circ$ C. Unknown: $P$ in atm. Choose $R = 0.08206$ L atm mol $^{-1}$ K $^{-1}$ . Step 1: Convert temperature to Kelvin: $T = 25.0 + 273.15 = 298.15$ K. Step 2: Rearrange the ideal gas law for $P$ : $P = (nRT)/V$ . Step 3: Substitute values: $P = (2.50 ext{ mol})(0.08206 ext{ L atm mol}^{-1} ext{ K}^{-1})(298.15 ext{ K}) / (5.00 ext{ L})$ . Step 4: Calculate the final value: $P = 12.23$ atm.

FAQ

Run your own problem

Answer form

References: OpenStax Chemistry 2e, Chapter 9: Gases · Zumdahl Chemistry, Chapter 5: Gases