   # Why do real gases not always behave ideally? Under what conditions does a real gas behave most ideally? Why? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 10RQ
Textbook Problem
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## Why do real gases not always behave ideally? Under what conditions does a real gas behave most ideally? Why?

Interpretation Introduction

Interpretation: The conditions at which ‘a real gas behaves most ideally’ should be explained.

Concept introduction:

• By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206Latm/Kmol )

T = temperature in kelvins

• Ideal gas is a hypothetical concept. No gases exactly follows the ideal gas law.
• Ideal gas law tends to hold best at low pressure and high temperature

A modified ideal gas equation for real gases on account of molecular size and molecular interaction forces    is termed as Van der Waals equation.

That is,                [P+a(nV)2](V-nb)=nRT

‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the individual gas

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

### Explanation of Solution

Explanation

At low pressure and high temperature the molar volume of gas will be relatively large and actual volume of the gas nb is very much smaller than the molar volume (V). So, these two terms can be neglected and Vander Waals equation becomes, PV=nRT

Van der Waals equation is

[P+a(nV)2](V-nb)=nRT

Byexpandingtheequation,[P+an2V2]×(V-nb)=nRTPV+an2VV2-nbP-an3bV2=nRTPV+an2V-nbP-an3bV2=nRT

At low pressure and high temperature molar volume of gas will be high

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