Question:

The compressibility factor of an ideal gas is

Updated On: Jun 14, 2022
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The Correct Option is A

Solution and Explanation

compressibility factor is defined as :

$Z=\frac{P V}{(P V) \text { ideal }}=\frac{P V}{n R T}$

for non ideal gases, $ Z \neq 1$

for ideal gases. $Z=1$
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Concepts Used:

Van Der Waals Equation

Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases.

Read More: Derivation of Van Der Waals Equation

Derivation of Van der Waals equation:

For a real gas containing β€˜n’ moles, the equation is written as

Where, P, V, T, n are the pressure, volume, temperature and moles of the gas. β€˜a’ and β€˜b’ constants specific to each gas.

Where,

Vm: molar volume of the gas

R: universal gas constant

T: temperature

P: pressure

V: volume

Thus, Van der Waals equation can be reduced to ideal gas law as PVm = RT.

The equation can further be written as;

  1. Cube power of volume:
  2. Reduced equation (Law of corresponding states) in terms of critical constants:

Units of Van der Waals equation Constants

a: atm litΒ² mol-Β²

b: litre mol-ΒΉ