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Q.

Molecules having the least RMS velocity at constant temperature are

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a

CO2

b

SO2

c

ClO2

d

NO2

answer is C.

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Detailed Solution

Mathematically, it can be written as:
Question Image
where,
R = universal gas constant
T= temperature of the gaseous system
M = molar mass of the gas

Calculation:

Question Image
Question Image

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.

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