Question

11. Molecules having the least RMS velocity at constant temperature are
A) CO2
B) SO2
c) ClO2
D) NO2
​

Answer 1

Answer:

c) ClO2

Explanation:

Crms = √[3RT/M]

R = gas constant

T = temperature

M = molecular mass

Crms is inversly proprotional to √[1/M]

therefore higher the molecular mass less will Crms

CO2 = 44

SO2 = 64

ClO2 = 67.45

NO2 = 46

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Answer 2

Answer:

ClO₂ will have the least RMS velocity at constant temperature among the following gases.

Explanation:

Different types of velocities of the gas molecules:

The molecules of a gas are always in a random motion (Brownian motion). The velocity of each individual molecule in a specific amount/volume of gas is too difficult to calculate since each molecule contains different kinetic energies, and thus varying velocity.

For our convenience, we calculate the 'mean' or rather the average velocity of the gas molecules.

It can be expressed in three ways:

1. Most probable velocity (C* or $C_{mp}$ or $\mu_{mp}$)
2. Average velocity ($C_{av}$ or $\mu_{av}$)
3. Root Mean Square velocity ($C_{rms}$ or $\mu_{rms}$)

What is the root mean square velocity of a gas?

It is defined as the square root of the arithmetic mean of the square of the velocities of the different molecules of gas at a given temperature.

Mathematically, it can be written as:
$C_{rms} = \sqrt{\frac{3RT}{M} }$
where,
R = universal gas constant
T= temperature of the gaseous system
M = molar mass of the gas

Calculation:

∵ $C_{rms} = \sqrt{\frac{3RT}{M} }$
∴ $C_{rms} \propto \frac{1}{\sqrt{M} }$

This means that if gas has a higher molar mass, then it will possess a low RMS speed and vice-versa.

Thus, let us now calculate the molar masses of the four gases, i.e., CO₂, SO₂, ClO₂, NO₂.

The molar mass of CO₂ = 44 gm
The molar mass of SO₂ = 64 gm
The molar mass of ClO₂ = 67 gm
The molar mass of NO₂ = 46 gm

∴ We can see that ClO₂ has the highest molar mass among the following gas molecules and so the RMS of ClO₂ will be the least.

For more information on RMS speed, you can refer to the links below:

The RMS speed of molecules of a certain gas at 300K is 400 m/s. What will be the RMS speed, if the gas is heated to 600 K?
https://brainly.in/question/38153934

Calculate the RMS speed of an ideal diatomic gas having a molecular weight of 32gm/mol at 0°c.
https://brainly.in/question/7728013

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