Explain: What is instantaneous rate? How is it determined?

(N/A) Definition: The rate of reaction at a particular moment of time is called instantaneous rate. It is expressed by $r_{inst}$.
Explanation: Instantaneous rate is the rate for an infinitely small time interval,say $dt$. During this time,if the decrease in the concentration of reactants is $d[R]$,then the instantaneous rate is expressed as follows: $r_{inst} = -\frac{d[R]}{dt}$.
The instantaneous rate is the limit of the average rate as the time interval $dt$ approaches zero. Mathematically,for an infinitesimally small $dt$,the instantaneous rate is given by:
As $\Delta t \rightarrow 0, \quad r_{inst} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$.
[Remember: Average rate $r_{av} = -\frac{\Delta[R]}{\Delta t} = \frac{\Delta[P]}{\Delta t}$].
The procedure to determine instantaneous rate: The instantaneous rate is determined graphically. It can be determined by drawing a tangent at time $t$ on either of the curves for concentration of $R$ and $P$ versus time $t$ and calculating its slope. Take the value of $d[R]$ or $d[P]$ and $dt$ and calculate $r_{inst}$ based on the slope of the tangent to the graph.