The following data were obtained during the first order thermal
decomposition of `SO_(2)Cl_(2)` at a constant volume `SO_(2)Cl_(2)(g)to SO_(2)(g)+Cl_(2)(g)`

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

Explanation

`SO_(2)Cl_(2)(g)toSO_(2)(g)+Cl_(2)(g)`
Proceeding exactly similar to Q. `4.20,k=(2.303)/(t)log""("P"_(0))/(2"P"_(0)-"P"_(t))`
When `t=100" s",k=(2.303)/(100" s")log""(0.5)/(2xx0.5-0.6)=(2.303)/(100s)log(1.25)=(2.303)/(100s)(0.0969)=2.2316xx10^(-3)s^(-1)`
When `P_(t)=0.65" atm, i.e.,"P_(0)+p=0.65" atm"`
`:.p=0.65-P_(0)=0.65-0.50=0.15" atm"`
`:." Pressure of "SO_(2)Cl_(2)" at time "t(p_(SO_(2)Cl_(2)))=P_(0)-p=0.50-0.15" atm"=0.35" atm"`
Rate at that time `=kxxp_(SO_(2)Cl_(2))=(2.2316xx10^(-3)s^(-1))(0.35" atm")=7.8xx10^(-5)" atm "s^(-1).`