   Chapter 10, Problem 49PS

Chapter
Section
Textbook Problem

A gas whose molar mass you wish to know effuses through an opening at a rate one third as fast as that of helium gas. What is the molar mass of the unknown gas?

Interpretation Introduction

Interpretation: The molar mass of the unknown gas should be determined by using the given condition that the gas effuses at one third rate as fast as that of helium gas.

Concept introduction:

Effusion:

The movement of gas particles through a small hole is defined as effusion. The rate of effusion for a gas is inversely proportional to the square root of the mass of gas particles.

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

μrms=(3RTM)1/2 (1)

(gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

Explanation

The molar mass of helium gas is 4 g/mol

Using Graham’s Law of effusion the molar mass of the unknown gas is calculated as follows,

rate of unkonwn gasrate of He = molar mass of Hemolar mass of unknown13=4molar mass of unknown4molar mass of unknown=19molar mass of unknown4=91molar mass of unknown=9×4

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