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Question

The half-life of a first-order reaction is 10 min. What % of the reaction will be completed in 100 min?

A
25%
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B
99.9%
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C
75%
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D
80%
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Solution

The correct option is B 99.9%
k=0.693t1/2

k=0.69310

k=0.0693 minutes1

Rate law expression for first order kinetics is given by:

t=2.303klogaax

where,

k = rate constant

t = time taken for the decay process

a = initial amount of the reactant

a - x = amount left after decay process

Putting values in above equation, we get:

100=2.3030.0693log100100x

x=99.9

Thus the amount decomposed is 9.9 and thus the percentage of the reaction completion is 99.9%.

Hence, the correct option is B

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