   Chapter 10, Problem 50PS

Chapter
Section
Textbook Problem

A sample of uranium fluoride is found to effuse at the rate of 17.7 mg/h. Under comparable conditions, gaseous I2 effuses at the rate of 15.0 mg/h. What is the molar mass of the uranium fluoride? (Hint: Rates must be converted to units of moles per time.)

Interpretation Introduction

Interpretation: The molar mass of the uranium fluoride gas with given effusion rate should be determined by using the given condition that the I2 gas effuses at rate of 15.0 mg/h.

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

Given,

Effuse rate of Uranium fluoride, r1 = 17.7mg/hEffuse rate of I2,r2=15mg/h

The molar mass of helium gas is 4 g/mol

Using Graham’s Law of effusion the molar mass of the uranium fluoride is calculated as follows,

Molar mass of uranium fluoride = MM1Molar mass of I2 = MM2r1r2 = MM2MMl(r1r2)2=MM2MMl

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