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Chemical Kinetics

Question
CBSEENCH12010172
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A first order reaction takes 40 minutes for 30% decomposition. Calculate t1/2 for this reaction.

 (Given log 1.428 = 0.1548)

Solution

                A   -->  P

T=0         a          0

T=t       (a-x)       x

Now, it takes 40 min for 30% decomposition i.e. reactant left after 40 min is 70% of its initial concentration.

So,
left parenthesis straight a minus straight x right parenthesis space equals 70 over 100 space straight x space straight a space equals 7 over 10 straight a straight k equals open parentheses fraction numerator 2.303 over denominator straight t end fraction close parentheses space log space fraction numerator straight a over denominator straight a minus straight x end fraction straight k equals open parentheses fraction numerator 2.303 over denominator 40 end fraction close parentheses space log space fraction numerator straight a over denominator left parenthesis 7 divided by 10 right parenthesis straight a end fraction equals space fraction numerator 2.303 space over denominator 40 end fraction log space 1.428 Therefroe comma straight K equals space 0.00891 space min to the power of negative 1 end exponent straight t subscript 1 half space end subscript space equals fraction numerator 0.693 over denominator straight k end fraction space equals space fraction numerator 0.693 over denominator 0.008913 end fraction equals space 77.78 space min

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

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

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