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A reaction that is of the first order with respect to reactant $A$ has a rate constant $6 \mathrm{~min}^{-1}$. If we start with $[A]=0.5 \mathrm{~mol} l^{-1}$, when would $[A]$ reach the value $0.05 \mathrm{~mol} l^{-1}$
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The correct answer is:
$0.384 \mathrm{~min}$
We know that for first order kinetics
$k=\frac{2.303}{t} \log \frac{a}{a-x}$
$(a-x)=0.05 \mathrm{~mol} \mathrm{L}$
$6=\frac{2.303}{t} \log \frac{0.5}{0.05}$
or $t=\frac{2.303}{6} \log \frac{0.5}{0.05}=\frac{2.303}{6}=0.384 \mathrm{~min}$
$k=\frac{2.303}{t} \log \frac{a}{a-x}$
$(a-x)=0.05 \mathrm{~mol} \mathrm{L}$
$6=\frac{2.303}{t} \log \frac{0.5}{0.05}$
or $t=\frac{2.303}{6} \log \frac{0.5}{0.05}=\frac{2.303}{6}=0.384 \mathrm{~min}$
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