The decomposition of `Cl_(2)O_(7)` at 400 K in the gas phase to `Cl_(2)`
and `O_(2)` is a first order reaction.
(i) After 50 seconds at 400 K, the pressure of `Cl_(2)O_(7)` falls
from 0.062 to 0.044 atm. Calculate the rate constant.
(ii) Calculate the pressure of `Cl_(2)O_(7)` after 100 sec of
decomposition at this temperature.

Explanation

`apropP_(0)" and "(a-x)propP_(t)."Hence, "k=(2.303)/(t)log""(P_(0))/(P_(t))" "(P_(t)=" pressure of "Cl_(2)O_(7)" at time t")`
(i) `t=50" sec",P_(0)=0.062" atm",P_(t)=0.044" atm. "k=(2.303)/(50" s")log""(0.062" atm")/(0.044" atm")=6.86xx10^(-3)s^(-1)`
(ii) `t=100" sec ",P_(t)=?k=6.86xx10^(-3)s^(-1)`
`6.86xx10^(-3)s^(-1)=(2.303)/(100s)log""(0.062" atm")/(P_(t))`
`log""(0.062)/(P_(t))=0.2979" or "(0.062)/(P_(t))="Antilog"0.2979=1.986" or "P_(t)=0.0312" atm"`