   Chapter 12, Problem 113IP

Chapter
Section
Textbook Problem

# Sulfuryl chloride undergoes first-order decomposition at 320.°C with a half-life of 8.75 h. SO 2 Cl 2 ( g ) → SO 2 ( g ) + Cl 2 ( g ) What is the value of the rate constant, k, in s−1? If the initial pressure of SO2Cl2 is 791 torr and the decomposition occurs in a 1.25-L container, how many molecules of SO2Cl2 remain after 12.5 h?

Interpretation Introduction

Interpretation: The decomposition reaction of SO2Cl2 and its half-life at known temperature is given. The rate constant is to be calculated. The number of molecules of SO2Cl2 remain after 12.5h is to be determined for the given conditions.

Concept introduction: The half-life is defined as the time required for the concentration of reactant to be reduced to one-half of its initial value.

The integrated rate law for the first order reaction is given by,

ln[A]=kt+ln[A]0

The formula of ideal gas law is,

PV=nRT

To determine: The rate constant for the given first order reaction and the number of molecules of SO2Cl2 remains in container after a given time.

Explanation

Explanation

Given

Half-life of SO2Cl2 is 8.75h .

Formula

The rate constant for the first order reaction is calculated using the formula,

k=0.693t1/2

Where,

• k isthe rate constant.
• t1/2 isthe half-life.

Substitute the values of t1/2 in the above equation.

k=0.693t1/2=0.6938.75h=0.0792h1

As, 1h=3600s therefore,

k=0.0792h1=0.07923600s1=2.2×105s1_

Initial pressure is 791torr .

Volume of containeris 1.25L .

The temperature is 320°C .

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence, the conversion of 320°C into Kelvin is,

T(K)=T(°C)+273=(320+273)K=593K

The conversion of torr into atmospheric pressure (atm) is done as,

1torr=1760atm

Hence, the conversion of 791torr into (atm) is,

791torr=(791×1760)atm=1.04atm

Formula

The formula of ideal gas law is,

PV=nRTn=PVRT

Where,

• P isinitial pressure

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