CHM110H5 Chap.4 Ideal Gas Law and Real Gas Behaviour
Ideal Gas Law and Real Gas Behaviour
Why gases get their own chapter
In CHM110H5 the gas laws sit inside the first unit alongside stoichiometry and solutions, and the learning outcome is specific: you should be able to describe the experiments that led to the ideal gas law, decide when it is safe to use, and explain the factors that make real gases stray from it.
The lecture topic list names both the ideal law and the van der Waals equation, so expect questions that move between a clean PV = nRT calculation and a short explanation of why that calculation is only approximate.
From three empirical laws to PV = nRT
Boyle found that pressure and volume are inversely related when temperature and amount are fixed.
Charles showed that volume grows in direct proportion to absolute temperature at constant pressure. Avogadro proposed that equal volumes of gas at the same temperature and pressure contain equal numbers of particles. Put the three proportionalities together and volume scales with nT/P; the constant that turns this into an equation is R, 0.08206 L atm per mol per kelvin, or 8.314 J per mol per kelvin.
Most lost marks in this topic come from units rather than ideas: kelvin, not Celsius; atmospheres or kilopascals that match the chosen R; litres, not millilitres.
The gas law in the Behaviour of Gases lab
Experiment 2 is where the law becomes a measuring tool. In Part A a metal ribbon reacts with hydrochloric acid in a gas burette, and the hydrogen it releases is collected over the acid solution.
The trapped gas is a mixture, so you subtract the vapour pressure of water, read from a temperature table, and correct for any difference in liquid levels before converting the hydrogen pressure, volume and temperature into moles. Stoichiometry then gives two candidate atomic masses, one for a 2+ ion and one for a 3+ ion, and the periodic table decides between them.
Part B, the Dumas method, heats a volatile liquid in a foil-capped flask until only vapour remains, then uses the mass of the condensed vapour together with P, V and T to find molar mass through PV = (m/M)RT.
When real gases misbehave
The ideal model treats molecules as points that never attract one another.
Real molecules occupy space and do attract, and the van der Waals equation adds one constant for each effect: b for the volume a mole of molecules excludes, and a for the strength of attraction. Deviations become important at high pressure, where molecular volume is a noticeable fraction of the container, and at low temperature, where slow molecules feel attractions more strongly and the gas approaches condensation.
Near room temperature and one atmosphere, as in the lab, both corrections are tiny, which justifies the ideal assumption the manual asks you to make.
What this chapter covers
- 01
Boyle, Charles and Avogadro laws
- 02
Deriving PV = nRT and choosing R
- 03
Hydrogen collected over water
- 04
Dumas molar mass of a vapour
- 05
Van der Waals constants a and b
- 06
High pressure and low temperature deviations
Worked example · free
Atomic mass of a metal from hydrogen collected over water
- 2Equal levels mean P(total) = P(atm). Subtract water vapour: p(H2) = 752 - 19.8 = 732.2 torr = 732.2/760 = 0.9634 atm.
- 3Convert T and V: T = 22 + 273.15 = 295.15 K, V = 0.0306 L. Then n(H2) = PV/RT = (0.9634)(0.0306)/(0.08206 x 295.15) = 0.02948/24.220 = 1.217 x 10^-3 mol.
- 2If n = 2, M + 2H+ gives one H2 per metal atom: moles of metal = 1.217 x 10^-3, so M = 0.0297/1.217 x 10^-3 = 24.4 g/mol.
- 1If n = 3, moles of metal = (2/3)(1.217 x 10^-3) = 8.11 x 10^-4, so M = 36.6 g/mol, which matches no common 3+ metal. The 24.4 g/mol value fits magnesium (24.31).
Key terms
- Ideal Gas Law
- The equation PV = nRT linking pressure, volume, amount and absolute temperature for a gas whose molecules have no volume and no mutual attraction.
- Gas Constant R
- The proportionality constant in PV = nRT, equal to 0.08206 L atm per mol per kelvin or 8.314 J per mol per kelvin; its units dictate which pressure and volume units you use.
- Partial Pressure
- The pressure one gas in a mixture would exert alone in the same volume; for hydrogen over water it equals total pressure minus the water vapour pressure.
- Dumas Method
- A molar mass technique that fills a flask of known volume with vapour at a known temperature and pressure, weighs the condensed vapour, and solves PV = (m/M)RT.
- Van der Waals Equation
- A real gas equation, (P + an²/V²)(V - nb) = nRT, that corrects ideal behaviour for molecular attraction through a and for molecular volume through b.
- Excluded Volume b
- The van der Waals constant giving the volume, in litres per mole, that molecules themselves occupy and that is therefore unavailable for motion.
Ideal Gas Law and Real Gas Behaviour FAQ
Why do I need to subtract water vapour when collecting hydrogen over water?
The burette holds a mixture of hydrogen and water vapour, and the measured total pressure includes both. Only the hydrogen came from the metal, so its partial pressure, found by removing the temperature-dependent vapour pressure of water, is what goes into PV = nRT.
Does a real gas give a higher or lower pressure than the ideal law predicts?
It depends which correction dominates. Attraction lowers the pressure on the walls, so at moderate pressures and low temperatures real values usually fall below ideal. At very high compression the finite size of molecules wins and pushes real pressure above the ideal value.
How can I tell which gas will deviate most from ideal behaviour?
Compare the van der Waals constants. A large a points to strong intermolecular attraction, common in polar or heavy molecules such as carbon dioxide or ammonia, while a large b indicates bulky molecules. Small a and b, as for helium or hydrogen, mean nearly ideal behaviour.
Exam move
Write the three empirical laws side by side and derive PV = nRT from them until you can do it from memory. Redo both lab calculations, hydrogen over water and the Dumas flask, with fresh numbers, converting every pressure to atm and every temperature to kelvin before substituting.
Then take one gas, look up its a and b, and compute ideal and van der Waals pressures at a large and a small volume; explaining the gap in one sentence each time builds exactly the reasoning the deviation outcome tests.
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