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The rate of reaction increases isgnifica...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(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)`
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Knowledge Check

  • 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 which of the following reactions k_(310)//k_(300) would be maximum?

    A
    `P + Q rarr R, E_(a) = 10 kJ`
    B
    `E + F rarr D, E_(a) = 21 kJ`
    C
    `A + B rarr C, E_(a) = 10.5 kJ`
    D
    `L+M rarr N, E_(a) = 5 kJ`

  • 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) Activation energies of two reaction are E_(a) and E_(a)' with E_(a) gt E'_(a) . If the temperature of the reacting systems is increased form T_(1) to T_(2) ( k' is rate constant at higher temperature).

    A
    `(k_(1)')/(k_(1)) = (k_(2)')/(k_(2))`
    B
    `(k_(1)')/(k_(1)) lt (k_(2)')/(k_(2))`
    C
    `(k_(1)')/(k_(1)) gt (k_(2)')/(k_(2))`
    D
    `(k_(1)')/(k_(1)) gt (2k_(2)')/(k_(2))`

  • 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 the given reactions, following data is given {:(PrarrQ,,,,k_(1) =10^(15)exp((-2000)/(T))),(CrarrD,,,,k_(2) = 10^(14)exp((-1000)/(T))):} Temperature at which k_(1) = k_(2) is

    A
    `434.22 K`
    B
    `1000 K`
    C
    `2000 K`
    D
    `868.44 K`

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