Question

What is the instantaneous Rate of Reaction? How is it determined?

Answer 1

Instantaneous Rate of Reaction

• To express the rate at a particular moment of time we determine the instantaneous rate.
• It is obtained when we consider the average rate at the smallest time interval say dt ( i.e. when ∆t approaches zero). Hence, mathematically for an infinitesimally small dt instantaneous rate is as follows:-
• $r_{\text{av}}=\frac{-∆\left[R\right]}{∆t}$
• As ∆t → 0
• $r_{\mathrm{ins}}=\frac{-d\left[R\right]}{dt}=\frac{d\left[P\right]}{dt}$

Calculation of instantaneous rate at $600\text{s}$

• The instantaneous rate of hydrolysis of butyl chloride is shown in the figure:-
• It can be determined graphically by drawing a tangent at time t on either of the curves for the concentration of R and P vs time t and calculating its slope.
• 
• So, the instantaneous rate at $600\text{s}$ is as follows:-
• $$\begin{gathered} \text{Instantaneous rate}=-\left(\frac{0.0165-0.037}{\left(800-400\right)\text{s}}\right){\text{mol L}}^{\text{-1}} \\ =5.12\times {10}^{-5}{\text{mol L}}^{\text{–1}}{\text{s}}^{\text{–1}} \end{gathered}$$