Chapter 19, Problem 19.37E

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437

Chapter
Section

### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437
Textbook Problem

# The mean free path depends on the ratio T / p . What value of T / p is necessary for the mean free path of He ( d = 65   pm ) to equal 130   pm ? How feasible do you think it will be to attain this ratio?

Interpretation Introduction

Interpretation:

The value of T/p that is necessary for He to have a mean free path of 130pm is to be calculated. The reason as to how it would be feasible to attain the corresponding ratio is to be stated.

Concept introduction:

The mean distance traveled by the same particle between two consecutive collisions is termed as a mean free path. The value of the mean free path of a gas depends on the pressure and temperature of the system. The mean free path of gas is represented as,

λ=kT2πd2p

Where,

T represents the temperature.

d collision diameter of a gas.

p represents the pressure.

k represents the Boltzmann constant with value 1.381×1023J/K.

Explanation

The collision diameter of He is 65â€‰pm.

The mean free path of He is 130â€‰pm.

The mean free path of gas is represented as,

Î»=kT2Ï€d2p â€¦(1)

Where,

â€¢ T represents the temperature.

â€¢ d collision diameter of a gas.

â€¢ p represents the pressure.

â€¢ k represents the Boltzmann constant with value 1.381Ã—10âˆ’23â€‰J/K.

Rearrange the equation (1) for the value of T/p the ratio.

Tp=2Ï€d2Î»k â€¦(2)

Substitute the value of k, d, Ï€ and Î» in the equation (2).

Tp=2(3.14)(65â€‰pm)2(10âˆ’12â€‰m1â€‰pm)3(130â€‰pm)(1

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