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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
States of Matter

NTA Abhyas 2020 · Chemistry · States of Matter

The diffusion coefficient of an ideal gas is proportional to its...

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

Correct answer

4

Step-by-step solution

Diffusion coefficient ∝∝ mean free path ×\times mean speed

D ∝ \overset{̄}{i} \times \overset{̄}{c}

But \overset{̄}{i} = \dfrac{1}{\sqrt{2}\pi{\sigma}^{2}}\dfrac{RT}{P{N}_{0}}

or \overset{̄}{i} ∝ \dfrac{T}{P} and \overset{̄}{c} = \sqrt{\dfrac{8RT}{\piM}}

or \overset{̄}{c} ∝ \sqrt{\dfrac{T}{M}}

So D∝TP.TMD ∝ \dfrac{T}{P} . \sqrt{\dfrac{T}{M}} or D∝T32PMD ∝ \dfrac{{T}^{\dfrac{3}{2}}}{P\sqrt{M}}

or D1D2=(T4T)32(2PP)=(14)32×2\dfrac{{D}_{1}}{{D}_{2}} = {\left(\dfrac{T}{4T}\right)}^{\dfrac{3}{2}}\left(\dfrac{2P}{P}\right) = {\left(\dfrac{1}{4}\right)}^{\dfrac{3}{2}} \times 2

=(12)3×2=14= {\left(\dfrac{1}{2}\right)}^{3} \times 2 = \dfrac{1}{4}

or D2=4D1{D}_{2} = 4{D}_{1}
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