The following results are obtained in one pseudo first order reaction:

Time $(s)$	$0$	$30$	$60$	$90$
Concentration $(mol \ L^{-1})$	$0.551$	$0.312$	$0.173$	$0.085$

$(a)$ Calculate the average rate of reaction between $30$ and $60$ seconds.
$(b)$ Calculate the rate constant $(k)$ of this first order reaction.

(N/A) Average rate $= -\frac{\Delta[R]}{\Delta t} = -\frac{0.173 - 0.312}{60 - 30} = -\frac{-0.139}{30} = 4.63 \times 10^{-3} \ mol \ L^{-1} \ s^{-1}$.
$(b)$ For a first order reaction,$k = \frac{2.303}{t} \log \frac{[R]_0}{[R]_t}$.
Using data at $t = 30 \ s$: $k = \frac{2.303}{30} \log \frac{0.551}{0.312} = 0.07677 \times \log(1.766) = 0.07677 \times 0.247 = 1.896 \times 10^{-2} \ s^{-1}$.
Using data at $t = 60 \ s$: $k = \frac{2.303}{60} \log \frac{0.551}{0.173} = 0.03838 \times \log(3.185) = 0.03838 \times 0.503 = 1.930 \times 10^{-2} \ s^{-1}$.
Taking the average,$k \approx 1.9 \times 10^{-2} \ s^{-1}$.