Ideal Gases

Objectives

Lesson outcomes

Use the mole and Avogadro constant to connect amount of substance with number of particles.
Explain the ideal gas condition pV proportional to T using thermodynamic temperature.
Recall and use pV = nRT and pV = NkT for ideal gases.
Use k = R / NA to connect the molar and molecular forms of the gas equation.

Syllabus

CIE 9702 syllabus points

5 linked

15.1.1 understand that amount of substance is an SI base quantity with the base unit mol
15.1.2 use molar quantities where one mole of any substance is the amount containing a number of particles of that substance equal to the Avogadro constant NA
15.2.1 understand that a gas obeying pV ∝ T, where T is the thermodynamic temperature, is known as an ideal gas
15.2.2 recall and use the equation of state for an ideal gas expressed as pV = nRT, where n = amount of substance (number of moles) and as pV = NkT, where N = number of molecules
15.2.3 recall that the Boltzmann constant k is given by k = R / NA

Lesson Notes

Student guidance and lesson notes

Overview

This lesson introduces the ideal gas model and the equations used to describe it. You connect moles, particles, pressure, volume, and thermodynamic temperature so that gas calculations can be handled from either a molar or molecular viewpoint.

What You Need to Know

Amount of substance is an SI base quantity measured in mol.
One mole contains Avogadro’s constant, NA, particles.
An ideal gas obeys pV proportional to T when T is measured in kelvin.
The equation of state can be written as pV = nRT or pV = NkT.
The Boltzmann constant links the two forms: k = R / NA.

How to Work Through It

Practise converting between number of particles and amount of substance in mol.
Decide whether each question gives n or N, then choose pV = nRT or pV = NkT.
Convert pressure, volume, and temperature into SI units before substituting.
Check whether the answer is physically sensible for the gas sample described.

Check Your Understanding

Why must temperature be in kelvin in pV = nRT?
How are n, N, and NA connected?
When would pV = NkT be more direct than pV = nRT?

Common Mistakes

Using Celsius temperatures in gas equations.
Confusing n, the amount in mol, with N, the number of molecules.
Forgetting to convert cm^3 or dm^3 into m^3.
Treating ideal-gas equations as valid without checking whether the model is appropriate.

Next Steps

Keep a clear symbol list for p, V, T, n, N, R, k, and NA.
Use the ideal gas equation as the starting point for the kinetic theory model next lesson.