Rate Equation for the Zero Order Reaction

Rate Equation for the Zero Order Reaction:

Consider the general reaction-

A ———-> Products

Let [A]₀ be the initial concentration of ‘A’ and [A] is the concentration at time ‘t’ sec.

As it is a zero-order reaction-

Rate = -d[A]/dt = k[A]^° = k₀ [Where ‘k₀‘ is rate constant of zero order
or -d[A] = k₀ dt ………(i)

Integrating both sides of the equation (i), we get
+ ∫d[A] = -k₀ ∫dt
⇒ + [A] = -k₀ . t + I ………(ii) [Where ‘I’ is constant of integration]

When t = 0 ; [A] = [A]₀
∴ [A]₀ = I ………(iii)

Put equation (iii) in equation (ii), we get-
[A] = -k₀ . t + [A]₀
or k₀ . t = [A]₀ – [A]
⇒ k₀ = 1/t {[A]₀ – [A]}
It is an integrated rate equation for zero order reaction.

Units of k₀ = (1/sec) (mole/litre) = mole litre^-1 sec^-1

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