From the given rate of effusion of two gases, molar mass of the unknown gas should be determined. Concept introduction: Effusion is used to describe the passage of a gas through a tiny particle into an evacuated chamber. The rate of effusion is the measure speed at which the gas is transferred to the chamber. According to Thomas Graham the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. The relative rate of effusion of two gases at the same temperature and pressure are the inverse ratio of the square root of the masses of the gases particles. That is, R a t e o f e f f u s i o n f o r g a s 1 R a t e o f e f f u s i o n f o r g a s 2 = M 2 M 1 o r R a t e 1 R a t e 2 = ( M 2 M 1 ) 1 / 2 M 1 and M 2 are the molar masses of twogases This equation is known as Graham’s law of effusion.

Question

An expression for the root mean square velocity, vrms, of a gas was derived. Using Maxwell’s velocity distribution, one can also calculate the mean velocity and the most probable velocity (mp) of a collection of molecules. The equations used for these two quantities are vmean=(8RT/πM)1/2 and vmp=(2RT/M)1/2 These values have a fixed relationship to each other.(a) Arrange these three quantities in order of increasing magnitude.(b) Show that the relative magnitudes are independent of the molar mass of the gas.(c) Use the smallest velocity as a reference for establishing the order of magnitude and determine the relationship between the larger and smaller values.

Answer 1

Question

Chapter 5, Problem 120E

Interpretation Introduction

Interpretation: From the given rate of effusion of two gases, molar mass of the unknown gas should be determined.

Concept introduction:

Effusion is used to describe the passage of a gas through a tiny particle into an evacuated chamber.

The rate of effusion is the measure speed at which the gas is transferred to the chamber.

According to Thomas Graham the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

The relative rate of effusion of two gases at the same temperature and pressure are the inverse ratio of the square root of the masses of the gases particles. That is,

Rate of effusion for gas 1Rate of effusion for gas 2 =M2M1orRate1Rate2 = (M2M1)1/2

M1 and M2 are the molar masses of twogases

This equation is known as Graham’s law of effusion.

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