The rate constant of a reaction at `700 K` and `760 K` are `0.011 M ^(-1) s^(-1)` and `0.105 M ^(-1) s^(-1)`respectively. Calculate the value of Arrhenius parameter.

Explanation

`"log" (k_2)/(k_1) = (E_a)/(2.303 R) xx [(T_2 - T_1)/(T_1 xx T_2)]` [A.E.]
`k_1 = 0.011 ms^(-1), T_1= 700 k, k_2 = 0.015 T_2= 760 K `
`"log" (0.105)/(0.11) = (E_a)/(2.303 xx 8.314)[(760 - 700)/(700 xx 760)]`
`0.9798 = (E_a xx 60)/(2.303 xx 8.314 xx 700 xx 760)`
`E_a = (0.9798 xx 2.303 xx 8.314 xx 700 xx 760)/(60)`
`E_a = 166.342 xx 10^3J "mol"^(-1)`
`= 166.342 KJ mo1^(-1)`
Now `log k = log A - (E_a)/(2.303 RT)`
`log A = log k + (E_a)/(2.303RT)`
`log A = log 0.011+ (166.342 xx 10^3)/(2.303 xx 8.3.14 xx 700 )`
`log A = - 1.9586 + 12.411 `
`A = log^(-1) 10,4524 `
`A = 10^10`