[Maximum number: 5]

An ideal gas has volume V and pressure p. For this gas, the product p V is given by the expression

p V=\frac{1}{3} N m<c^{2}>

where m is the mass of a molecule of the gas.

(a)

A gas cylinder of volume $2.1 \times 10^{4} \mathrm{~cm}^{3}$ contains helium-4 gas at pressure $6.1 \times 10^{5} \mathrm{~Pa}$ and temperature $12^{\circ} \mathrm{C}$ . Helium-4 may be assumed to be an ideal gas.

[ 5 ]

(i)

Determine, for the helium gas,
1. the amount, in mol,
amount = mol [3]
2. the number of atoms.
number =

[ 5 ]

[Maximum number: 2]

the rate h of thermal energy gained by the ice from the surroundings.

h=

W

(a)

The variation with volume V of the pressure p of an ideal gas as it undergoes a cycle ABCA of changes is shown in Fig. 2.1.

Fig. 2.1

The temperature of the gas at A is 290 K . The temperature at B is 870 K .

Determine

[ 2 ]

(i)

the amount, in mol, of gas, amount = mol

[ 2 ]

[Maximum number: 3]

+w.

(a)

Explain what is meant by the Avogadro constant.

[ 2 ]

(b)

Argon-40 $\left({ }_{18}^{40} \mathrm{Ar}\right)$ may be assumed to be an ideal gas.

A mass of 3.2 g of argon- 40 has a volume of $210 \mathrm{~cm}^{3}$ at a temperature of $37^{\circ} \mathrm{C}$ .
Determine, for this mass of argon-40 gas,

[ 1 ]

(i)

the amount, in mol,
amount = mol

[ 1 ]

(a)

State what is meant by a mole.

[ 2 ]

[Maximum number: 2]

electric potential energy.
energy = J

(a)

Helium-4 may be assumed to behave as an ideal gas.

A cylinder has a constant volume of $7.8 \times 10^{3} \mathrm{~cm}^{3}$ and contains helium-4 gas at a pressure of $2.1 \times 10^{7} \mathrm{~Pa}$ and at a temperature of 290 K .

Calculate, for the helium gas,

[ 2 ]

(i)

the amount of gas,
amount = mol

[ 2 ]

(a)

A sealed vessel contains a mass of 0.0424 kg of an ideal gas at $227^{\circ} \mathrm{C}$ . The pressure of the gas is $1.37 \times 10^{5} \mathrm{~Pa}$ and the volume of the gas is $0.640 \mathrm{~m}^{3}$ .

Calculate:

[ 1 ]

(i)

the mass of one molecule of the gas

mass =kg [1]

[ 1 ]

(a)

State what is meant by the Avogadro constant $N_{\mathrm{A}}$ .

[ 1 ]

(a)

A storage cylinder for an ideal gas has a volume of $3.0 \times 10^{-4} \mathrm{~m}^{3}$ . The gas is at a temperature of $23^{\circ} \mathrm{C}$ and a pressure of $5.0 \times 10^{7} \mathrm{~Pa}$ .

[ 3 ]

(i)

The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40 %. The temperature remains constant.
Calculate the average rate, in atoms per second, at which gas atoms escape from the cylinder.

[ 3 ]

(a)

A storage cylinder for an ideal gas has a volume of $3.0 \times 10^{-4} \mathrm{~m}^{3}$ . The gas is at a temperature of $23^{\circ} \mathrm{C}$ and a pressure of $5.0 \times 10^{7} \mathrm{~Pa}$ .

(i)

The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40 %. The temperature remains constant.
Calculate the average rate, in atoms per second, at which gas atoms escape from the cylinder.

(a)

A sample of $0.26 \mathrm{~m}^{3}$ of an ideal gas is at pressure $2.0 \times 10^{5} \mathrm{~Pa}$ and temperature 290 K .

Determine:

(i)

the number N of molecules of the gas