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# Solution - Derive the Relation Between Half Life and Rate Constant for a First Order Reaction - Integrated Rate Equations - Half-life of a Reaction

ConceptIntegrated Rate Equations Half-life of a Reaction

#### Question

Derive the relation between half life and rate constant for a first order reaction

#### Solution

The integrated rate law for the first order reaction is given by the equation

k= 2.303/t log_10"[A]_o/[A]_t

Where [A]0 = initial concentration of the reactant at t = 0

The concentration falls to [A]t at time t from the start of the reaction.

The concentration of the reactant falls to [A]0/2 at time t1/2.
Therefore, t = t1/2
[A]t = [A]0/2
So, the equation can be written as

k= 2.303/t_(1/2) log_10"[A]_o /([A]_o/2)

=2.303/(t_1/2)log_10 2

=2.303/(t_1/2)*0.301=0.693/(t_1/2)

t_(1/2)=0.693/k

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March)
Question 2.4 | 2 marks
2016-2017 (March)
Question 2.2 | 2 marks
2013-2014 (March)
Question 3.4 | 2 marks

#### Video TutorialsVIEW ALL [1]

Solution for question: Derive the Relation Between Half Life and Rate Constant for a First Order Reaction concept: Integrated Rate Equations - Half-life of a Reaction. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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