MHT CET · Chemistry · States of Matter

If \(P_1\) partial pressure of a gas and \(x_1\) is its mole fraction in a mixture, then correct relation between \(P_1\) and \(x_1\) is

A \(\mathrm{P}_{\text {total }}=\mathrm{P}_1 \mathrm{X}_1\)
B \(\mathrm{x}_1=\frac{\mathrm{P}_1}{\mathrm{P}_{\text {total }}}\)
C \(\mathrm{P}_{\text {total }}=1-\mathrm{P}_1 \mathrm{x}_1\)
D \(\mathrm{P}_{\text {total }}=\mathrm{P}_1\left(1-\mathrm{x}_1\right)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{x}_1=\frac{\mathrm{P}_1}{\mathrm{P}_{\text {total }}}\)

Step-by-step Solution

Detailed explanation

The correct relation between the partial pressure of a gas \(\left(P_1\right)\) and its mole fraction \(\left(x_1\right)\) in a mixture is given by Dalton's Law of Partial Pressures. According to this law, the partial pressure of a gas in a mixture is proportional to its mole fraction and the total pressure of the mixture. The expression can be written as:
\(P_1=x_1 \cdot P_{\text {total }}\)
From this relationship, we can derive the mole fraction as:
\(x_1=\frac{P_1}{P_{\text {total }}}\)
This corresponds to Option B:
\(x_1=\frac{P_1}{P_{\text {total }}}\)

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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