This question is about a monatomic ideal gas.
(a)
Outline what is meant by an ideal monatomic gas.
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(b)
Neon gas is kept in a container of volume 7.1 × 10–2 m3 , temperature 325 K and pressure 3.7 × 105 Pa.
(i)
Calculate the number of moles of neon in the container.
[2]
(ii)
Calculate the number of atoms in the gas.
[2]
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(c)
The volume of the gas is increased to 4.2 × 10–2 m3 at a constant temperature.
(i)
Calculate the new pressure of the gas in Pa
[2]
(ii)
Explain this change in pressure, in terms of molecular motion.
[2]
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Energy is supplied to the gas at a rate of 10 J s–1 for 10 minutes. The specific heat capacity of neon is 904 J kg–1 K–1 and its atomic mass number is 21. The volume of the gas does not change.
(d)
Determine the new pressure of the gas.
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This question is about an ideal gas in a container.
An ideal gas is held in a glass gas syringe.
(a)
Calculate the temperature of 0.726 mol of an ideal gas kept in a cylinder of volume 2.6 × 10–3 m3 at a pressure of 2.32 × 105 Pa.
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(b)
The average kinetic energy of the gas is directly proportional to one particular property of the gas.
(i)
Identify this property.
[1]
(ii)
Calculate the average kinetic energy,
, per molecule of the gas.
[1]
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Energy is supplied to the gas at a rate of 0.5 J s–1 for 4 minutes. The specific heat capacity of the gas is 519 J kg–1 K–1 .
(c)
Calculate the change in kinetic energy per molecule of the gas.
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The gas is heated until its temperature doubles.
(d)
Determine the factor the average speed of the molecules increases by.
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This question is about the specific heat capacity of an ideal gas.
(a)
Outline two assumptions made in the kinetic model of an ideal
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Xenon–131 behaves as an ideal gas over a large range of temperatures and pressures.
(b)
One mole of Xenon–131 is stored at 20 °C in a cylinder of fixed volume. The Xenon gas is heated at a constant rate and the internal energy increased by 450 J. The new temperature of the Xenon gas is 41.7 °C.
(i)
Define one mole of Xenon.
[1]
(ii)
Calculate the specific heat capacity of gaseous Xenon–131.
[2]
(iii)
Calculate the average kinetic energy of the molecules of Xenon at this new temperature.
[2]
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The volume of the sealed container is 0.054 m3 .
(c)
Calculate the change in pressure of the gas due to the energy supplied in part (b).
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One end of the container is replaced with a moveable piston. The piston is compressed until the pressure of the container is 67000 Pa.
(d)
Determine the new volume of the container.
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This question is about an experiment to investigate the variation in the pressure p of an ideal gas with changing volume V .
The gas is trapped in a cylindrical tube of radius 0.5 cm above a column of oil.
The pump forces the oil to move up the tube and so reduces the volume of the gas. The scientist measures the pressure p of the gas and the height H of the column of gas.
(a)
Calculate the volume of the gas when the height is 1 cm.
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When the system is at a constant temperature of 20 °C, the pressure is 9600 Pa.
(b)
Calculate:
(i)
the amount of moles of gas trapped in the cylinder
[2]
(ii)
the average kinetic energy of the molecules of trapped gas
[1]
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The scientist plots their results of p against
(c)
Explain the shape of the graph and why this is to be expected.
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(d)
When conducting the experiment, the scientist waits for a period of time between taking each reading.
(i)
Explain the reason for waiting this short period of time.
[1]
(ii)
Describe what will happen to the shape of the graph if the scientist does not wait a sufficient period of time between readings.
[2]
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(a)
State the Pressure law of ideal gases.
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The pressure exerted by an ideal gas containing 9.7 × 1020 molecules in a container of volume 1.5 × 10–5 m3 is 2.8 × 105 Pa.
(b)
Calculate the temperature of the gas in the container in °C.
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The pressure of the gas is measured at different temperatures whilst the volume of the container and the mass of the gas remain constant.
(c)
On the grid, sketch a graph to show how the pressure varies with the temperature.
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The container described in part (a) has a release valve that allows gas to escape when the pressure exceeds 3.5 × 105 Pa.
(d)
Calculate the number of gas molecules that escape when the temperature of the gas is raised to 380°C.
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