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Consider a certain reaction A ® Products with k = 2.0 × 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.

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

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M manish

Given that,
k = =2\times 10^{-2}
t = 100 s
[A]_0= 1\ mol\ L^{-1}
Here the unit of k is in per sec, it means it is a first-order reaction.
therefore, 
k = \frac{2.303}{t}\log\frac{[A]_o}{[A]}
\\2\times 10^{-2} = \frac{2.303}{100}\log\frac{1}{[A]}\\ 2\times 10^{-2} = -\frac{2.303}{100}\log[A]\\ \log[A]=-\frac{2}{2.303}\\
\\A = anti\log\frac{-2}{2.303}\\ A= 0.135 mol\ L^{-1}

Hence the concentration of rest test sample is 0.135 mol/L

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