The decomposition reaction `2N_(2)O_(5) (g) rarr 2N_(2) O_(4) (g) +O_(2) (g)` is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After `Yxx10^(3)` s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is `5xx10^(-4) s^(-1)`, assuming ideal gas behavior, the value of Y is

Answer

2.3

Explanation

For the reaction
`N_(2)O_(5) (g) overset(triangle)to N_(2)O_(4)(g)+1/2 O_(2)(g)`
`"At t =0 1 0 0"`
`"At t =t 1-x x x/2"`
It is given that 1-x+x+(x/2)=1.45. Therefore, x/2=1.45 or x=0.9. Now that rate constant is `5 xx 10^(-4)s`. As this is a first order reaction, the rate constant is given as
`k=(2.303)/(2t) log (p_(0)/p_(t)) .......(1)`
where `p_(t)=1-x=1-0.9=0.1` atm. Substituting values in Eq. (1) we get
`5 xx 10^(-4) =(2.303)/(2 xx t) log ((1.0)/(1-0.9))`
`t=(2.303)/(2 xx 5 xx 10^(-4)) log ((1.0)/(1-0.9)) rArr t=(2.303)/(2 xx 5 xx 10^(-4)) =2.3 xx 10^(3) s`