# Consider a certain reaction A → Products

Question:

Consider a certain reaction A → Products with = 2.0 × 10−2 s−1. Calculate the concentration of remaining after 100 s if the initial concentration of is 1.0 mol L−1.

Solution:

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, $k=\frac{2.303}{t} \log \frac{[\mathrm{A}]_{0}}{[\mathrm{~A}]}$

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

$\Rightarrow 2.0 \times 10^{-2} \mathrm{~s}^{-1}=\frac{2.303}{100 \mathrm{~s}}(-\log [\mathrm{A}])$

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

$\Rightarrow[\mathrm{A}]=\operatorname{anti} \log \left(-\frac{2.0 \times 10^{-2} \times 100}{2.303}\right)$

= 0.135 mol L−1 (approximately)

Hence, the remaining concentration of A is 0.135 mol L−1.