Gases and gas laws

What the exam asks

Expect a numerical item on the combined gas law, a mixture item on partial pressures, and an effusion comparison. The trap that costs the most marks is the temperature scale: a gas warmed from 20 to 40 degrees Celsius does not double in volume, because 293 K to 313 K is a rise of about 7%. Any time a temperature appears, convert before you do anything else. The second trap is Graham's law without the root. Oxygen is sixteen times the mass of hydrogen, so hydrogen effuses four times faster, not sixteen. If your effusion ratio equals the mass ratio, you have dropped the square root, and the distractor for it will be sitting in the options.

The whole topic sits on one equation, PV = nRT, and one picture: a gas is a swarm of particles that are mostly empty space, moving fast, and hitting the walls. Pressure is those collisions. Temperature is the average kinetic energy of the swarm. Everything else, the named gas laws included, is PV = nRT with something held constant.

Because of that, you do not need Boyle's law and Charles's law as separate facts. Hold n and T fixed and PV is a constant, which is Boyle. Hold n and P fixed and V is proportional to T, which is Charles. If you can rearrange one equation you have all of them, and you have the combined gas law too, which is just the same relation written at two moments.

Two things are examined beyond the equation. Dalton's law says each gas in a mixture contributes pressure in proportion to how many of its molecules are present, and it does not care what they are. Graham's law says lighter molecules move faster at the same temperature, and it comes with a square root that candidates lose. Both are arithmetic you do by hand, which means both are chosen to cancel.

What to hold

• PV = nRT holds only with temperature in kelvin, because the equation says volume goes to zero as T does, and that is only true on a scale whose zero is absolute zero.
• The named gas laws are all PV = nRT with a variable pinned: Boyle holds T, Charles holds P, Gay-Lussac holds V, and Avogadro says V is proportional to n.
• The combined gas law, P1V1/T1 = P2V2/T2, is the same equation at two moments, and it is the fastest route through most numerical gas items.
• Equal volumes of any gases at the same temperature and pressure contain equal numbers of molecules, which is why gas volumes react in whole number ratios.
• At 0 degrees Celsius and 1 atmosphere, one mole of an ideal gas occupies 22.4 litres, but a stem may set different conditions and will tell you if so.
• Total pressure is the sum of the partial pressures, and each partial pressure is the total times that gas's mole fraction.
• Partial pressure depends on how many molecules of a gas are present and not at all on what the gas is, so a mole of hydrogen and a mole of xenon exert the same pressure.
• Adding an unreactive gas at constant volume raises the total pressure but changes no partial pressure, because the original molecules still hit the walls exactly as often.
• At a given temperature every gas has the same average kinetic energy, so lighter molecules must move faster to carry it, and speed goes as one over the square root of molar mass.
• Graham's law is that ratio: the rate for gas 1 over the rate for gas 2 equals the square root of M2 over M1, and effusion is escape through a pinhole while diffusion is spreading through another gas.
• Gas density is PM/RT, so at the same temperature and pressure the denser gas is the one with the larger molar mass.
• The ideal gas model assumes the molecules take up no volume and do not attract each other, so it fails at high pressure and low temperature, where they are crowded and too slow to escape each other.