1. 1
   A sealed steel cylinder of internal volume 0.050 m³ contains helium at a temperature of 290 K and a pressure of 2.4 × 10⁶ Pa. Helium can be treated as an ideal monatomic gas.

   (a)

   What is the amount of helium in the cylinder?

   [1 mark]

   • A50 mol
   • B850 mol
   • C3.0 × 10²⁵ mol
   • D0.020 mol

   (b)

   What is the internal energy of the helium in the cylinder?

   [1 mark]

   • A1.2 × 10⁵ J
   • B3.6 × 10³ J
   • C6.0 × 10⁻²¹ J
   • D1.8 × 10⁵ J

   (c)

   Some helium is released from the cylinder while the temperature stays at 290 K, until the pressure falls to 1.6 × 10⁶ Pa. Calculate the amount of helium that escaped.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Nitrogen gas in a laboratory is at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K. Under these conditions its density is 1.12 kg m⁻³. The gas can be treated as ideal.

   (a)

   Which statement is not an assumption of the kinetic model of an ideal gas?

   [1 mark]

   • ACollisions between molecules and with the walls are elastic
   • BAll the molecules move with the same speed
   • CThe volume of the molecules is negligible compared with the volume of the container
   • DThere are no intermolecular forces except during collisions

   (b)

   What is the root mean square speed of the nitrogen molecules?

   [1 mark]

   • A300 m s⁻¹
   • B170 m s⁻¹
   • C520 m s⁻¹
   • D2.7 × 10⁵ m s⁻¹

   (c)

   The nitrogen is heated to 600 K at constant pressure. Deduce the new root mean square speed of the molecules.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student investigates how the pressure of a fixed mass of air in a sealed glass flask varies with temperature. The flask is immersed in a water bath and connected to a pressure sensor; the volume of the air stays constant. Her readings are: at 20 °C the pressure is 101 kPa; at 40 °C, 108 kPa; at 60 °C, 115 kPa; at 80 °C, 122 kPa. The pressure sensor reads to the nearest 1 kPa.

   (a)

   Using the data, show that the results are consistent with the pressure of the air being proportional to its absolute temperature.

   [3 marks]

   (b)

   The student extrapolates her results to estimate absolute zero. Estimate the temperature, in °C, at which the pressure would become zero, and evaluate the reliability of this estimate.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company plans to store carbon dioxide in steel tanks at 320 K. A technician measures the pressure exerted by 1.00 mol of carbon dioxide at 320 K in two different sealed containers. In a container of volume 24.0 dm³ the pressure is 110.4 kPa. In a container of volume 0.250 dm³ the pressure is 7.1 MPa.

   (a)

   Explain, with reference to molecular collisions, how the kinetic model accounts for the pressure of a gas, and hence explain why the pressure of an ideal gas is proportional to its absolute temperature at constant volume.

   [6 marks]

   (b)

   Using the data, evaluate whether the ideal gas model is a suitable approximation for designing the storage tanks. Explain any differences between the measured and ideal pressures in terms of the kinetic model.

   [6 marks]

   Total for question 4: 12 marks

End of questions