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For a first order reaction A $\rightarrow$ B the reaction rate at reactant concentration of 0.01 M is found to be $2.0 \times 10^{-5}$ mole L$^{-1}$ s$^{-1}$. The half life period of the reaction is :-
A
300 s
B
30 s
C
220 s
D
347 s
Detailed Solution
For a first order reaction, rate $= k[A]$
$k = \dfrac{\text{rate}}{[A]} = \dfrac{2.0 \times 10^{-5}}{0.01}$
$k = 2.0 \times 10^{-3}$ s$^{-1}$
Half-life: $t_{1/2} = \dfrac{0.693}{k}$
$t_{1/2} = \dfrac{0.693}{2 \times 10^{-3}}$
$t_{1/2} = 346.5 \approx 347$ s
$k = \dfrac{\text{rate}}{[A]} = \dfrac{2.0 \times 10^{-5}}{0.01}$
$k = 2.0 \times 10^{-3}$ s$^{-1}$
Half-life: $t_{1/2} = \dfrac{0.693}{k}$
$t_{1/2} = \dfrac{0.693}{2 \times 10^{-3}}$
$t_{1/2} = 346.5 \approx 347$ s