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JEE Advanced

Exam: JEE Advanced
Subject: Chemistry
Chapter: States of Matter

JEE Advanced · Chemistry · States of Matter

Select the incorrect option about collision frequency(z) for a...

Select the incorrect option about collision frequency(z) for a given gas

Options

AAt constant temperature Z increases with increase in pressure
BAt constant pressure $\mathbf{Z}$ decreases with increase in temperature
CAt constant volume Z increases with increase in pressure
DAt constant volume $\mathbf{Z}$ decreases with increase in temperature

Correct answer

D. At constant volume $\mathbf{Z}$ decreases with increase in temperature

Step-by-step solution

\begin{aligned} & Z=\frac{\pi d^2 \sqrt{2} \overline{\mathbf{C}} P}{k T} \\ & Z \propto \overline{\mathbf{C}} \times \frac{\mathbf{P}}{\mathbf{T}} \propto \sqrt{\mathrm{T}} \times \frac{\mathbf{P}}{\mathbf{T}} \propto \frac{\mathbf{P}}{\sqrt{T}} \end{aligned}

So, when

T

is constant

Z \propto P

When

P

is constant

Z \propto \frac{1}{\sqrt{T}}

At constant

\mathrm{V}, \mathrm{Z}

is governed by

\overline{\mathrm{C}}

, here

\mathbf{Z} \propto \sqrt{\mathbf{P}}

or

\sqrt{\mathbf{T}}

So, when volume is constant

\mathbf{Z} \propto \sqrt{\mathbf{T}} \notin \mathbf{Z} \propto \sqrt{\mathbf{P}}

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