Question

Three bulbs are filled with CH4, CO2 and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be_______atm. (Nearest integer)

Answer 1

Correct Answer: 3

The final pressure of the system, $P_f$, is calculated using Dalton's law: \[ P_f V_f = P_1 V_1 + P_2 V_2 + P_3 V_3 \] Given: \[ P_1 = 2 \, \text{atm}, \, V_1 = 2 \, \text{L}, \, P_2 = 4 \, \text{atm}, \, V_2 = 3 \, \text{L}, \, P_3 = 3 \, \text{atm}, \, V_3 = 4 \, \text{L} \] Total volume: \[ V_f = V_1 + V_2 + V_3 = 2 + 3 + 4 = 9 \, \text{L} \] Total pressure contribution: \[ P_f V_f = (2 \times 2) + (4 \times 3) + (3 \times 4) = 4 + 12 + 12 = 28 \, \text{atm.L} \] Final pressure: \[ P_f = \frac{28}{9} \approx 3.11 \, \text{atm} \] Thus, $P_f \approx 3$ atm.