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Chemical Kinetics

Question
CBSEENCH12011047
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The rate of a first-order reaction is 0.04 mol L-1s-1 at 10 sec and 0.03 mol-1L-1 s-1 at 20 sec after initiation of the reaction. the half-life period of the reaction is 

  • 34.1 s

  • 44.1 s

  • 54.1 s

  • 24.1 s

Solution

D.

24.1 s

Given comma order space of space reaction space equals 1 Rate space of space reaction space at space 10 space straight s space space equals negative 0.04 space mol space straight L to the power of negative 1 end exponent space straight s to the power of negative 1 end exponent Rate space of space reaction space at space 20 space straight s space equals straight s space equals 0.03 space mol space straight L space to the power of negative 1 end exponent space straight s to the power of negative 1 end exponent therefore space Half minus life space period space left parenthesis straight t subscript 1 divided by 2 end subscript right parenthesis space equals space ? We space have space the space equation space for space rate minus constant apostrophe straight k apostrophe space in space first space order space reaction straight k space equals space fraction numerator 2.303 over denominator straight t end fraction log space straight A subscript straight t over straight A subscript 0 equals space fraction numerator 2.303 over denominator 105 end fraction log fraction numerator 0.04 over denominator 0.03 end fraction equals space fraction numerator 2.303 over denominator 105 end fraction space straight x 0.124 straight k equals space 0.028 space straight s to the power of negative 1 end exponent We space know space that comma straight t subscript 1 divided by 2 end subscript space equals space fraction numerator 0.693 over denominator straight k end fraction equals fraction numerator 0.693 over denominator 0.028773391 space end fraction space equals space 24.14 space straight s space equals space 24.1 space straight s

Some More Questions From Chemical Kinetics Chapter

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

The rate law for the decomposition of N2O5 is rate = k[N2O5]. What is the significance of k in this equation?

Define activation energy of a reaction.

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