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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 $$99.9$$%
$$k=\cfrac{0.693}{t_{1/2}}$$

$$k=\cfrac{0.693}{10}$$

$$k=0.0693$$ minutes$$^{-1}$$

Rate law expression for first order kinetics is given by:

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

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:

$$100=\cfrac{2.303}{0.0693}\log\cfrac{100}{100-x}$$

$$x=99.9$$

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

Hence, the correct option is $$\text{B}$$

Chemistry

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