In the case of a first-order reaction, the half-life (which is the time taken for half of the reactant to be used up in the reaction) can be calculated using the following formula: t1∕2=
0.693
k
where t1∕2 is the half-life and k is the rate constant of the reaction. Given that the rate constant k=2.772×10−3s−1, we can plug this into our formula to find the half-life: t1∕2=
0.693
2.772×10−3s−1
To calculate this, first divide 0.693 by 2.772×10−3 : t1∕2=
0.693
2.772×10−3
t1∕2=250s Therefore, the half-life of the reaction is 250 seconds. The correct option is: Option B : 250s