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The rate constant of a reaction is 1.5 x...

The rate constant of a reaction is `1.5 xx 10^(7)s^(-1)` at `50^(@)C` and `4.5 xx 10^(7) s^(-1)` at `100^(@)C`. Evaluate the Arrhenius parameters `A` and `E_(a)`.

Text Solution

Verified by Experts

Given that
`T_1 = 50^@C + 273 = 323K` `T_2 = 100^@C C + 273 = 373K`
`k_1` is the rate constant at `T_1= 1.5xx 10^7 s^(-1)` (for first order reaction)
`k_2` is the rate constant at `T_2 = 4.5 xx 10^7s^(-1)` (for first order reaction)
R = 8.314 J/K/mol
On the basis of modified form of Arrhenius equation following equation is written for two different absolute termperatures.
`log_10""k_2/k_1 =E_a/(2.303R) ((T_2-T_1)/(T_1T_2))`
`E_a = 2.2 xx 10^4 J//mol^(-1)`
Now `k = Ae^(-E_a//RT)` (Arrhenius equation)
`4.5 xx 10^7 = Ae^(-2.2xx 10^4//8.314 xx 300)`
Frequency factor (A) `=5.42 xx 10^10s^(-1)`
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