Show that in first order reaction time required for completion of 99.9% is 10 times of half-life (t_1/2) of the reaction.

Solution

For first order reaction

$t = \frac{2.303}{k} \log \frac{a}{a - x}$

   $t_{0.999} = \frac{2.303}{k} \log \frac{a}{(a - 0.999 a)} [∵ x = 0.999 a] = \frac{2.303}{k} \log \frac{a}{0.001 a} = \frac{2.303}{k} \log 1000 = \frac{2.303}{k} \times 3 . . . (i)$

and

$t_{1 / 2} = \frac{2.303}{k} \log \frac{a}{(a - 0.5 a)} = \frac{2.303}{k} \log 2 = \frac{2.303}{k} \times 0.3010$ ......(ii)

Dividing (i) by (ii), we get

$\frac{t_{0.999}}{t_{0.5}} = \frac{2.303}{k} \times 3 \times \frac{k}{2.303 \times 0.3010} = 10$

or    $t_{0.999} = 10 \times t_{0.5}$

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

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Chemical Kinetics

Show that in first order reaction time required for completion of 99.9% is 10 times of half-life (t_1/2) of the reaction.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Chemical Kinetics

Show that in first order reaction time required for completion of 99.9% is 10 times of half-life (t1/2) of the reaction.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Show that in first order reaction time required for completion of 99.9% is 10 times of half-life (t_1/2) of the reaction.