Question

Oxygen gas and sulphur dioxide gas are at same temperature. What is the ratio of the average velocity

Answer 1

Answer: At 327K, the root mean square velocity of both the gases will be equal.

Explanation: Root mean square velocity is related to the temperature and molar mass of the gas. It's expression is given by:



Where,

R = Gas constant

T = Temperature (in Kelvin)

M = Molar mass of gas

Now, we need to find the temperature at which root mean square velocity of and is same



Squaring and cancelling the terms on both the sides.













Putting values in above equation:







This is the temperature of at which root mean square vales of both the gases will be equal.

Answer 2

Graham law states that the rate of diffusion of a gas is inversely proportional to the square root of its atomic mass. And since they are at same temperature, the ratio of velocity would simply be ratio of the square root of their atomic masses.

Atomic mass of oxygen gas = 32 amu

Atomic mass of sulphur dioxide = 64 amu

ratio = rate of SO2 / rate of O2

= (32^1/2) ÷( 64^1/2)

Amswer = (32^1/2). ÷ (64^1/2)

NOTE -

x^1/2 symbolises square root of x

Hope it helps!

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