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Question

A first order reaction is 75% completed in 100 minutes. How long time will it take for its 87.5% completion?

A
125 min
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B
150 min
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C
175 min
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D
200 min
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Solution

The correct option is B 150 min
For first order reaction,
t=2.303klog10R0Rinitial concentrationleft out concentration
75% reaction completed in 100 min than rate constant is R0=100;R=10075=25
k=2.303tlog1010025
k=2.303100log1010025
k=2.303100log104
Time taken for completion of 87.5% of the reaction; (R0=100;R=10087.5=12.5)
t=2.303klog1010012.5
On substituting the value of k in equation we get,
t=2.303log1082.303100log104=100×log108log104
=100×1.5
=150 min

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