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

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## Instantaneous Rate of ReactionTo 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:- $\text{Instantaneousrate}=-\left(\frac{0.0165-0.037}{\left(800-400\right)\text{s}}\right){\text{molL}}^{\text{-1}}\phantom{\rule{0ex}{0ex}}=5.12×{10}^{-5}{\text{molL}}^{\text{–1}}{\text{s}}^{\text{–1}}\phantom{\rule{0ex}{0ex}}$

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