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# Solve A first order reaction takes 40 minutes for 30% decomposition. Calculate its half life. - Chemistry

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A first-order reaction takes 40 minutes for 30% decomposition. Calculate its half-life.

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#### Solution

Given:

[A]0 = 100%, [A]t = 100 - 30 = 70%, t = 40 min

To find:

Half life of reaction (t1/2)

Formula:

"k" = 2.303/"t" "log"_10 ["A"]_0/["A"]_"t"

Calculation:

Substitution of these in above

"k" = 2.303/"t" "log"_10 100/70

= 2.303/"40 min" "log"_10 (1.429)

= 2.303/"40 min" xx 0.155

= 0.008924 min-1

t1/2 = 0.693/"k" = 0.693/(0.008924  "min"^-1) = 77.66  "min"

The half life of reaction is 77.66 min.

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#### APPEARS IN

Balbharati Chemistry 12th Standard HSC for Maharashtra State Board
Chapter 6 Chemical Kinetics
Exercise | Q 4.7 | Page 137
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