i. To determine the instantaneous rate of a reaction, the progress of a reaction is followed by measuring the concentrations of a reactant or product for different time intervals.

ii. The concentration of a reactant or a product is plotted against time.

iii. A tangent drawn to the curve at time \(t_1\) gives the rate of the reaction. The slope thus obtained gives the instantaneous rate of the reaction at time \(t_1\).

Determination of Instantaneous Rate

iv. Mathematically, the instantaneous rate is expressed by replacing \(\Delta\) with the derivative \(\frac{{dc}}{{dt}}\) in the expression of the average rate.

Instantaneous rate = \(\frac{{d[C]}}{{dt}}\)

v. For a reaction \(\ce{A \rightarrow B}\)

Instantaneous rate of consumption of A at time \(t\) = \(-\frac{{d[A]}}{{dt}}\)

Instantaneous rate of the formation of B at time \(t\) = \(\frac{{d[B]}}{{dt}}\)

Therefore, the instantaneous rate of the reaction at time \(t\) is equal to: \(-\frac{{d[A]}}{{dt}} = \frac{{d[B]}}{{dt}}\)