   # Carbon dioxide, CO 2 , was shown lo effuse through a porous plate at the rate of 0.033 mol/min. The same quantity of an unknown gas, 0.033 moles, is found to effuse through the same porous barrier in 104 seconds. Calculate the molar mass of the unknown gas. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 10, Problem 83GQ
Textbook Problem
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## Carbon dioxide, CO2, was shown lo effuse through a porous plate at the rate of 0.033 mol/min. The same quantity of an unknown gas, 0.033 moles, is found to effuse through the same porous barrier in 104 seconds. Calculate the molar mass of the unknown gas.

Interpretation Introduction

Interpretation:

The molar mass of the unknown gas has to be calculated.

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 of Solution

Given,

rate of CO2=0.033mol/minmass of unknown gas0.033molesrate of unknown gas =104s

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 CO2 rate of unkonwn gas = molar mass of unknownmolar mass of CO20.033mol/min104 s = molar mass of unknown44molar mass of unknown=3×44

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