Question

Consider a certain reaction $A$ $→$ $Products$ with $k = 2.0 \times 10^{-2 }s^{-1}$ . Calculate the concentration of A remaining after 100 s if the initial concentration of A is 1.0 mol L-1.

Answer 1

k= 2.0 × 10-2 s-1

T= 100 s

[A]o= 1.0 moL-1

Since the unit of k is $s^{-1}$ , the given reaction is a first order reaction.

Therefore, $k = \frac {2.303}{t} log\ \frac {[A]_0}{[A]}$

⇒ $2.0 \times 10^{-2} s^{-1} = \frac {2.303}{100\ s} log\ \frac {1.0}{[A]}$

⇒ $2.0 \times 10^{-2} s^{-1} = \frac {2.303}{100 \ s} (-log\ A)$

⇒ $-log [A] = \frac {2.0\times 10^{-2} \times 100}{2.303}$

⇒ $[A] = Antilog\ (-\frac {2.0 \times 10^{-2}\times 100}{2.303})$

⇒ $[A]= 0.135\ mol \ L^{-1} (approximately)$

Hence, the remaining concentration of A is $0.135\ mol \ L^{-1}$.