The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.
SO2Cl2(g)→SO2(g)+Cl2(g)
ExperimentTime/s−1Total pressure/atm100.521000.6
Calculate the rate of the reaction when total pressure is 0.65 atm.
SO2Cl2(g)→SO2(g)+Cl2(g)Initiallypi00After time tpi−ppp
Total pressure after time t i.e.,
pt=pi−p+p+p=pi+p
So, a=pi
a−x=pi−(pt−pi)=pi−pt+pi=2pi−pt
Substitutions of the value of a and (a-x) gives
k=2.303tlogpi(2pi−pt)
(a) Calculation of rate constant k
Given pi=0.5 atm;pt=0.6 atmk=2.303tlogpi(2pi−pt)=2.303(100 s)log0.5 atm0.4 atm=2.303(100 s)log1.25=2.303(100 s)×0.0969=2.23×10−3 s−1
(b) Calculation of reaction rate when total pressure is 0.65 atm
pSO2Cl2=0.5−(0.65−0.50)=(1−0.65)=0.35 atmk=2.23×10−3s−1
Rate =k×pSO2Cl2=(2.23×10−3 s−1)×(0.35 atm)
Rate =7.8×10−4 atm s−1