Consider a certain reaction; A $\to$ 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 $1.0 m o l L^{- 1}$ .

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Solution

For the first order reaction
$t = \frac{2.303}{k} l o g \frac{[A]_{0}}{[A]} o r l o g \frac{[A]_{0}}{[A]} = \frac{k \times t}{2.303} k = 2.0 \times 10^{- 2} s^{- 1}; t = 100 s; [A]_{0} = 1.0 m o l L^{- 1} = 1.0 M l o g \frac{[A]_{0}}{[A]} = \frac{(2.0 \times 10^{- 2} s^{- 1}) \times (100 s)}{2.303} = 0.8684 \frac{[A]_{0}}{[A]} = A n t i l o g 0.8684 = 7.3858 [A] = \frac{[A]_{0}}{7.3858} = \frac{[1 M]}{7.3858} = 0.135 M [A] = 0.135 M$

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