Using Dalton's law of partial pressures


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




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.


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