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Chemical Kinetics

Question
CBSEENCH12010242

Nitrogen pentoxide decomposes according to equation: 2N2O5(g)--->  4NO2(g) + O2(g) 

This first order reaction was allowed to proceed at 40° C and the data below were collected:

[N2O5] (M)

Time (min)

0.400

0.00

0.289

20.0

0.209

40.0

0.151

60.0

0.109

80.0

 

(a) Calculate the rate constant. Include units with your answer. 

(b) What will be the concentration of N2O5 after 100 minutes? 

(c) Calculate the initial rate of reaction.

Solution
(a) The plot of [N2O5] v/s t is as follows


[N2O5] (M)

Time (min)

log (N2O5]

0.400

0.00

-0.3979

0.289

20.0

-0.5391

0.209

40.0

-0.6798

0.151

60.0

-0.8210

0.109

80.0

-0.9625






From the plot, log [N2O5] v/s t, we obtain by
Slope space equals fraction numerator negative 0.70 minus left parenthesis negative 0.60 right parenthesis over denominator 40 minus 20 end fraction

equals fraction numerator negative 0.70 plus 0.60 over denominator 20 end fraction space equals fraction numerator negative 0.10 over denominator 20 end fraction

Also comma space slope space of space the space line space of space he space plot space equals fraction numerator negative straight k over denominator 2.303 end fraction space equals fraction numerator 0.10 over denominator 20 end fraction

Or space space straight k equals space fraction numerator 0.10 over denominator 20 end fraction straight x space 2.303 space equals space 0.01151

Or comma space straight k equals space 1.15 space straight x space 10 to the power of negative 3 end exponent min to the power of negative 1 end exponent

straight b right parenthesis space After space 100 space min

straight k equals space fraction numerator 2.303 over denominator straight t end fraction log fraction numerator left square bracket straight N subscript 2 straight O subscript 5 right square bracket subscript 0 over denominator left square bracket straight N subscript 2 straight O subscript 5 right square bracket subscript straight f end fraction
After space 100 space min

straight k equals space fraction numerator 2.303 over denominator straight t end fraction log fraction numerator 0.400 over denominator 0.098 end fraction

straight c right parenthesis space The space initial space rate space of space reaction
straight r equals space straight k left square bracket straight N subscript 2 straight O subscript 5 right square bracket
space equals space 1.15 space straight x space 10 to the power of negative 3 end exponent space straight x space 0.400
space equals space 4.6 space straight x space 10 to the power of negative 4 end exponent space straight S to the power of negative 1 end exponent