A student performs a comprehensive investigation of gas behaviour. She uses the apparatus shown in Fig. 67.1 to study both Boyle's law and the pressure law....

Part (a) [1 mark]

For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume [1].

Mathematically: \(pV = \text{constant}\), or equivalently \(p \propto \frac{1}{V}\). Doubling the volume halves the pressure, because the same number of molecules now has twice the space and strikes the walls half as often per unit area.

Part (b) [2 marks]

• W is the Bourdon gauge (pressure gauge) [1]
• X is the plunger (piston) of the gas syringe [1]

The Bourdon gauge contains a curved metal tube that straightens under increased pressure, moving a pointer across a scale. The plunger slides within the syringe barrel to change the volume of the trapped gas.

Part (c) [2 marks]

Close the three-way tap to the syringe so that only the flask is connected to the Bourdon gauge [1]. Heat the water bath slowly, stir to ensure uniform temperature, and record the pressure reading at regular temperature intervals after allowing each reading to stabilise [1].

Stirring ensures all the water (and therefore the flask) reaches a uniform temperature. Waiting for the reading to stabilise ensures the gas inside the flask has reached thermal equilibrium with the water bath.

Part (d) [4 marks]

(i) Boyle's law calculation:

\(p_1 V_1 = p_2 V_2\) [1]

\(V_2 = \frac{p_1 V_1}{p_2} = \frac{100 \times 80}{200} = 40\) cm³ [1]

To double the pressure, the volume must be halved (from 80 cm³ to 40 cm³).

(ii) Pressure law calculation:

Convert to kelvin: \(T_1 = 20 + 273 = 293\) K, \(T_2 = 80 + 273 = 353\) K [1]

\(\frac{p_1}{T_1} = \frac{p_2}{T_2}\)

\(p_2 = \frac{p_1 \times T_2}{T_1} = \frac{100 \times 353}{293} = 120.5\) kPa (accept 120 kPa) [1]

Heating the gas by 60 °C increases the absolute temperature by about 20%, so the pressure also rises by about 20%. The pressure law requires absolute temperatures because pressure is proportional to the average kinetic energy of the particles, which is measured from absolute zero.

Part (e) [2 marks]

Compressing the gas may cause a slight temperature rise even if done slowly, affecting the Boyle's law results [1]. The gas may not behave perfectly as an ideal gas, there may be small gas leaks at the joints, or the gauge may have a zero error [1].

Part (f) [2 marks]

Any two valid improvements, for example: use a data logger for more precise and frequent readings [1]; repeat each measurement three times and calculate an average to reduce random errors [1].

Other acceptable improvements include insulating the syringe to maintain constant temperature, using a more precise digital pressure sensor, or allowing longer equilibration time between readings.