Question

Sulfonation of benzene has the following mechanism:(b) Write the overall rate law in terms of the initial rate of the reaction.

Answer 1

The overall rate law in terms of the initial rate of the reaction is:

= $k_{overall} [H_{2} SO_{4} ]^{2} [C_{6}H_{6}]$

The Sulfonation of benzene has the following mechanism:

(1)  $2H_{2} SO_{4}$ ⇌ $H_{3}O^{+} + HSO_{4} + SO_{3}$

[fast]

(2) $SO_{3} + C_{6} H_{6}$ → $H(C_{6} H_{5}^{+} )SO_{3}^{-}$

[slow]

(3) $H(C_{6} H_{5}^{+} )SO_{3}^{-}$$+ HSO_{4}^{-}$ → $C_{6} H_{5} SO_{3}^{-} + H_{2} SO_{4}$

[fast]

(4) $C_{6} H_{5} SO_{3}^{-} + H_{3}O^{+}$ → $C_{6} H_{5} SO_{3} H + H_{2} O$

[fast]

Calculation of rate law:

Given that the reaction's slowest step is the rate-dependent step, the following is the definition of rate law:

Rate = $k_{2} [SO_{3} ][C_{6} H_{6} ]$    

However, the issue is that because $SO_{3}$ is an intermediate, it cannot be accounted for in the general rate legislation.

The following rate rule governs the synthesis of $SO_{3}$ :

Rate = $k_{1}[H_{2} SO_{4} ]^{2}$

Consequently, if we replace equation 1 with equation 2,

Rate is determined to be = $k_{overall} [H_{2} SO_{4} ]^{2} [C_{6}H_{6}]$

Hence, the overall rate law in terms of the initial rate of the reaction is:

= $k_{overall} [H_{2} SO_{4} ]^{2} [C_{6}H_{6}]$

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brainly.com/question/4222261

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