# Problem: Sulfonation of benzene has the following mechanism:(1) 2H2SO4 ⟶ H3O+ + HSO4- + SO3                                      [fast](2) SO3 + C6H6 ⟶ H(C6H5+)SO3-                                                        [slow](3) H(C6H5+)SO3- + HSO4- ⟶ C6H5SO3- + H2SO4                [fast](4) C6H5SO3- + H3O+ ⟶  C6H5SO3H + H2O                         [fast](b) Write the overall rate law in terms of the initial rate of the reaction.

###### FREE Expert Solution

When a reaction mechanism is given, the rate law can be determined using the slow step in the reaction mechanism.

▪rate law only involves the reactants
▪ the
coefficients of the reactants in the slow step are the order of the reaction with respect to that reactant
▪ Rate Law has a general form of:

$\overline{){\mathbf{rate}}{\mathbf{=}}{\mathbf{k}}{\mathbf{\left[}\mathbf{X}\mathbf{\right]}}^{{\mathbf{a}}}{\mathbf{\left[}\mathbf{Y}\mathbf{\right]}}^{{\mathbf{b}}}}$

(1) 2H2SO4 H3O+ + HSO4- + SO3                                      [fast]
(2) SO3 + C6H6
H(C6H5+)SO3-                                                        [slow]
(3) H(C6H5+)SO3- + HSO4-
C6H5SO3- + H2SO4                [fast]
(4) C6H5SO3- + H3O+
C6H5SO3H + H2O                         [fast]

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###### Problem Details

Sulfonation of benzene has the following mechanism:

(1) 2H2SO4 ⟶ H3O+ + HSO4- + SO3                                      [fast]
(2) SO3 + C6H6 ⟶ H(C6H5+)SO3-                                                        [slow]
(3) H(C6H5+)SO3- + HSO4- ⟶ C6H5SO3- + H2SO4                [fast]
(4) C6H5SO3- + H3O+ ⟶  C6H5SO3H + H2O                         [fast]

(b) Write the overall rate law in terms of the initial rate of the reaction.