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Question

For a first order reaction, the initial concentration of a reactant is 0.05 M. After 45 minute it is decreased by 0.015 M. Calculate half-reaction time (t1/2).

A
87.42min
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B
25.90min
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C
78.72min
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D
77.20min
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Solution

The correct option is A 87.42min
For Ist order reaction, the half-life (t1/2) is:

t1/2=0.693k ....(i)

k=2.303tlog[N0]N

where N0= Initial concentration
N= Final concentration

k=2.30345log0.05M0.050.015M

k=2.30345log0.050.035

=2.30345log107

=2.30345[log10log7]

=2.30345[10.8450]

=2.30345×0.154

k=0.00792

Put the value of k in equation (i), we get

t1/2=0.6930.00792

t1/2=87.5min

Hence, the correct option is B

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