Question:
The RMS velocity of $CO$ gas molecules at $27^{\circ}$C is approximately $1000\, m/s$. For $N_2$ molecules at $600 \,K$ the RMS velocity is approximately
The RMS velocity of $CO$ gas molecules at $27^{\circ}$C is approximately $1000\, m/s$. For $N_2$ molecules at $600 \,K$ the RMS velocity is approximately
Updated On: Feb 15, 2024
- 2000 m/s
- 1414 m/s
- 1000 m/s
- 1500 m/s
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The Correct Option is B
Solution and Explanation
As from the formula, $v_{ rms }=\sqrt{\frac{3 R T}{M}}$
Given that $\left(v_{ rms }\right)_{\infty}=1000\, m / s$
$( Temp .)_{ CO }=27^{\circ} C =300 K$
(Temp.) $_{ N _{2}}=600\, K$
Now putting the values, we get
$\frac{\left(v_{ rms }\right)_{ CO }}{\left(v_{ rms }\right)_{ N _{2}}}=\sqrt{\frac{3 R}{3 R} \times \frac{T_{ CO }}{M_{ CO }} \times \frac{M_{ N _{2}}}{T_{ N _{2}}}}$
$\frac{1000}{\left(v_{m s}\right)_{N_{2}}}=\sqrt{\frac{300}{28} \times \frac{28}{600}}$
$=\frac{1}{\sqrt{2}}$
or, $\left(v_{ ms }\right)_{ N _{2}}=1000 \times 1.414$
$=1414\, m / s$
Given that $\left(v_{ rms }\right)_{\infty}=1000\, m / s$
$( Temp .)_{ CO }=27^{\circ} C =300 K$
(Temp.) $_{ N _{2}}=600\, K$
Now putting the values, we get
$\frac{\left(v_{ rms }\right)_{ CO }}{\left(v_{ rms }\right)_{ N _{2}}}=\sqrt{\frac{3 R}{3 R} \times \frac{T_{ CO }}{M_{ CO }} \times \frac{M_{ N _{2}}}{T_{ N _{2}}}}$
$\frac{1000}{\left(v_{m s}\right)_{N_{2}}}=\sqrt{\frac{300}{28} \times \frac{28}{600}}$
$=\frac{1}{\sqrt{2}}$
or, $\left(v_{ ms }\right)_{ N _{2}}=1000 \times 1.414$
$=1414\, m / s$
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Concepts Used:
States of Matter
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
There are three States of Matter:
The three states of matter are as follows:
Solid State:
- The solid-state is one of the fundamental states of matter.
- Solids differ from liquids and gases by the characteristic of rigidity.
- The molecules of solids are tightly packed because of strong intermolecular forces; they only oscillate about their mean positions.
Liquid State:
- The molecules in a liquid are closely packed due to weak intermolecular forces.
- These forces are weaker than solids but stronger than that of gases.
- There is much space in between the molecules of liquids which makes their flowing ability easy.
Gaseous State:
- In this state of matter, distances between the molecules are large (intermolecular distance is in the range of 10-7-10-5 cm.
- The intermolecular forces experienced between them are negligible.
- Thus, translatory, rotatory and vibratory motions are observed prominently in gases.