Question

A quantity of 22 g dry ice is taken in an open bottle of one litre capacity and the bottle is then closed properly. If the temperature of bottle is maintained at 27°C for long time, in which all the CO₂ is sublimed, then the pressure in bottle is (Ambient condition is 1 atm and 27°C)

• A. 13.315 atm
• B. 12.315 atm
• C. 11.315 atm
• D. 1.0 atm

Answer 1

Answer: (A)

13.315 atm

Answer 2

The total pressure is the sum of the partial pressure of the trapped air and the partial pressure of the CO₂ gas.

1. Moles of CO₂: $n_{CO_2} = \frac{22 \text{ g}}{44 \text{ g/mol}} = 0.5 \text{ mol}$.
2. Partial Pressure of CO₂ ($P_{CO_2}$): Using the Ideal Gas Law, $P_{CO_2} = \frac{n_{CO_2}RT}{V} = \frac{0.5 \text{ mol} \times 0.0821 \text{ L·atm/(mol·K)} \times 300 \text{ K}}{1 \text{ L}} = 12.315 \text{ atm}$.
3. Partial Pressure of Trapped Air ($P_{air}$): Since the bottle was open to the atmosphere at 1 atm, $P_{air} = 1 \text{ atm}$.
4. Total Pressure ($P_{total}$): $P_{total} = P_{air} + P_{CO_2} = 1 \text{ atm} + 12.315 \text{ atm} = 13.315 \text{ atm}$.