At very high pressures, the compressibility factor of one mole of a gas is given by :

1 + \frac{p b}{R T}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 - \frac{p b}{R T}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 - \frac{b}{(V R T)}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{p b}{R T}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1 + \frac{p b}{R T}$
At very high pressures, the compressibility factor of one mole of a gas is given by :

$1 + \frac{p b}{R T}$

The vander waals equation for 1 mole of gas is :

$(p + \frac{a}{V^{2}}) (V - b) = R T$

At very high pressure, the ratio $\frac{a}{V^{2}}$ can be neglected in comparison to p, the equation becomes :

$p (V - b) = R T$

$p V = R T + p b$

Hence, the compressibility factor :

$Z = \frac{p V}{R T} = 1 + \frac{p b}{R T}$

Hence, the correct option is A.

Suggest Corrections

Similar questions

Q. The compressibility factors for 1 mole of real gases at low pressure, high pressure and that of gases of very low molar masses are

Z_{1}, Z_{2}

and

Z_{3}

. These are

Q. If

Z

is a compresibility factor, van der waals equation at low pressure can be written as:

Q. Match the van der Waal's equation for one mole of gas given in column B to the conditions given in column A.

Column A	Column B
(A) High pressure	(i) $P V = R T + P b$
(B) Low pressure	(ii) $P V = R T - \frac{a}{V}$
(C) $P \to 0$	(iii) $P V = R T$
(D) Neither $a$ nor $b$ is negligible	(iv) $(P + \frac{a}{V^{2}}) (V - b) = R T$

Q. Assertion :The compressibility factor for

H_{2}

and

H e

[1 + \frac{P b}{R T}]

. Reason: The compressibility factor for

H_{2}

and

H e

can be derived from van der Waal's equation.

The given graph in Fig represents the variation of Z $(c o m p r e s s i b i l i t y f a c t o r = \frac{p V}{n R T}$ ) vs.P , for the three real gases A,B and C.identify the only incorrect statement
$1 - \frac{p b}{R T}$

Join BYJU'S Learning Program