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Matter: Very Simple

The equation of state for an ideal gas

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on what each symbol means, converting between particle and molar forms, calculating moles, particles and a new pressure, why kelvin is required, and what pressure times volume represents.

What you need to know

Answer each one before you reveal it.

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Key term

In pV = NkT, what does each symbol stand for?

Numbers

A cylinder of volume 0.020 m³ holds gas at 2.5 × 10⁵ Pa and 300 K. Calculate the number of moles present.

Numbers

A sealed flask of volume 5.0 × 10⁻⁴ m³ contains gas at 1.0 × 10⁵ Pa and 290 K. Calculate the number of particles.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    In pV = NkT, what does each symbol stand for?

    Model answer

    p is the pressure, V the volume, N the number of particles, k the Boltzmann constant and T the absolute temperature.

  2. 2

    How is the particle form pV = NkT turned into the molar form pV = nRT?

    Model answer

    Substituting N = nNₐ and R = Nₐ k replaces Nk by nR, so NkT becomes nRT.

  3. 3

    A cylinder of volume 0.020 m³ holds gas at 2.5 × 10⁵ Pa and 300 K. Calculate the number of moles present.

    Model answer

    n = pV/RT = (2.5 × 10⁵ × 0.020) ÷ (8.31 × 300) = 2.0 mol.

  4. 4

    A sealed flask of volume 5.0 × 10⁻⁴ m³ contains gas at 1.0 × 10⁵ Pa and 290 K. Calculate the number of particles.

    Model answer

    N = pV/kT = (1.0 × 10⁵ × 5.0 × 10⁻⁴) ÷ (1.38 × 10⁻²³ × 290) = 1.2 × 10²² particles.

  5. 5

    What happens to the pressure of a fixed mass of ideal gas if both its absolute temperature and its volume are doubled?

    Model answer

    The pressure is unchanged, because pV = NkT and both sides of the relationship double.

  6. 6

    A gas occupying 1.0 m³ at 1.0 × 10⁵ Pa and 300 K is compressed to 0.25 m³ and heated to 450 K. Calculate the new pressure.

    Model answer

    The new pressure is 1.0 × 10⁵ × (1.0 ÷ 0.25) × (450 ÷ 300) = 6.0 × 10⁵ Pa.

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