Question

When speafic rate constant is 2 min-1. The half life period of a first order reaction is ​

Answer 1

Answer:

The order of the reaction is second, and the value of k is 0.0269 M-2s-1. Since the reaction order is second, the formula for t1/2 = k-1[A]o-1. This means that the half life of the reaction is 0.0259 seconds.

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1/Concentration(M-1) Time (s)

1 10

2 20

3 30

Explanation:

Answer 2

Answer and Explanation:

$\diamond$ Specific rate constant or rate constant is the proportionality constant for rate equation

$\diamond$ We know that, rate of reaction is proportional to concentration of reactants

$\diamond$ For a reaction, $A+B \rightarrow C + D$

$r \propto [A]^x[B]^y$

$r = k[A]^x[B]^y$

Hence,

$k = \dfrac{r}{[A]^x[B]^y}$

$\diamond$ Here, (x + y) is known as the overall order of the reaction

$\diamond$ For different order reaction, there is different units for rate constant

$\diamond$ For first order reaction,

$k = \dfrac{r}{[A]^x[B]^y}$

$k = \dfrac{r}{[A]^1}$

Unit of k = $\dfrac{mol \ L^{-1} s^{-1}}{(mol \ L^{-1})^{ 1}}$

Unit of k = s⁻¹ or min⁻¹

$\diamond$ Hence, for a first order reaction, unit of rate constant is the inverse of unit of time

$\diamond$ In this case it is 2 min⁻¹

$\diamond$ The half life time-period of a first order reaction is given by

$\boxed{t_{\frac{1}{2} }=\dfrac{0.693}{k} }$