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Chemical Kinetics

Question
CBSEENCH12011342

The bromination of acetone cytosine and guanine solution is represented by this equation.
 CH3COCH3 (aq) + Br2 (aq) →CH3COCH2Br (aq) + H+ (aq) + Br- (aq)
These kinetic data were obtained for given reaction concentrations.

Initial Concentrations, M
[CH3COOH] [Br2] [H+]
0.30 0.05 0.05
0.30 0.10 0.05
0.30 0.10 0.10
0.40 0.05 0.20

Initial rate, disappearance of Br2, ms-1
                   5.7 x 10-5
                   5.7 x 10-5
                   1.2 x 10-4
                   3.1 x  10-4
Based on these data, the rate equation is
  • Rate = k[CH3COCH3][H+]

  • Rate = k[CH=COCH3][Br2]

  • Rate = k [CH3COCH3][Br2][H+]

  • Rate = k [CH3COCH3][Br2][H+]

Solution

A.

Rate = k[CH3COCH3][H+]

By comparing the rate and concentration, the order of the reaction can be calculated.
Let the rate of the reaction wrt [CH3COCH3], [Br2] and [H+] are x,y and z respectively. Thus, 
Rate space proportional to space left square bracket CH subscript 3 COOH subscript 3 right square bracket to the power of straight x left square bracket Br subscript 2 right square bracket to the power of straight y left square bracket straight H to the power of plus right square bracket to the power of straight z
5.7 space straight x space 10 to the power of negative 5 end exponent space equals space left square bracket 0.30 right square bracket to the power of straight x left square bracket 0.05 right square bracket to the power of straight y left square bracket 0.05 right square bracket to the power of straight z space space space... left parenthesis straight i right parenthesis
5.7 space straight x space 10 to the power of negative 5 end exponent space equals space left square bracket 0.30 right square bracket to the power of straight x left parenthesis 0.10 right parenthesis to the power of straight y left parenthesis 0.05 right parenthesis to the power of straight z space space... space left parenthesis ii right parenthesis
1.2 space straight x space 10 to the power of 4 space equals space left square bracket 0.30 right square bracket to the power of straight x left parenthesis 0.10 right parenthesis to the power of straight y left parenthesis 0.10 right parenthesis to the power of straight z... space left parenthesis iii right parenthesis
3.1 space straight x space 10 to the power of negative 4 end exponent space equals space left square bracket 0.40 right square bracket to the power of straight x left parenthesis 0.05 right parenthesis to the power of straight y space left parenthesis 0.20 right parenthesis to the power of straight z... space left parenthesis iv right parenthesis
From space eqs space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space
straight y equals space 0
From space eqs space left parenthesis ii right parenthesis thin space and space left parenthesis iii right parenthesis
straight z equals 1
From space eqs space left parenthesis thin space straight i right parenthesis space and space left parenthesis thin space iv right parenthesis
space straight x equals space 1
Thus comma space rate space law space proportional to space left square bracket CH subscript 3 COCH subscript 3 right square bracket left square bracket straight H to the power of plus right square bracket
equals space straight k space left square bracket CH subscript 3 COCH subscript 3 right square bracket left square bracket straight H to the power of plus right square bracket