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The diffusion coefficient of an ideal gas is proportional to i

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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is....

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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases

x

times. The value of

x

is....

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Text solutionVerified

(4) (DC) Diffusion coefficient

\propto λ

(mean free path)

\propto U_{mean}

Thus

(DC) \propto λ U_{mean}

But,

λ = \frac{RT}{2 N _{0} σ p} \Rightarrow λ \propto \frac{T}{p}

and

U_{mean} = \frac{8 RT}{π M} \Rightarrow U_{mean} \propto T

∴ DC \propto \frac{( T ) ^{3/2}}{p}

\frac{( DC ) _{2}}{( DC ) _{1}} (x) = (\frac{p _{1}}{p _{2}}) (\frac{T _{2}}{T _{1}})^{3/2} = (\frac{p _{1}}{2 p _{1}}) (\frac{4 T _{1}}{T _{1}})^{3/2} = (\frac{1}{2}) (8) = 4

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Question Text	The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is....
Updated On	Feb 7, 2023
Topic	States of Matter
Subject	Chemistry
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	526
Avg. Video Duration	5 min

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is....

Text solutionVerified

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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is....

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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases $x$ times. The value of $x$ is....