At a moderate pressure, the van der Waals' equation is written as [p+(a/V2)] V=R T The compressibility factor is equal to

Question

At a moderate pressure, the van der Waals' equation is written as [p+(a/V2)] V=R T The compressibility factor is equal to (A) (1-(a/R T V)) (B) (1-(R T V/a)) (C) (1+(a/R T V)) (D) (1+(R T V/a))

Tardigrade Admin · Accepted Answer

From the given equation [p+(a/V2)] V=R T p V+(a/V)=R T (p V/R T)+(a/R T V)=1 (p V/R T)=Z text (Compressibility factor) =(1-(a/R T V))

Q. At a moderate pressure, the van der Waals' equation is written as
$[p + \frac{a}{V ^{2}}] V = RT$
The compressibility factor is equal to

$(1 - \frac{a}{RT V})$

$(1 - \frac{RT V}{a})$

$(1 + \frac{a}{RT V})$

$(1 + \frac{RT V}{a})$

From the given equation
$[p + \frac{a}{V ^{2}}] V = RT$
$p V + \frac{a}{V} = RT$
$\frac{p V}{RT} + \frac{a}{RT V} = 1$
$\frac{p V}{RT} = Z (Compressibility factor) = (1 - \frac{a}{RT V})$

Q. At a moderate pressure, the van der Waals' equation is written as [p+V2a​]V=RT The compressibility factor is equal to

(1−RTVa​)

(1−aRTV​)

(1+RTVa​)

(1+aRTV​)