On introducing a ctatlyst at 500 K, the rate of a first order reaction increases by 1.718 times. The activation energy in the presence of a catalyst is `60.5 kJ "mol"^(-1)`. The slop of the plot of In k `(sec^(-1))` against 1/T in the absence of catalyst is :

Options

A. `+1`
B. `-1`
C. `+1000`
D. `-1000`

Explanation

`("Rate in presence of catalyst")/("Rate in absence of catalyst")="Antilog"[(+DeltaE)/(2.030R)]`
`1.718="Antilog"=(E_(a)-E_(p))/(2.303xx8.314xx500)`
`E_(a)-E_(p)=2.25 kJ`
`E_(a)=E_(p)+2.25=6.05+2.25=8.30 kJ"mol"^(-1)`
`=8.3 kJ "mol"^(-1)`
In k= In `A-(E_(a))/(R)xx(1)/(T)`
Slope `=(-E_(a))/(R)=(-8.3xx1000)/(8.3)=-1000`