TS EAMCET · Chemistry · States of Matter

1 mole of a real gas is kept at high pressure of 100 bar at \(300 \mathrm{~K}\). If van der Waals constant \(b\) is \(0.005 \mathrm{~L} / \mathrm{mol}\), what are the values of compressibility factor \(\mathrm{Z}\) of the gas and \(\%\) deviation of volume from ideality? \(\begin{array}{llc} & \mathbf{Z} & \text { \% Deviation } \end{array}\)

A \(1.10 \quad 10\)
B \(1.2 \quad 20\)
C \(1.02 \quad 2\)
D \(1.2 \quad 15\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1.02 \quad 2\)

Step-by-step Solution

Detailed explanation

\(\mathrm{P}(\mathrm{V}-\mathrm{nb})=\mathrm{nRT} ; \mathrm{n}=1\) mole, \(\mathrm{T}=300 \mathrm{~K}, \mathrm{P}=100 \mathrm{bar}\) \(\therefore \quad 100(\mathrm{~V}-0.005)=1 \times 0.082 \times 1.013 \times 300\) or, \(\mathrm{V}=(0.249+0.005) \mathrm{L}\) or,…

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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