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Question

Chemistry Question on Chemical Kinetics

The rate constant for the first order reaction is 60 s−160\text{ }{{s}^{-1}} . How much time will it take to reduce the concentration of the reactant to 116\frac{1}{16} th value?

A

4.6×10−2s4.6\times {{10}^{-2}}s

B

4.6×104s4.6\times {{10}^{4}}s

C

4.6×102s4.6\times {{10}^{2}}s

D

4.6×10−4s4.6\times {{10}^{-4}}s

Answer

4.6×10−2s4.6\times {{10}^{-2}}s

Explanation

Solution

t=2.303klog⁡[A]0[A]t=\frac{2.303}{k}\log \frac{{{[A]}_{0}}}{[A]} If [A]0=1{{[A]}_{0}}=1 then [A]=116[A]=\frac{1}{16} t=2.30360log⁡16t=\frac{2.303}{60}\log 16 =4.6×10−2s=4.6\times {{10}^{-2}}s