The rate constant and half-life of a first order reaction at temperature `T_(1) " are " k_(1)"min"^(-1) and x_(1) min` , respectively and those at temperature `T_(2) " are "k_(2) "min"^(-1) and x_(2)` min , respectively. If `T_(2)gtT_(1)` , which is greater , `x_(1) " or, " x_(2)` ?

Explanation

The half -life of a first order reaction , `t_(1//2) = (0.693)/(k) ` where k = rate constant.
At `T_(1)K,x_(1)=(0.693)/(k_(1)) " min and at "T_(2)K,x_(2)=(0.693)/(k_(2))"min"`
The value of the rate constant increases with rise in temperature.
Since `T_(2)gtT_(1),k_(2)gtk_(1)and x_(1)gtx_(2)`