Question

For a first order reaction $A\to B$, the reaction rate at reactant concentration of 0.01 M is found to be $2.0\times {10}^{-5}mol{L}^{-1}{s}^{-1}$. The half-life period of the reaction is:

• A. 220 s
• B. 30 s
• C. 300 s
• D. 347 s

Answer 1

The correct option is D 347 s

For first order reaction,
$A⟶B$

Rate $=k\times \left[A\right]$

Given, rate $=2.0\times {10}^{-5}mol{L}^{-1}{s}^{-1}$
[A] = Conc. of A = 0.01 M

So, $2.0\times {10}^{-5}=k\times 0.01$

$k=\frac{2.0\times {10}^{-5}}{0.01}{s}^{-1}$

$=2.0\times {10}^{-3}{s}^{-1}$

For first order reaction,

$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{2.0\times {10}^{-3}}$

$=346.5=347s$