Question

The energy of activation of a first order reaction is $187.06kJmo{l}^{-1}$ at 750 K and the value of pre-exponential factor A is $1.97\times {10}^{12}{s}^{-1}$. Calculate the half life. $(e^{-30}=9.35\times {10}^{-14})$

• A. 9.76s
• B. 5.76s
• C. 8.76s
• D. 3.76s

Answer 1

The correct option is D 3.76s

Let’s start from half life.

For first order reaction,
Half life $\left(t_{1/2}\right)=\frac{0.693}{k}$

But we don’t know the rate constant.
But wait, we can calculate the rate constant easily by Arrhenius Equation.

We know $E_a$, A and T.

$E_a=187.06kJmo{l}^{-1}$

T = 750 K

$R=8.314J{K}^{-1}mo{l}^{-1}$

We know,
$k=A{e}^{-Ea/RT}$

$\therefore \frac{E_a}{RT}=\frac{187.06\times {10}^3}{8.314\times 750}=30$

$\therefore k=A{e}^{-30}=1.97\times {10}^{12}\times 9.35\times {10}^{-14}k=0.184s^{-1}Halflife\left(t_{1/2}\right)=\frac{0.693}{k}=\frac{0.693}{0.184}=3.76s$