(i) the equation of state of an ideal gas pV = nRT , where n is the number…

The idea

The equation of state for an ideal gas is pV = nRT, where p is pressure in pascals, V is volume in cubic metres, n is the number of moles, R is the molar gas constant (8.31 J mol⁻¹ K⁻¹) and T is thermodynamic temperature in kelvin. It combines Boyle's law, Charles's law and Avogadro's law. For a fixed mass of gas, pV/T is constant. For example, compressing 2.0 mol of gas at 300 K into 0.050 m³ gives p = nRT/V = (2.0 × 8.31 × 300) / 0.050 = 1.0 × 10⁵ Pa. The equation assumes ideal behaviour: negligible molecular volume and no intermolecular forces.

What earns the marks

• pV = nRT with p in Pa, V in m³, n in mol, T in K and R = 8.31 J mol⁻¹ K⁻¹.
• n is the number of moles of gas.
• The equation applies to an ideal gas and combines the gas laws.
• For a fixed mass of gas, pV/T = constant.
• The equation can be rearranged to find any one variable given the others.

Common mistakes and how to put them right

• Using degrees Celsius instead of kelvin.

  Put it right: Convert T to K by adding 273.

• Using volume in cm³ or litres instead of m³.

  Put it right: Convert to m³ (1 cm³ = 1 × 10⁻⁶ m³).

• Forgetting that n is number of moles, not number of molecules.

  Put it right: Use N = nN_A if needed.

Exam tips

• List the known quantities with their units before substituting into pV = nRT.
• Rearrange the equation algebraically before inserting numbers to reduce errors.
• Check that the final answer has the correct unit and magnitude.