[Maximum number: 6]

The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

(a)

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

[ 2 ]

(b)

The cross-sectional area of the tube is $1.3 \times 10^{-3} \mathrm{~m}^{2}$ and the temperature of air is 300 K . Estimate the number of moles of air in the tube.

[ 2 ]

(c)

The equation in (b) may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$ . Suggest why this will be an unreliable estimate of the pressure.

[ 2 ]

[Maximum number: 1]

A swimming pool contains $18 \times 10^{6} \mathrm{~kg}$ of pure water. The molar mass of water is $18 \mathrm{~g} \mathrm{~mol}^{-1}$ . What is the correct estimate of the number of water molecules in the swimming pool?

A

$10^{4}$

B

$10^{24}$

C

$10^{25}$

D

$10^{33}$

[Maximum number: 8]

The air in a kitchen has pressure $1.0 \times 10^{5} \mathrm{~Pa}$ and temperature $22^{\circ} \mathrm{C}$ . A refrigerator of internal volume $0.36 \mathrm{~m}^{3}$ is installed in the kitchen.

(a)

With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.

[ 2 ]

(b)

The refrigerator door is closed. The air in the refrigerator is cooled to $5.0^{\circ} \mathrm{C}$ and the number of air molecules in the refrigerator stays the same.

[ 6 ]

(i)

Determine the pressure of the air inside the refrigerator.

[ 2 ]

(ii)

The door of the refrigerator has an area of $0.72 \mathrm{~m}^{2}$ . Show that the minimum force needed to open the refrigerator door is about 4 kN .

[ 2 ]

(iii)

Comment on the magnitude of the force in (b)(ii).

[ 2 ]

(a)

At night the outside temperature falls below $13^{\circ} \mathrm{C}$ . The heater is turned off at time t=0. The graph shows the variation with time t of the temperature T of the room.

[ 3 ]

(i)

The pressure and volume of the air in the room remain constant but the number of molecules has increased. Determine the percentage increase in the number of molecules of air in the room between t=0 and $t=120 \mathrm{~min}$ .

[ 3 ]

[Maximum number: 6]

The graph shows the variation with temperature T of the pressure P of a fixed mass of helium gas trapped in a container with a fixed volume of $1.0 \times 10^{-3} \mathrm{~m}^{3}$ .

(a)

Deduce whether helium behaves as an ideal gas over the temperature range 250 K to 500 K .

[ 2 ]

(b)

Helium has a molar mass of 4.0 g . Calculate the mass of gas in the container.

[ 2 ]

(c)

A second container, of the same volume as the original container, contains twice as many helium atoms. The graph of the variation of P with T is determined for the gas in the second container.

Predict how the graph for the second container will differ from the graph for the first container.

[ 2 ]

[Maximum number: 1]

A container holds 40 g of argon- $40\left({ }_{18}^{40} \mathrm{Ar}\right)$ and 8 g of helium- $4\left({ }_{2}^{4} \mathrm{He}\right)$ .

What is the $\frac{\text { number of atoms of argon }}{\text { number of atoms of helium }}$ in the container?

A

$\frac{1}{2}$

B

$\frac{2}{9}$

C

$\frac{2}{1}$

D

$\frac{9}{2}$

[Maximum number: 1]

A gas is held in a container. An identical container holds the same number of more massive molecules of another gas at the same temperature.

What is true about the density and pressure in both containers?

Density in both containers

Pressure in both containers

same

different

same

different

(a)

An ideal monatomic gas is kept in a container of volume $2.1 \times 10^{-4} \mathrm{~m}^{3}$ , temperature 310 K and pressure $5.3 \times 10^{5} \mathrm{~Pa}$ .

[ 4 ]

(i)

State what is meant by an ideal gas.

[ 1 ]

(ii)

Calculate the number of atoms in the gas.

[ 1 ]

(iii)

Calculate, in J , the internal energy of the gas.

[ 2 ]

(b)

The volume of the gas in (a) is increased to $6.8 \times 10^{-4} \mathrm{~m}^{3}$ at constant temperature.

[ 3 ]

(i)

Calculate, in Pa , the new pressure of the gas.

[ 1 ]

(ii)

Explain, in terms of molecular motion, this change in pressure.

[ 2 ]

[Maximum number: 1]

A rigid vessel of volume V contains N molecules of an ideal monatomic gas. The average kinetic energy of the molecules is $E_{k}$ . What is the pressure in the vessel?

A

$\frac{2 N}{3 V E_{k}}$

B

$\frac{2 N E_{k}}{3 V}$

C

$\frac{3 N}{2 V E_{k}}$

D

$\frac{3 N E_{k}}{2 V}$

[Maximum number: 1]

What is the definition of the mole?

A

The amount of substance that has the same mass as $6.02 \times 10^{23}$ atoms of carbon-12.

B

The amount of substance that contains as many nuclei as the number of nuclei in 12 g of carbon-12.

C

The amount of substance that has the same mass as one atom of carbon-12.

D

The amount of substance that contains as many elementary entities as the number of atoms in 12 g of carbon-12.

Question 1

Question 1(c)

Question 1(d)

Question 1(e)

Question 2

Question 2

Question 2(a)

Question 2(b)

Question 2(b)(i)

Question 2(b)(ii)

Question 2(b)(iii)

Question 2

Question 2(c)

Question 2(c)(ii)

Question 2

Question 2(a)

Question 2(b)

Question 2(c)

Question 8

Question 8

Question 2

Question 2(a)

Question 2(a)(i)

Question 2(a)(ii)

Question 2(a)(iii)

Question 2(b)

Question 2(b)(i)

Question 2(b)(ii)

Question 9

Question 9