Question

A container contains 1 mole of a gas at 1 atm pressure and 27°C, and its volume is 24.6 litres. If pressure is 10 atm and temperature 327°C then new volume is approximately

(a) 2 litre

(b) 48 litre

(c) 10 litre

(d) 4.92 litre

Answer 1

Correct option is (d) 4.92 litre

Initial pressure (P₁) = 1 atm

Initial temperature (T₁) = 27°C = 300 K

Initial volume (V₁) = 24.6 litres

Number of moles (n) = 1 mole

The ideal gas law formula is given by: \(PV = nRT\)

Initially, for the container:

\(P_1V_1 = nRT_1\)

\(1 \times 24.6 = 1 \times R \times 300\)

\(R = 24.6/300\)

Now, for the final state:

\(P_2V_2 = nRT_2\)

\(10 \times V_2 = 1 \times(24.6/300) \times600\)

\(V_2 = (24.6/300) \times 600 / 10\)

\(V_2 = 4.92 \text{ litres}\)

Therefore, the new volume when pressure is 10 atm and temperature is 327°C is approximately 4.92 litres.