Question

What is first order reaction? Derive the integrated rate equation for first order reaction.

Answer 1

Hey mate here's your answer

A reaction is said to be first order if its rate is determined by the change of one concentration term only.

One can say that a first order reaction is one whose rate varies as 1st power of the concentration of the reactant i.e. the rate increases as number of times as the number of times the concentration of reactant is increased.

Consider the reaction

A → products

Let

[A]O = Initaial Concentration of A

[A]t = The concentration of A after time t

For the reaction to be of first order..

Rate = -\frac{d[A]]}{dt} = k[A]

\Rightarrow \frac{d[A]}{[A]} =-kdt...(i)

Intigrating this equation

\int_{[A]_o}^{[A]} \frac{d[A]}{[A]} =-k\int_{0}^{t}dt

we get

ln [A] - ln[A]o = -K(t-0)

ln\frac{[A]}{[A]_o} = -kt

\Rightarrow ln\frac{[A]_o}{[A]} = kt…...... (ii)

\Rightarrow log\frac{[A]_o}{[A]} = \frac{kt}{2.303}...(iii)

\Rightarrow k= \frac{1}{t}ln\frac{[A]_o}{[A]}....(iv)

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