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11 REACTION KINETICS eLearn.Punjab

11.1.1 Instantaneous and Average Rate

The rate at any one instant during the interval is called the instantaneous rate. The rate of
reaction between two specific time intervals is called the average rate of reaction.
The average rate and instantaneous rate are equal for only one instant in any time interval. At first,
the instantaneous rate is higher than the average rate. At the end of the interval the instantaneous
rate becomes lower than the average rate. As the time interval becomes smaller, the average rate
becomes closer to the instantaneous rate.
The average rate will be equal to the instantaneous rate when the time interval approaches
zero. Thus the rate of reaction is instantaneous change in the concentration of a reactant or a
product at a given moment of time.

Rate of reaction = dx
dt

Where dx is a very small change in the concentration of a product in a very small time interval
dt. Hence, dx/dt is also called rate of change of concentration with respect to time.
The rate of a general reaction, A → B , can be expressed in terms of rate of disappearance of
the reactant A or jthe rate of appearance of the product B. Mathematically,

Rate of reaction = -d[A] = + d[B]
dt dt

Where d[A] and d[B] are the changes in the concentrations of A and B, respectively. The
negative sign in the term indicates a decrease in the concentration of the reactant A. Since the
concentration of product increases with time, the sign in rate expression involving the change of
concentration of product is positive.

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