Question

In: Chemistry

The following rate data was collected for a reaction X + Y -> Products      Exp.     ...

The following rate data was collected for a reaction X + Y -> Products

     Exp.            [X]                         [Y]                Rate of formation of a product

     1                0.23 M                 0.17 M                    0.33 M/h

    2                0.46 M                 0.17 M                    0.66 M/h

    3               0.23 M                0.51 M                    0.99 M/h

           

a. Determine the orders with respect to the two reactants and write the rate law for the reaction

b. Calculate the value of the rate constant and include the units of the rate constant

Solutions

Expert Solution

X + Y Products

Let the Rate of the reaction be , r = k[X]m[Y]n        ----(1)

Where m = order of reaction with respect to X & n is w.r.t Y

Now considering the values given in the table .

(1) Exp.            [X]                         [Y]                Rate of formation of a product

     1                0.23 M                 0.17 M                    0.33 M/h

For these values the rate of the reaction is :                 0.33 = k[0.23]m[0.17]n        ----(2)

For the second values in the tabular form the rate be 0.66 = k[0.46]m[0.17]n        ----(3)

For the third values in the tabular form the rate be       0.33 = k[0.23]m[0.51]n        ----(4)

(3)/(2) gives    2m = 2

                    ---> m = 1

(4) / (1) gives    3n = 1

                   ---> n = 0

Therefore the order of the reaction with respect to X is 1 & that of Y is 0

So the rate law be r = k[X]1[Y]0

                          r = k[X] this is the rate law for the given equation

Consider the first values in the given table then sustitute those values in the above rate law we get

   0.33 M/h = k ( 0.23 M)

k = 0.33(M/h) / 0.23M

   = 1.43 h-1

Therefore the rate constant , k = 1.43 h-1


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