The ideal gas equation and kinetic theoryEdexcel International A Level Physics: Subtopic test

1. 1
   A sealed flask of volume 2.0 × 10⁻³ m³ contains an ideal gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 300 K. The Boltzmann constant is k = 1.38 × 10⁻²³ J K⁻¹.

   (a)

   How many molecules are in the flask?

   [1 mark]

   • A5.4 × 10²³
   • B4.8 × 10²²
   • C2.1 × 10⁻²³
   • D4.1 × 10⁻²¹

   (b)

   The flask is sealed and heated to 600 K. What is the new pressure of the gas?

   [1 mark]

   • A1.0 × 10⁵ Pa
   • B5.0 × 10⁴ Pa
   • C4.0 × 10⁵ Pa
   • D2.0 × 10⁵ Pa

   (c)

   Calculate the mean kinetic energy of a molecule of the gas.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A class investigates the relationship between the pressure and volume of a fixed mass of air at constant temperature. The air is trapped in a syringe connected to a pressure gauge, and the students change the volume with the plunger and record the pressure each time.

   (a)

   Which graph of the results should be a straight line through the origin?

   [1 mark]

   • Ap against V
   • Bp against V²
   • Cp against 1/V
   • DV against p

   (b)

   Which procedure helps to keep the temperature of the air constant?

   [1 mark]

   • ACompress the air as quickly as possible
   • BMove the plunger slowly and wait before each reading
   • CWarm the syringe gently throughout
   • DUse a thicker plastic for the syringe

   (c)

   The air is at a pressure of 1.00 × 10⁵ Pa when its volume is 60 cm³. The students compress it to 24 cm³ at constant temperature. Calculate the new pressure.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Helium is used to fill a weather balloon. A helium atom has mass 6.64 × 10⁻²⁷ kg. The gas can be treated as ideal and is at a temperature of 300 K. The Boltzmann constant is k = 1.38 × 10⁻²³ J K⁻¹. Argon atoms have a mass of 6.63 × 10⁻²⁶ kg.

   (a)

   Calculate the root mean square speed of the helium atoms.

   [3 marks]

   (b)

   Calculate the root mean square speed of argon atoms at the same temperature, explaining why it differs from that of helium.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A physics teacher uses a sealed flask of nitrogen to demonstrate kinetic theory. The flask has a volume of 1.0 × 10⁻³ m³ and holds 2.4 × 10²² molecules at a temperature of 300 K. Each molecule has a mass of 4.65 × 10⁻²⁶ kg. The teacher shows how the equation for the mean kinetic energy of a molecule follows from two equations for the pressure of an ideal gas, pV = ⅓Nm⟨c²⟩ from kinetic theory and pV = NkT from the equation of state. The Boltzmann constant is k = 1.38 × 10⁻²³ J K⁻¹.

   (a)

   Derive the equation ½m⟨c²⟩ = (3/2)kT from the two equations for pV, and state what the equation shows about the molecules.

   [6 marks]

   (b)

   Calculate the pressure of the gas in the flask, the mean kinetic energy of a molecule and the root mean square speed of the molecules.

   [6 marks]

   Total for question 4: 12 marks

End of questions