The reaction
`2NO_(2)rarr2NO+O_(2)`
has an activation energy of `110 KJ mol^(-)`. At `400^(@)C`, the rate constant is `7.8mol^(-1)Ls^(-1)`. What is the value of rate constant at `430^(@)C` ?

Explanation

We know that
`log.(k_(2))/(k_(1))=(E_(a))/(2.303R)[(1)/(T_(1))-(1)/(T_(2))]`
`E_(a) = 110 KJmol^(-1)`
`=110xx10^(3)Jmol^(-1), R= 8.314 mol^(-1)K^(-1)`
`{:(k_(1)=7.8mol^(-1)L s^(-1),,T_(1) = 400+273 = 673K,,),(k_(2)=?,,T_(2) = 430 + 273 = 703 K,,):}`
Substituting the values,
`:. log.(k_(2))/(7.8) = (110 xx 10^(3))/(2.303 xx 8.314)[(1)/(673)-(1)/(703)]`
`= (110 xx 10^(3) xx (703-673))/(2.303 xx 8.314 xx 673 xx 703)`
`= 0.3643 or (k_(2))/(7.8) = 2.31`
or `k_(2) = 2.31 = 7.8 = 18.0 mol^(-1) L s^(-1)`