Gases: Class 11 Chemistry

Key points

A gas has no fixed shape or volume. It fills its container, is easily compressed, mixes completely with other gases and exerts pressure on the walls of its container. The state of a gas is described by four variables: pressure (P), volume (V), temperature (T) and amount in moles (n).

Pressure is force per unit area. The SI unit is the pascal (Pa), equal to 1 N m⁻². Other units are the atmosphere (atm), torr and mmHg. Standard atmospheric pressure is 1 atm = 760 torr = 760 mmHg = 101325 Pa = 101.325 kPa. A barometer measures atmospheric pressure and a manometer measures the pressure of a gas sample. Gas temperatures must always be in kelvin: T (K) = t (°C) + 273.

Boyle's law: at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure. So PV = constant and P₁V₁ = P₂V₂. A graph of P against V is a curve (hyperbola) and a graph of P against 1/V is a straight line through the origin. The reason is that a smaller volume makes molecules strike the walls more often.

Charles's law: at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. So V/T = constant and V₁/T₁ = V₂/T₂. The volume of a gas changes by 1/273 of its volume at 0 °C for each degree Celsius. If the V against t line is extended it meets the temperature axis at −273 °C, called absolute zero, which is 0 K. Gay-Lussac's pressure law similarly gives P/T = constant at constant volume.

Avogadro's law: equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. So V is proportional to n. One mole of any gas occupies 22.4 dm³ at STP (273 K and 1 atm) and contains 6.02 × 10²³ molecules. Combining the three laws gives the general gas equation PV = nRT, where R is the gas constant.

Values of the gas constant R depend on the units used:

• 8.314 J K⁻¹ mol⁻¹ (with P in Pa and V in m³)
• 0.0821 dm³ atm K⁻¹ mol⁻¹ (with P in atm and V in dm³)
• 62.4 dm³ torr K⁻¹ mol⁻¹ (with P in torr)

The gas equation gives the density and molar mass of a gas. Since n = m/M, PV = (m/M)RT, so density d = PM/RT and M = dRT/P. A heavier gas has a higher density at the same T and P. Hot air is lighter than cold air for this reason, and a hot air balloon rises.

Dalton's law of partial pressures: the total pressure of a mixture of non-reacting gases is the sum of the partial pressures of the individual gases. P(total) = P₁ + P₂ + P₃. The partial pressure of a gas is its mole fraction times the total pressure. A gas collected over water is mixed with water vapour, so the pressure of the dry gas is the total pressure minus the vapour pressure of water at that temperature.

Diffusion is the spontaneous mixing of gases. Effusion is the escape of a gas through a tiny hole. Graham's law: at constant temperature and pressure, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its density or molar mass. So rate₁/rate₂ = √(M₂/M₁). Hydrogen therefore diffuses four times faster than oxygen. The law is used to separate isotopes such as uranium-235 and uranium-238.

Kinetic molecular theory explains gas behaviour. Its main postulates are:

• A gas consists of very small particles that are far apart, so their volume is negligible compared with the container.
• The particles move randomly in straight lines and collide elastically with each other and with the walls. Pressure comes from these collisions.
• There are no attractive or repulsive forces between particles.
• The average kinetic energy is directly proportional to the absolute temperature and is the same for all gases at the same temperature.

Real gases deviate from ideal behaviour, most at high pressure and low temperature. At these conditions molecules are close together, so their volume and the attractions between them cannot be ignored. Van der Waals corrected the gas equation to (P + an²/V²)(V − nb) = nRT. The constant a corrects for attractions and b for the volume of the molecules. A real gas behaves most ideally at low pressure and high temperature.

Liquefaction of gases needs low temperature and high pressure. Every gas has a critical temperature, above which it cannot be liquefied by pressure alone. The Joule-Thomson effect is the cooling of a gas when it expands through a small hole into a region of lower pressure, and it is used in the Linde process. Plasma, made of ions and electrons, is often called the fourth state of matter.

Study tip: Write the given data with units in a list, convert to kelvin and consistent units before substituting, and name the law you use. Practise drawing and labelling the Boyle's and Charles's law graphs, as they are asked often. For theory, learn the kinetic theory postulates as a numbered list.

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Short questions with model answers

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Common mistakes

• Using temperature in °C in gas law equations. Always convert to kelvin first.
• Mixing units of R, for example using 0.0821 with pressure in kPa or volume in cm³.
• Forgetting to subtract the vapour pressure of water when a gas is collected over water.
• Writing Graham's law with the masses the wrong way round. The lighter gas diffuses faster, so the heavier mass goes on top inside the root.
• Stating that real gases are ideal at high pressure. They are closest to ideal at low pressure and high temperature.

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