MHT CET · Chemistry · States of Matter

If the mixture of \(7 g\) of \(N_2\) and \(8 g\) of \(\mathrm{Ar}\) in a cylinder has the total pressure \(27 \mathrm{bar}\). What is the partial pressure of \(N_2\) ? (Atomic mass of \(N=14 \mathrm{~g} \mathrm{~mol}^{-1}, \mathrm{Ar}=40 \mathrm{~g} \mathrm{~mol}^{-1}\) )

A 18 bar
B 12 bar
C 15 bar
D 9 bar

Verified Solution

Answer & Solution

Correct Answer

(C) 15 bar

Step-by-step Solution

Detailed explanation

Moles of \(N_2=\frac{7}{28}=\frac{1}{4}\)
Moles of \(\mathrm{Ar}=\frac{8}{40}=\frac{1}{5}\)
Partial pressure \(=X_{N_2} \times P_T\)
Partial pressure of
\(\begin{aligned}
N_2 & =\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{5}} \times 27 \\
& =\frac{\frac{1}{4}}{\frac{9}{20}} \times 27 \\
& =\frac{1}{4} \times \frac{20}{9} \times 27 \\
& =15 \mathrm{bar}
\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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