Ch 1 · The gaseous state: ideal and real gases and pV = nRT · AS & A Level Chemistry 9701
Topic 1 of 2 in States of matter — AS & A Level Chemistry 9701 — 39 lessons.
Introduction
The ideal gas model is a simplification that works remarkably well for real gases under everyday laboratory conditions, and it gives chemists a direct route from measurable quantities — pressure, volume, temperature — to the amount, and hence the molar mass, of a gas. Cambridge questions test the model's assumptions, its equation in calculations, and the specific conditions under which real gases stop obeying it.
Key ideas — The origin of gas pressure
Gas pressure arises from the continual, random collisions of gas molecules with the walls of their container. Each collision exerts a tiny force as a molecule's momentum changes on rebounding from the wall; the sum of these enormous numbers of collisions per second, over the whole wall area, produces a measurable, steady pressure. Increasing the temperature or reducing the volume increases the frequency and/or force of these collisions, increasing the pressure.
🧑🏫 Teacher's explanation
Imagine a massive stadium filled with thousands of tiny, hyperactive bouncy balls. If you stand on the sidelines, you don't feel each individual ball hitting you, but you do feel a constant, steady 'push' against the stadium walls as the balls bounce off them. This 'push' is exactly what gas pressure is.
📖 Definitions
🔍 Worked example — Easy
A sample of 0.5 moles of an ideal gas is contained in a 2.0 ext L flask at a temperature of 300 ext K. Calculate the pressure in $ ext{Pa}$. (Use R = 8.31 ext J K^-1 ext mol^-1)
🔍 Worked example — Exam-style
A 0.100 ext g sample of an unknown gas occupies 250 ext cm^3 at 300 ext K and 101 ext kPa. Determine the relative molecular mass (M_r) of the gas. (Use R = 8.31 ext J K^-1 ext mol^-1)
⚠️ Common errors
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🎯 Exam question
Key ideas — Assumptions of an ideal gas
An ideal gas is a theoretical gas whose behaviour exactly follows the gas laws under all conditions. Two key assumptions define it: the particles themselves have zero volume (they are treated as point masses occupying negligible space compared with the volume of their container), and there are no intermolecular forces of attraction between particles, so collisions between molecules are perfectly elastic and molecules move independently of one another between collisions.
🧑🏫 Teacher's explanation
Imagine a crowded ballroom where everyone is dancing. In a 'real' ballroom, people have physical size and sometimes bump into each other or pull away from others to maintain personal space. However, in an 'ideal' gas, we pretend the dancers are tiny, weightless points that can pass right through each other without feeling any attraction or repulsion. They only interact when they physically smash into the walls.
📖 Definitions
⚠️ Common errors
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🎯 Exam question
Key ideas — The ideal gas equation
The ideal gas equation, pV = nRT, relates pressure p (in Pa), volume V (in m³), amount n (in mol) and thermodynamic temperature T (in K), with the gas constant R = 8.31\ mathrmJ K^-1 mol^-1. Rearranging to n = pV/RT allows the amount of gas to be found from measurable quantities; combined with a measured mass, this gives the molar mass, M = m/n, of a gas or a volatile liquid. Care is needed with units: pressure must be converted to pascals (1 kPa = 1000 Pa; 1 atm = 1.01 × 10^5 Pa), volume to cubic metres (1 dm³ = 1 × 10^-3 m³; 1 cm³ = 1 × 10^-6 m³), and temperature to kelvin (T/K = θ/°C + 273).
🧑🏫 Teacher's explanation
Imagine a crowded room filled with bouncy balls. The pressure you feel against the walls isn't caused by the balls sitting there, but by the constant, rapid-fire collisions of the balls hitting the walls. In a gas, pressure is simply the cumulative force of billions of tiny molecules slamming into the container walls every second.
📖 Definitions
🔍 Worked example — Exam-style
A gas is contained in a 5.0 dm^3 vessel at 2.0× 10^5 Pa and 300 K. If the volume is halved while temperature is kept constant, what is the new pressure? (Assume ideal behavior)
⚠️ Common errors
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🎯 Exam question
Key ideas — Deviations of real gases from ideal behaviour
Real gases deviate most from ideal behaviour at high pressure and at low temperature. At high pressure, molecules are forced much closer together, so their own volume becomes a significant fraction of the total volume, and the "zero particle volume" assumption breaks down. At low temperature, molecules move more slowly, so the previously negligible intermolecular forces of attraction have time to act between molecules and pull them together, reducing the measured pressure or volume below the ideal prediction. Real gases behave most nearly ideally at low pressure and high temperature, where molecules are far apart and moving fast, making their own volume and their mutual attractions negligible by comparison.
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. In an 'ideal' world, the dancers are tiny specks that don't feel each other's presence; they just zip around and occasionally hit the walls. The pressure they exert is just the sum of those tiny bounces. However, in the 'real' world, dancers have physical size and they tend to stick together if they get too close or move too slowly.
📖 Definitions
🔍 Worked example — Easy
Calculate the volume occupied by 0.50 moles of an ideal gas at 273 K and 100 kPa.
🔍 Worked example — Standard
A real gas is measured at 10 atm and 200 K. Predict whether the measured pressure will be higher or lower than the ideal pressure predicted by pV = nRT.
⚠️ Common errors
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🎯 Exam question
(a) Explain why the actual volume of the gas is larger than the volume predicted by the ideal gas equation pV = nRT. [2] (b) Explain why the actual pressure of the gas is lower than the pressure predicted by the ideal gas equation at 200 K and 100 atm. [2] [4 marks]
Worked example
Question. A volatile liquid of mass 0.44 g is completely vaporised, producing 250 cm³ of gas measured at a pressure of 1.00 × 10^5 Pa and a temperature of 400 K. Calculate the relative molecular mass of the liquid. [4]
🔍 Worked example — Exam-style
A volatile liquid of mass 0.44 g is completely vaporised, producing 250 cm^3 of gas measured at a pressure of 1.00 × 10^5 Pa and a temperature of 400 K. Calculate the relative molecular mass of the liquid.
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Practice
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