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The particulate nature of matter · Question 8

The particulate nature of matter · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
11
Topics
2
Answer
Complete
Sealed rigid container holding nitrogen gasnitrogen gasV = 5.0 × 10⁻³ m³p = 2.4 × 10⁵ PaT = 290 Ksealed rigid container
Figure 3A rectangular container with thick walls and a stopper in its top is labelled sealed rigid container. Inside, ten molecules are drawn as dots, each carrying a short arrow of its own direction and length so that the molecules are moving randomly, several of them towards the walls. To the right of the container stand the labels nitrogen gas, V = 5.0 × 10⁻³ m³, p = 2.4 × 10⁵ Pa and T = 290 K.
structured11 marks

A sealed rigid container of volume 5.0 × 10⁻³ m³ holds nitrogen gas at a pressure of 2.4 × 10⁵ Pa and a temperature of 290 K. Nitrogen may be treated as an ideal gas.

  1. (a)

    Calculate Calculate the amount of gas in the container, in moles.

    2 marks
  2. (b)

    Determine Determine the average kinetic energy of a nitrogen molecule in the container.

    2 marks
  3. (c)

    Explain The container is warmed to 350 K. Explain, in terms of the behaviour of the molecules, why the pressure increases.

    3 marks
  4. (d)

    Explain Outline two assumptions of the ideal gas model, and explain why real nitrogen behaves less like an ideal gas at very high pressure.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: n = pV/RT = (2.4 × 10⁵ × 5.0 × 10⁻³)/(8.31 × 290) n = 0.50 mol E_k = (3/2)k_BT = 1.5 × 1.38 × 10⁻²³ × 290
01

(a)

2 marks

Calculate Calculate the amount of gas in the container, in moles.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    n = pV/RT = (2.4 × 10⁵ × 5.0 × 10⁻³)/(8.31 × 290)

  2. 2

    n = 0.50 mol

02

(b)

2 marks

Determine Determine the average kinetic energy of a nitrogen molecule in the container.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    E_k = (3/2)k_BT = 1.5 × 1.38 × 10⁻²³ × 290

  2. 2

    E_k = 6.0 × 10⁻²¹ J

03

(c)

3 marks

Explain The container is warmed to 350 K. Explain, in terms of the behaviour of the molecules, why the pressure increases.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    the average kinetic energy of the molecules increases, so their mean speed increases

  2. 2

    each molecule therefore strikes the walls more frequently

  3. 3

    and each collision produces a larger change of momentum, so the average force per unit area on the walls rises

04

(d)

4 marks

Explain Outline two assumptions of the ideal gas model, and explain why real nitrogen behaves less like an ideal gas at very high pressure.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    the molecules have negligible volume compared with the volume of the container

  2. 2

    there are no intermolecular forces except during collisions, and all collisions are elastic

  3. 3

    at very high pressure the molecules are pushed close together, so their own volume is no longer negligible compared with the space available

  4. 4

    and at those separations the intermolecular attractions are significant, so the molecules exert less force on the walls than the model predicts

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