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Half-Life of a First Order Reaction
Appears in
Concepts tested here
- Half-life is independent of concentration
- Rate constant from rate and concentration
All Questions
2007 AIPMT-PRE 1 question
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In a first-order reaction $A \rightarrow B$, if $k$ is rate constant and initial concentration of the reactant A is 0.5 M, then the half-life isFor a first order reaction: $k = \dfrac{2.303}{t}\log_{10}\dfrac{a}{a - x}$
When $t = t_{1/2}$, $x = \dfrac{a}{2}$
$k = \dfrac{2.303}{t_{1/2}}\log_{10}\dfrac{a}{a - a/2}$
$k = \dfrac{2.303}{t_{1/2}}\log_{10}2$
$t_{1/2} = \dfrac{2.303}{k}\log_{10}2 = \dfrac{\ln 2}{k} = \dfrac{0.693}{k}$
The initial concentration cancels out, so the half-life of a first order reaction does not depend on the initial concentration (0.5 M here).
So the half-life is $\dfrac{\ln 2}{k}$.
2005 AIPMT 1 question
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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 :-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