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Question

The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.

SO2Cl2(g)SO2(g)+Cl2(g)

ExperimentTime/s1Total pressure/atm100.521000.6

Calculate the rate of the reaction when total pressure is 0.65 atm.

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Solution

SO2Cl2(g)SO2(g)+Cl2(g)Initiallypi00After time tpippp
Total pressure after time t i.e.,
pt=pip+p+p=pi+p
So, a=pi
ax=pi(ptpi)=pipt+pi=2pipt
Substitutions of the value of a and (a-x) gives
k=2.303tlogpi(2pipt)

(a) Calculation of rate constant k
Given pi=0.5 atm;pt=0.6 atmk=2.303tlogpi(2pipt)=2.303(100 s)log0.5 atm0.4 atm=2.303(100 s)log1.25=2.303(100 s)×0.0969=2.23×103 s1

(b) Calculation of reaction rate when total pressure is 0.65 atm
pSO2Cl2=0.5(0.650.50)=(10.65)=0.35 atmk=2.23×103s1
Rate =k×pSO2Cl2=(2.23×103 s1)×(0.35 atm)
Rate =7.8×104 atm s1


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