Worked example 1

A container holds $0.50 \text{ mol}$ of an ideal gas at a pressure of $1.5 \times 10^5 \text{ Pa}$ and a temperature of $27^\circ\text{C}$ . Calculate the volume occupied by the gas. (Use $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$ )

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Convert temperature to Kelvin: $T_K = 27 + 273 = 300 \text{ K}$ .
Identify known values: $n = 0.50 \text{ mol}$ , $P = 1.5 \times 10^5 \text{ Pa}$ , $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$ , $T = 300 \text{ K}$ .
Rearrange the Ideal Gas Equation ( $PV = nRT$ ) to solve for V: $V = nRT / P$ .
Substitute the values: $V = (0.50 \times 8.31 \times 300) / (1.5 \times 10^5)$ .
Calculate the volume: $V = 1246.5 / 150000 = 0.00831 \text{ m}^3$ .

Worked example 2

A rigid cylinder of volume 0.050 m³ contains 8.0 g of helium gas at a temperature of 25°C. The molar mass of helium is 4.0 g/mol. Assuming helium behaves as an ideal gas, calculate the pressure inside the cylinder. (Use R = 8.31 J mol⁻¹ K⁻¹)

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Convert all units to SI base units.
- Mass (m): $8.0 \text{ g} = 0.0080 \text{ kg}$
- Molar Mass (M): $4.0 \text{ g/mol} = 0.0040 \text{ kg/mol}$
- Temperature (T): $25°\text{C} + 273 = 298 \text{ K}$
- Volume (V): $0.050 \text{ m}^3$ (already in SI)
Calculate the number of moles (n) of helium.
- Use the formula $n = m/M$ .
- $n = 0.0080 \text{ kg} / 0.0040 \text{ kg/mol} = 2.0 \text{ mol}$
Use the Ideal Gas Equation to find the pressure (P).
- Rearrange $PV = nRT$ to solve for P: $P = nRT / V$ .
Substitute the values and calculate.
- $P = (2.0 \text{ mol} \times 8.31 \text{ J mol}^{-1} \text{ K}^{-1} \times 298 \text{ K}) / 0.050 \text{ m}^3$
- $P = 4954.76 / 0.050 = 99095.2 \text{ Pa}$
State the final answer to appropriate significant figures.
- The input values (8.0 g, 0.050 m³, 25°C) are given to 2 significant figures. Therefore, the answer should also be given to 2 s.f.
- $P \approx 99000 \text{ Pa}$ or $9.9 \times 10^4 \text{ Pa}$ .

The mole — practice questions

Worked example 1

Worked example 2