The rate of reaction increases isgnificantly with increase in temperature. Generally, rate of reactions are doubled for every `10^(@)C` rise in temperature. Temperature coefficient gives us an idea about the change in the rate of a reaction for every `10^(@)C` change in temperature.
`"Temperature coefficient" (mu) = ("Rate constant of" (T + 10)^(@)C)/("Rate constant at" T^(@)C)`
Arrhenius gave an equation which describes aret constant `k` as a function of temperature
`k = Ae^(-E_(a)//RT)`
where `k` is the rate constant, `A` is the frequency factor or pre-exponential factor, `E_(a)` is the activation energy, `T` is the temperature in kelvin, `R` is the universal gas constant.
Equation when expressed in logarithmic form becomes
`log k = log A - (E_(a))/(2.303 RT)`
For a reaction `E_(a) = 0` and `k = 3.2 xx 10^(8)s^(-1)` at `325 K`. The value of `k` at `335 K` would be

Options

A. `3.2 xx 10^(8) s^(-1)`
B. `6.4 xx 10^(8) s^(-1)`
C. `12.8 xx 10^(8) s^(-1)`
D. `25.6 xx 10^(8) s^(-1)`

Answer

A

Explanation

`(k_(325))/(k_(335)) = (Ae^(-E_(a)//Rxx325))/(Ae^(-E_(a)//Rxx335))`
or `(3.2 xx 10^(8)s^(-1))/(k_(335)) = (e^(-0//Rxx325))/(e^(-0//Rxx335)) or e^(0) = 1`
`:. k_(335) = 3.2 xx 10^(-8) s^(-1)`