Question

diagram 1 above shows equimolar samples of two gases inside a container fitted with a removable barrier placed so that each gas occupies the same volume. the barrier is carefully removed as the temperature is held constant. diagram 2 above shows the gases soon after the barrier is removed. which statement describes the changes to the initial pressure of each gas and the final partial pressure of each gas in the mixture and also indicates the final total pressure?
a the partial pressure of each gas in the mixture is double its initial pressure; the final total pressure is half the sum of the initial pressures of the two gases.
b the partial pressure of each gas in the mixture is double its initial pressure; the final total pressure is twice the sum of the initial pressures of the two gases.
c the partial pressure of each gas in the mixture is half its initial pressure; the final total pressure is half the sum of the initial pressures of the two gases.
d the partial pressure of each gas in the mixture is half its initial pressure; the final total pressure is the same as the sum of the initial pressures of the two gases.

Explanation:

Step1: Apply Boyle's Law

Boyle's law is $P_1V_1 = P_2V_2$ for a given amount of gas at constant temperature. Initially, each gas occupies volume $V$. After the barrier is removed, the volume for each gas doubles to $2V$. Let the initial pressure of each gas be $P_{1i}$. For each gas, $P_{1i}V=P_{2i}(2V)$. Solving for $P_{2i}$ gives $P_{2i}=\frac{P_{1i}}{2}$, so the partial - pressure of each gas in the mixture is half its initial pressure.

Step2: Use Dalton's Law of Partial Pressures

Dalton's law states that $P_{total}=\sum P_{i}$. Initially, if the pressures of the two gases are $P_{1}$ and $P_{2}$, and their partial - pressures after mixing are $P_{1f}$ and $P_{2f}$, where $P_{1f}=\frac{P_{1}}{2}$ and $P_{2f}=\frac{P_{2}}{2}$. Then $P_{total,f}=P_{1f} + P_{2f}=\frac{P_{1}+P_{2}}{2}$, which is half the sum of the initial pressures of the two gases.

Answer:

C. The partial pressure of each gas in the mixture is half its initial pressure; the final total pressure is half the sum of the initial pressures of the two gases.