Real gases do not always follow the ideal gas law because gas particles have volume and attract each other. This cheat sheet helps students compare ideal and real gases, understand when deviations become important, and use the Van der Waals equation correctly. It is especially useful for high-pressure, low-temperature, and intermolecular force problems in chemistry.
The ideal gas law assumes particles have no volume and no attractions, but real gases need corrections. The Van der Waals equation adjusts pressure for attractions and volume for particle size. The constants and depend on the gas and help predict how strongly a gas deviates from ideal behavior.
Key Facts
- The ideal gas law is , where is pressure, is volume, is moles, is the gas constant, and is temperature in kelvin.
- Real gases behave most ideally at high temperature and low pressure because particles are far apart and moving fast.
- The Van der Waals equation is .
- The pressure correction accounts for attractive forces that make the measured pressure lower than ideal.
- The volume correction accounts for the actual volume occupied by gas particles, so the free space is .
- A larger value means stronger intermolecular attractions and greater pressure deviation from ideal behavior.
- A larger value means larger particle volume and greater excluded-volume deviation from ideal behavior.
- The compressibility factor is , with for an ideal gas, when attractions dominate, and when particle volume dominates.
Vocabulary
- Real gas
- A gas that deviates from ideal behavior because its particles have volume and experience intermolecular forces.
- Ideal gas
- A theoretical gas whose particles have no volume, no attractions, and obey exactly.
- Van der Waals equation
- An equation of state, , that corrects the ideal gas law for real gas behavior.
- Pressure correction
- The term added to pressure to account for attractions between gas particles.
- Volume correction
- The term subtracted from volume to account for the space occupied by gas particles themselves.
- Compressibility factor
- The ratio that shows how much a gas deviates from ideal behavior.
Common Mistakes to Avoid
- Using Celsius instead of kelvin, which is wrong because gas law equations require absolute temperature, so use .
- Forgetting to square in the pressure correction, which is wrong because the attraction correction is , not .
- Subtracting from pressure instead of volume, which is wrong because corrects the available volume and must appear as .
- Assuming all gases have the same and values, which is wrong because these constants depend on particle size and intermolecular forces.
- Treating as particle-volume dominance, which is wrong because usually means attractions lower the pressure below the ideal value.
Practice Questions
- 1 Calculate the ideal pressure of of gas in a container at using .
- 2 For of a gas with in a container, calculate the pressure correction .
- 3 For of a gas with in a container, calculate the corrected volume .
- 4 Explain why a gas at high pressure and low temperature is more likely to deviate from than the same gas at low pressure and high temperature.
Understanding Real Gases & Van der Waals Equation
The pressure of a gas comes from particles striking the walls of a container. In an ideal model, every collision with a wall is treated as if particles travel independently until they bounce. Real molecules pull on one another over short distances.
A molecule approaching a wall can be pulled back by nearby molecules before it hits. Its collision is then less forceful, so the wall records less pressure than a simple model predicts.
This effect is strongest when molecules spend much of their time close together. It explains why gases can eventually condense into liquids when cooling or compression brings particles sufficiently near.
The two corrections do not always matter by the same amount. Attractions usually show up first as a pressure that is lower than expected. At still greater compression, the finite size of molecules becomes more important.
Molecules cannot be squeezed into the space already occupied by other molecules. The remaining space for motion becomes very small, and pressure rises sharply. This is why a real gas can change from behaving more compressibly than an ideal gas to behaving less compressibly as pressure increases.
A graph of compressibility against pressure often dips below one before rising above one. The shape of that graph gives evidence about the balance between attraction and excluded volume.
Different gases depart from ideal behavior in different ways because their molecules differ in size, shape, and polarity. Carbon dioxide has noticeable attractions and can be liquefied under suitable conditions. Helium has very weak attractions and remains closer to ideal behavior over many ordinary conditions.
Water vapor can show strong deviations because water molecules attract through hydrogen bonding. Students meet these ideas in aerosol cans, gas cylinders, refrigeration systems, weather calculations, and the storage of industrial gases. Engineers need real gas models when a small pressure error could affect safety, fuel amount, or equipment design.
When solving a real gas problem, start by checking units carefully. Temperature must be on the absolute kelvin scale. Use one consistent set of pressure and volume units with the chosen gas constant and the gas-specific constants.
Keep track of whether volume means total container volume or available space after the particle-volume correction. The real gas equation is usually harder to rearrange than the ideal gas law, so trial values, graphs, or a calculator may be needed.
Check whether the final result makes physical sense. A calculated available volume cannot be zero or negative, and predicted conditions near liquefaction need extra caution because a gas-only equation becomes less reliable there.