Calculate the instantaneous rate $(r_{inst})$ based on the example problem $-1$ graphically for the times $250\ s$,$350\ s$,$450\ s$,and $600\ s$.

(N/A) The instantaneous rate $(r_{inst})$ is determined for an infinitesimally small time interval $dt$ as follows:
When $\Delta t \rightarrow 0$,$r_{inst} = -\frac{d[R]}{dt} = \frac{d[P]}{dt}$.
For the given decomposition of butyl chloride,$r_{inst} = -\frac{d[C_4H_9Cl]}{dt}$. By plotting the graph of $[C_4H_9Cl]$ versus time $(t)$,the instantaneous rate is determined by calculating the slope of the tangent drawn to the curve at the specific time.
$1$. For $t = 600\ s$:
$r_{inst} = -\frac{d[C_4H_9Cl]}{dt} = -\frac{(0.0165 - 0.037)\ mol\ L^{-1}}{(800 - 400)\ s} = 5.12 \times 10^{-5}\ mol\ L^{-1}\ s^{-1}$.
$2$. For $t = 250\ s$:
$r_{inst} \approx 1.22 \times 10^{-4}\ mol\ L^{-1}\ s^{-1}$.
$3$. For $t = 350\ s$:
$r_{inst} \approx 1.0 \times 10^{-4}\ mol\ L^{-1}\ s^{-1}$.
$4$. For $t = 450\ s$:
$r_{inst} \approx 6.4 \times 10^{-5}\ mol\ L^{-1}\ s^{-1}$.