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The rate of decomposition for methyl nit...

The rate of decomposition for methyl nitrite and ethyl nitrite can be given in terms of rate constant `k_(1)` and `k_(2)` respectively. The energy of activation for the two reactions are `152.30 kJ mol^(-1)` and `157.7 kg mol^(-1)` as well as frequency factors are `10^(13)` and `10^(14)` respectively for the decomposition of methyl and ethyl nitrite. Calculate the temperature at which rate constant will be same for the two reactions.

Text Solution

Verified by Experts

According to Arrhenius equation, `k=Ae^(-E_(a)//"RT")`
For methyl nitrite, `k_(1)=10^(13)e^(-152300//8.314" T")`
For ethy nitrite, `k_(2)=10^(14)e^(-157700//8.314" T")`
It T is the temperature at which the rate constants are equal,
then `10^(13)e^(-152300//8.314" T")=10^(14)e^(-157700//8.314" T")`
or `e^(-152300//8.314" T")=10" e"^(-157700//8.314" T")`
Taking natural logarithm of both sides,
`(-152300)/(8.314" T")="ln " 10-(157700)/(8.314" T")`
or `(1)/(8.314" T")(157700-152300)=2.303" or "(1)/(8.314" T")=(2.303)/(5400)" or "T=282" K"`
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Knowledge Check

  • The rate of decomposition for methylnitrite and ethylnitrite can be given in terms of rate constant (in s^(-1))k_1 and k_2 . The energy of activations for the two reactions are 152.30 kJ // mol and 157.7 kJ // mol as well as frequency factors are 10^(13) and 10^(14) for the decomposition of methyl and ethyl nitrite. The temperature at which rate constant will be same for the two reactions is

    A
    298 K
    B
    287 K
    C
    282 K
    D
    273 K

  • The energy of activation of a first order reaction is 187.06 kJ mol^(-1) at 750 K and the value of pre-exponential factor A is 1.97xx10^(12)s^(-1) . Calculate the rate constant and half life. (e^(-30)= 9.35xx10^(-14))

    A
    k=0.184`s^(-1)` and `t_(1//2)`=3.76s
    B
    k=0.154`s^(-1)` and `t_(1//2)`=3.76s
    C
    k=0.184`s^(-1)` and `t_(1//2)`=2.76s
    D
    none of the above

  • The rate constant K_(1) of a reaction is found to be double that of rate constant K_(2) of another reaction. The relationship between corresponding activation energies of the two reaction at same temperature (E_(1) "and" E_(2)) can be represented as:

    A
    `E_(1) gt E_(2)`
    B
    `E_(1) lt E_(2)`
    C
    `E_(1)=E_(2)`
    D
    None of these