Two flasks X and Y are filled with an ideal gas and are connected by a tube of negligible volume compared to that of the flasks - AQA - A-Level Physics - Question 9 - 2018 - Paper 2

To find the mass of gas in flask X, we can use the ideal gas law:

$PV = nRT$

Where:

• $P$ is the pressure
• $V$ is the volume
• $n$ is the number of moles
• $R$ is the ideal gas constant
• $T$ is the temperature

Let the volume of flask Y be $V_Y$; therefore, the volume of flask X is $2V_Y$. Thus, we can state:

For flask X: $P_X(2V_Y) = n_XR(150)$

For flask Y: $P_Y(V_Y) = n_YR(300)$

Assuming that both flasks are at the same pressure ($P_X = P_Y$), we can express the number of moles ($n_X$ and $n_Y$) in terms of mass using the molar mass $M$:

$n = \frac{m}{M}$

Thus, converting the above equations gives us:

$\frac{m_X}{M} = \frac{P_Y V_Y (300)}{R}$

$\frac{m_Y}{M} = \frac{P_Y V_Y (150)}{R}$

Dividing these two equations yields the mass ratio:

$\frac{m_X}{m_Y} = \frac{300}{150} \times \frac{\text{Volume ratio of X to Y}}{2} = \frac{300 \times 2}{150} = 4$