Question

By taking a suitable example, describe the initial rate method for the determination of the order of a reaction.

Answer 1

\[\ce{A + B + C -> Products}\]

The initial rate of this reaction can be expressed as

(Rate)_{t = 0} = [A]^P [B]^q [C]^r

Suppose that the reaction's initial rate is R. The following process is used to determine the values of p, q, and r.

1. The concentration of A is doubled while the concentrations of B and C remain unchanged. Once more, the reaction's beginning rate is established. Assume that the new rate is 4R, meaning that when the concentration of A doubles, the rate increases four times. Of course,
   Rate ∝ [A]²
   Thus, the reaction is of second order with respect to A and p = 2.
2. At this point, the concentration of B has doubled while A and C are kept at constant levels. Again, the reaction's initial rate is determined. Suppose that the new rate is R, meaning that changing the concentration of B has no effect on the rate of reaction. Of course,
   Rate ∝ [B]⁰
   Thus, the reaction is of zero order with respect to B, and q = 0.
3. When the concentration of C is doubled, the concentrations of A and B remain unchanged. Again, the starting rate is determined. Suppose that 2R is the new rate. Therefore, when the concentration of C doubles, the rate doubles as well. Therefore,
   Rate ∝ [C]¹
   Hence, the reaction is of first order with respect to C, and r = 1.
4. Thus, the rate law of the reaction can be written as
   Rate = k[A]²[B]⁰ [C]¹.
5. The overall order of reaction = 2 + 0 + 1 = 3.