A substance reacts according to the first order rate law and the specific reaction rate for the reaction is 1×10−2s−1. If the initial concentration is 1.0 M. What is the reaction rate after 1 minute ? 10−0.26≈5.5
A
5.5×10−6molL−1s−1
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B
5.5×10−3molL−1s−1
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C
5.5×10−1molL−1s−1
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D
None of the above
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Solution
The correct option is B5.5×10−3molL−1s−1 Initial rate of a first order reaction = kC =1×10−2×1.0 =1×10−2molL−1s−1
Concentration after 60 seconds is calculated by applying first order kinetic equation, k=2.30360log101(1−x)
or 1×10−2=2.30360[−log(1−x)]
or 60×10−22.303=−log(1−x)=0.2605 log(1−x)=−0.2605
(1−x)= antilog(−0.26)=0.55mol L^{-1}
Rate of reaction after 1 minute =k×C =1×10−2×0.55 =5.5×10−3molL−1s−1