At 400K, the decomposition of gaseous `Cl_(2)O_(7) " to "Cl_(2) and O_(2)(g)` follows first order kinetics. (1 ) After 55s at 400k, the pressure of `Cl_(2)O_(7)(g)` falls from 0.062 to 0.044atm. Calculate k. (2) Calculate the pressure of `Cl_(2)O_(7)` at 100s after the beginning of decomposition.

Explanation

`" "Cl_(2)O_(7)(g)rarrCl_(2)(g)+(7)/(2)O_(2)(g)`
`{:("Initial pressure":,P_(i),0,0),("Pressure at 100s:",(P_(i)-p),p,(7)/(2)p):}`
[p = decrease in pressure of `Cl_(2)O_(7) " at " t=100s]`
(1) Given : `P_(i)=0.062"atm"and P_(i)-p=0.044"atm"`
For a first order reaction , `k=(2.303)/(t)log.(a)/(a-x)`
Here, `aprop P_(i) and (a-x)prop (P_(i)-p)`
`thereforek=(2.303)/(t)log.(P_(i))/(P_(i)-p)=(2.303)/(55)log.(0.062)/(0.044)=6.23xx10^(-3)s^(-1)`
(2) Given : t = 100s `thereforek=(2.303)/(t)log.(P_(i))/(P_(i)-p)`
or, `6.23xx10^(-3)=(2.303)/(100)log.(0.062)/((P_(i)-p))`
or, `P_(i)-p=0.033"atm"`
`therefore` The pressure of `Cl_(2)O_(7) " at" 100s= 0.033"atm"`