Question

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

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

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 constantt = time taken for the decay processa = initial amount of the reactanta - x = amount left after decay processPutting 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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