MHT CET · Chemistry · States of Matter

Which of the following formula is used to calculate compressibility factor?

A \(\mathrm{Z}=\frac{\mathrm{PVT}}{\mathrm{R}}\)
B \(\mathrm{Z}=\frac{\mathrm{nRT}}{\mathrm{PV}}\)
C \(\mathrm{Z}=\frac{\mathrm{PV}}{\mathrm{nRT}}\)
D \(\mathrm{Z}=\left(\frac{\mathrm{PV}}{\mathrm{RT}}\right) \times \mathrm{n}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{Z}=\frac{\mathrm{PV}}{\mathrm{nRT}}\)

Step-by-step Solution

Detailed explanation

(1) \(Z=\frac{P V T}{R}\) : This is incorrect because the units on both sides don't match.
(2) \(Z=\frac{n R T}{P V}\) : This is incorrect because it's the inverse of the correct formula.
(3) \(Z=\frac{P V}{n R T}\) : This is the correct formula for the compressibility factor.
(4) \(Z=\frac{(P V)}{R T} \times n\) : This is also incorrect because it doesn't match the standard formula for \(Z\).

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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