Statement : At high pressure, the value of the compression factor Z is (1 + (p b)/(R T)). Reason : At high pressure, the Van der Waals equation becomes P(V-b) = RT. A : If both the statement and the reason are true and the reason correctly explains the statement. B : If both the statement and the reason are true but the reason does not correctly explain the statement. C : If the statement is true but the reason is false. D : If both the statement and the reason are false.
Question
Statement: At high pressure, the value of the compression factor $\mathrm{Z}$ is $\left(1+\frac{p b}{R T}\right)$.
Reason: At high pressure, the Van der Waals equation becomes $P(V-b)=RT$.
- A: If both the statement and the reason are true and the reason correctly explains the statement.
- B: If both the statement and the reason are true but the reason does not correctly explain the statement.
- C: If the statement is true but the reason is false.
- D: If both the statement and the reason are false.
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Answer
The correct answer is: A
According to the van der Waals equation: $$ \left(P + \frac{a}{V^2}\right)(V - b) = RT $$
At high pressure, the equation simplifies to: $$ P(V - b) = RT \implies PV - Pb = RT $$
Dividing the entire equation by $RT$, we get: $$ \frac{PV}{RT} = 1 + \frac{Pb}{RT} $$
Given that $ \frac{PV}{RT} = Z $, the compressibility factor $Z$ can be expressed as: $$ Z = 1 + \frac{Pb}{RT} $$