Question

For a real gas at high pressure, the compression factor is:

A. 1

B. $$1 + \frac{Pb}{RT}$$

C. $$1 - \frac{Pb}{RT}$$

D. $$1 + \frac{RT}{Pb}$$

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Answer

:

The correct answer is B.

For one mole of a real gas, the Van der Waals equation is given by:

$$ \left(P + \frac{a}{V^2}\right)(V - b) = RT $$

Rewriting this, we get:

$$ PV = RT + Pb + \frac{ab}{V^2} - \frac{a}{V} $$

At high pressure, the Van der Waals equation simplifies to:

$$ PV = RT + Pb $$

Dividing through by $RT$, we have:

$$ \frac{PV}{RT} = 1 + \frac{Pb}{RT} $$

Thus, the compressibility factor (Z) is:

$$ Z = \frac{PV}{RT} = 1 + \frac{Pb}{RT} $$

Hence, the correct option is B.


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