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enter image description here Two chambers are connected as shown in the figure. The total pressure of the first chamber that contains Ar and He gas is 98.4 atm. If the faucet is released, find the total pressure. (There's 1 mol of Nitrogen gas on the second chamber)

(A) 52.2 atm (B) 61.5 atm (C)98.4 atm (D)123 atm (E)172.2 atm

My attempt:

Because of Ar and He are inert gas I only calculate the second chamber's partial pressure.

$$\begin{aligned} P_2&=\frac{1\cdot0.082\cdot300}{1}\\ &=24.6\mbox{ atm}\\\\ P_{tot}&=P_1+P_2\\&=123\mbox{ atm}\\\\ \end{aligned}$$ My other attempt: $$\begin{aligned} n_2&=\frac{1\cdot98.4}{0.082\cdot300}\\ &=4\mbox{ mol}\\\\ n_{tot}&=n_1+n_2\\&=5\mbox{ mol}\\\\ P_{total}&=\frac{5\cdot0.082\cdot300}{2}\\&=61.5\mbox{ atm} \end{aligned}$$

My question is which one is the correct method and why.

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    $\begingroup$ Suppose you open a door from one room of your house to another. Do the pressures add up? $\endgroup$
    – Ivan Neretin
    Commented May 4, 2019 at 8:06
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    $\begingroup$ Always write the values with the correct units and carry the units through the calculation. Do not omit the units while performing intermediate steps and do not just reintroduce units at the end of the calculation. $\endgroup$
    – user7951
    Commented May 5, 2019 at 19:47

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