A first order reaction has rate constant k=5.5X10^-14s^-1 find its half life period. Also find time taken for 75% of reaction to over.

Dear Student

Rate Constant, k = 5.5 x 10^-14 s^-1

t_1/2 = ???

We know, 

t_1/2 = $\frac{0.693}{k}$

       = ​$\frac{0.693}{5.5. x {10}^{-14} s^{-1}}$ = 0.126 x 10¹⁴ sec or 1.26 x 10¹³ sec


We know, for First Order Reaction-

Rate Constant, k = $\frac{2.303}{t} \log$ ($\frac{a}{a - x}$)
Now, t = ??? and x = 0.75 a

Therefore, t = $\frac{2.303}{5.5 x {10}^{-14} s^{-1}} \log$ ($\frac{a}{a - 0.75 a}$)

                     = ​$\frac{2.303}{5.5 x {10}^{-14} s^{-1}} \log$ (​$\frac{1}{0.25}$) = 0.418 x 10¹⁴ log (​$\frac{1}{0.25}$) = 4.18 x 10¹³ log 4

                   = ​4.18 x 10¹³ x 0.6020 = 2.516 x 10¹³ s


Regards