Q.Define average rate and instantaneous rate.

Step 1. The average rate of a reaction over a finite time interval $\Delta t=t_2-t_1$ is $\text{Rate}_{\text{avg}}=-\dfrac{\Delta[A]}{\Delta t}=-\dfrac{[A]_2-[A]_1}{t_2-t_1}$ -- it reports how fast the concentration changed ON AVERAGE across that whole window, and its numeric value depends on exactly which window is chosen (a narrower or wider interval gives a different average).

Step 2. The instantaneous rate is the rate at ONE particular moment, obtained by shrinking the time interval down to zero: $\text{Rate}_{\text{inst}}=\displaystyle\lim_{\Delta t\to0}\left(-\frac{\Delta[A]}{\Delta t}\right)=-\frac{d[A]}{dt}$.

Step 3. Graphically, on a plot of concentration against time, the instantaneous rate at any chosen point is the slope of the TANGENT line drawn to the curve at that exact point -- unlike the average rate, which is the slope of a straight (chord) line connecting two separated points on the curve.

State both definitions with their formulas, and note the key distinction: average rate depends on the chosen interval, instantaneous rate is a single well-defined value obtained by taking $\Delta t\rightarrow0$.

• Describing average and instantaneous rate as though they were always numerically the same -- they only coincide in the special case of a reaction proceeding at a genuinely constant rate.