Using Dalton's law of partial pressures

Question

A container of volume $\pu{4.0 L}$ contains nitrogen at $\pu{25 °C}$ and $\pu{803 kPa}.$ This container is connected by a valve to another container of volume $\pu{10.0 L}$ that contains argon at $\pu{25 °C}$ and $\pu{47.2 kPa}.$ We now open the valve so that the two gases are mixing.

Calculate the partial pressure of each gas after the mixing and the total pressure of the mixture.

Using the Dalton's law of partial pressures, isn't the partial pressure of each gas exactly $\pu{803 kPa}$ and $\pu{47.2 kPa}$ and the total pressure $\pu{803 kPa} + \pu{47.2 kPa}?$

What am I missing here?

Answer 1

Dalton's law of partial pressures means that the total pressure in the final volume $V=V_1+V_2$ is equal to the sum of the partial pressures P(N₂) + P(Ar) in this volume. However, the partial pressure of N₂ in the total volume $V$ is not the same as the pressure of N₂ in its initial volume $V_1$. You have to account for the expansion. This probably means you also need to use the ideal gas law for that.