Half-life of a first order reaction at 25° C is 15 min. At 32°, half-life of same reaction is 10 min. Determine the ratio of the rate constants at the given temperatures.

Explanation

For a first order reaction, `t_(1//2)=(0.693)/(k)`
If `k_(1)` is the rate constant at `25^(@)C , k_(2)` is the rate constant at `32^(@)C` , then ,
`k_(1)=(0.693)/(t_(1//2))=(0.693)/(15)"min"^(-1)and k_(2)(0.693)/(t_(1//2))=(0.693)/(10)"min"^(-1)`
`therefore` The ratio of the rate constants, `(k_(1))/(k_(2))=(0.693//15)/(0.693//10)=0.666`