The energy of activation of a first order reaction is 187.06 kJ mol−1 at 750 K and the value of pre-exponential factor A is 1.97×1012s−1. Calculate the half life. (e−30=9.35×10−14)
3.76s
Let’s start from half life.
For first order reaction,
Half life (t1/2) = 0.693k
But we don’t know the rate constant.
But wait, we can calculate the rate constant easily by Arrhenius Equation.
We know Ea, A and T.
Ea= 187.06 kJ mol−1
T = 750 K
R=8.314 J K−1 mol−1
We know,
k=Ae−Ea/RT
∴EaRT=187.06×1038.314×750=30
∴k=Ae−30=1.97×1012×9.35×10−14
k = 0.184 s−1
Half life (t1/2) = 0.693k = 0.6930.184 = 3.76s