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  • A reaction has half life of 1 min. The tie required for 99.9% completion of the reaction is _________ min. (Rounded off to the nearest integer) [Use; ln 2= 0.69, ln 10 = 2.3]Option: 1 10Option: 2 -Option: 3 -

A reaction has half life of 1 min. The tie required for 99.9% completion of the reaction is _________ min. (Rounded off to the nearest integer) [Use; ln 2= 0.69, ln 10 = 2.3]
 

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best_answer

Given,

A reaction has a half-life of 1 min.

we know,

\mathrm{t=\frac{1}{K}ln\frac{a}{a-x}}

Now, at t = 50 % = t1/2

\mathrm{t_{1/2}=\frac{1}{K}ln2=1\ min}

so, K = ln2

Now, at t = 99.9 %

\mathrm{t_{99.9%}=\frac{1}{K}ln\frac{100}{100-99.9}}

\mathrm{t_{99.9%}=\frac{1}{K}ln\frac{1000}{1}}=\mathrm{\frac{3}{K}ln10}

\mathrm{t_{99.9%}=\frac{3}{ln2}ln10=\frac{3}{ln2}}\mathrm{\mathrm{t_{99.9%}=\frac{3}{0.3}}=10\ min}

Ans = 10

Posted by

Kuldeep Maurya

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