$$ \begin{array}{|c|c|} \hline \text{Gas} & \text{Amount} \\ \hline \hline \ce{Ar} & \pu{0.35 mol} \\ \hline \ce{CH4} & \pu{0.90 mol} \\ \hline \ce{N2} & \pu{0.25 mol} \\ \hline \end{array} $$

Three gases in the amounts shown in the table above are added to a previously evacuated rigid tank. If the total pressure in the tank is 3.0 atm at 25\(\degree\)C, the partial pressure of \(\ce{N2(g)}\) in the tank is closest to

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The partial pressure of a gas can determined through its mole fraction.

$$ P_{\ce{N2(g)}}=P_{\text{total}} \cdot \dfrac{n_{\ce{N2(g)}}}{n_{\text{total}}} $$ $$ P = (3.0 \text{ atm})\cdot \frac{0.25 \text{ mol}}{0.35+0.90+0.25 \text{mol}} $$ $$ P = 3.0 \cdot \frac{0.25}{1.4} \text{ atm} $$ $$ P = 3 \cdot \frac{1}{4} \cdot \frac{10}{14} \text{ atm}$$ $$ P = \frac{15}{28} \text{ atm}$$ $$ P \approx \frac{14}{28} = \boxed{0.50 \text{ atm}} $$