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(B) The half-life $(t_{1/2})$ of an $n^{th}$ order reaction is related to the initial concentration $(a)$ of the reactant as $t_{1/2} \propto a^{1-n}$

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The half-life $(t_{1/2})$ of an $n^{th}$ order reaction is related to the initial concentration $(a)$ of the reactant as $t_{1/2} \propto a^{1-n}$.For two different initial concentrations,we have the relation: $\frac{(t_{1/2})_1}{(t_{1/2})_2} = \left(\frac{a_2}{a_1}ight)^{n-1}$.Given: $(t_{1/2})_1 = 5 \ 	ext{min}$,$a_1 = 0.1 \ M$ and $(t_{1/2})_2 = 50 \ 	ext{min}$,$a_2 = 0.01 \ M$.Substituting the values: $\frac{5}{50} = \left(\frac{0.01}{0.1}ight)^{n-1}$.$\frac{1}{10} = (0.1)^{n-1}$.$0.1^1 = (0.1)^{n-1}$.Comparing the exponents: $1 = n - 1$,which gives $n = 2$.

Initial Pressure $p$ (torr)	$707$	$79$	$37.5$
Half-life $t_{1/2}$ (min)	$84$	$84$	$84$

Observation	$[A] \ (mol \ L^{-1})$	$[B] \ (mol \ L^{-1})$	Rate $(mol \ L^{-1} \ sec^{-1})$
$1$	$0.1$	$0.1$	$2 \times 10^{-3}$
$2$	$0.4$	$0.1$	$3.2 \times 10^{-3}$
$3$	$0.1$	$0.2$	$8 \times 10^{-3}$

Half-life periods for a reaction at initial concentrations of $0.1 \ M$ and $0.01 \ M$ are $5$ and $50$ minutes,respectively. The order of reaction is

Similar Questions

The half-life periods of decomposition of $PH_3$ for different initial pressures are given below $:$
Initial Pressure $p$ (torr) $707$ $79$ $37.5$
Half-life $t_{1/2}$ (min) $84$ $84$ $84$
Determine the order of the reaction.

What is the order of reaction $A + B \to C$?

Observation $[A] \ (mol \ L^{-1})$ $[B] \ (mol \ L^{-1})$ Rate $(mol \ L^{-1} \ sec^{-1})$

$1$ $0.1$ $0.1$ $2 \times 10^{-3}$

$2$ $0.4$ $0.1$ $3.2 \times 10^{-3}$

$3$ $0.1$ $0.2$ $8 \times 10^{-3}$

Half-life of a reaction is found to be inversely proportional to the fifth power of its initial concentration,the order of reaction is

Which of the following statements is true regarding the order of a reaction?

Write the general equation of a reaction and explain what the order of reaction is. What are its possible values?

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