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Question

a) Derive integrated rate equation for the first order reaction.
b) According to collision theory, what are the two factors that lead to effective collisions?

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Solution

a) Integrated rate equation for the first order reaction:
The differential rate equation for the first order reaction is d[A]dt=k[A]
Rearrange and integrate between the limits
[A]=[A]0 at t=0 and [A]=[A]t at t=t
reaction is [A]t[A]0d[A][A]=kt0dt
[ln[A]][A]t[A]0=k(t)t0
ln[A]tln[A]0=kt
ln[A]t[A]0=kt
k=1tln[A]0[A]t
k=2.303tlog[A]0[A]t
b) According to collision theory, the two factors that lead to effective collisions are
(i) Molecules must collide with a certain minimum kinetic energy which is required to arrange outer electrons in breaking and making of bonds.
(ii) Molecules must collide with a certain minimum kinetic energy called activation energy.

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