DPST1031 Chap.7 Ideal Gases, Real Gases and Raoult's Law
Ideal Gases, Real Gases and Raoult's Law
Gases and liquid mixtures are where intermolecular forces become numbers. This chapter applies the ideal gas law and Dalton's law of partial pressures with careful unit conversion, then explains why real gases deviate at high pressure and low temperature and what the van der Waals constants a and b correct.
It moves on to vapour pressure and liquid-vapour equilibrium, uses Raoult's law to calculate the vapour pressure of a binary liquid mixture and the composition of the vapour above it, links positive and negative deviations to intermolecular forces, and closes with Henry's law for the solubility of a gas in water.
What this chapter covers
- 01
The ideal gas law and the two values of R
- 02
Pressure, volume and temperature conversions
- 03
Dalton's law and mole fractions
- 04
Real gases and the van der Waals equation
- 05
Vapour pressure and liquid-vapour equilibrium
- 06
Raoult's law for binary mixtures
- 07
Positive and negative deviations
- 08
Henry's law and gas solubility
Worked example · free
How far compressed carbon dioxide strays from ideal
- +1Ideal: p = nRT/V = 0.08206 × 300 ÷ 0.500 = 49.2 atm.
- +1van der Waals: p = nRT/(V − nb) − n²a/V² = 24.62 ÷ 0.4573 − 3.59 ÷ 0.250 = 53.8 − 14.4 = 39.5 atm.
- +1Deviation: (49.2 − 39.5) ÷ 49.2 = 20% below the ideal value.
- +1The attraction term outweighs the excluded-volume term at this density, so the real pressure is lower.
Key terms
- Ideal gas
- A model gas of point particles with no attractions, obeying pV = nRT exactly.
- Partial pressure
- The pressure a component of a gas mixture would exert alone in the same volume.
- Mole fraction
- The amount of one component divided by the total amount of all components.
- Excluded volume
- The volume occupied by gas molecules themselves, corrected by the constant b.
- Raoult's law
- The rule that a component's vapour pressure above an ideal solution is its mole fraction times its pure vapour pressure.
- Henry's law
- The rule that a gas's solubility in a liquid is proportional to its partial pressure above the liquid.
- Boiling point
- The temperature at which a liquid's vapour pressure equals the external pressure.
Ideal Gases, Real Gases and Raoult's Law FAQ
Which value of R should I use?
Use 0.08206 L atm mol⁻¹ K⁻¹ when pressure is in atmospheres and volume in litres. Use 8.314 J mol⁻¹ K⁻¹ when pressure is in pascals and volume in cubic metres, or whenever an energy is involved. Temperature must always be in kelvin with either value.
When does a gas stop behaving ideally?
Deviations become large at high pressure and low temperature. Then molecules are close together, so their own volume is no longer negligible, and they move slowly enough for attractions to reduce the pressure. Gases with strong intermolecular forces, such as ammonia and water, deviate most.
What does a positive deviation from Raoult's law mean?
It means the measured vapour pressure of the mixture is higher than Raoult's law predicts. The attractions between unlike molecules are weaker than those in the pure liquids, so molecules escape the surface more easily. A negative deviation means the unlike attractions are stronger.
Why is the vapour richer in the more volatile liquid?
The more volatile liquid has the higher pure vapour pressure, so at the same liquid mole fraction it contributes a larger partial pressure. Its share of the total vapour pressure, which equals its vapour mole fraction, is therefore larger than its share of the liquid.
How do I convert a gas pressure from kPa to atm?
Divide by 101.3, because the data sheet gives 1 atm = 101.3 kPa. A pressure of 152 kPa is therefore 1.50 atm. For mmHg or torr, divide by 760, and for bar divide by 1.013. Convert before substituting into pV = nRT so that the units match the chosen value of R.
Exam move
Drill unit conversions until they are automatic: Celsius to kelvin, kPa and mmHg to atm, mL to L. Then solve gas law problems in both unit systems and confirm the answers match. For real gases, learn the meaning of a and b in words and practise predicting which of two gases has the larger value.
For Raoult's law, set every problem out as a small table of x, p° and partial pressure for each liquid, add the partial pressures, then divide to get the vapour mole fractions. Finish with Henry's law problems that require converting a percentage composition into a partial pressure.
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