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It is observed that rate of reaction of two isotopologues of benzene, $\ce{C6D6}$ and $\ce{C6H6}$, is the same for electrophilic aromatic reactions, as the deprotonation is not the rate limiting step. Instead the carbocation is usually limiting.

Do iodination and sulphonation somehow do show different rates with these isotopologues? Is $\ce{C6H6}$ the faster of the two, due to stronger C-D bond (smaller size of D)? If this is correct what is the reason?

Does the protonation becomes the rate limiting step? if yes, then why in only with iodination and sulphonation?

Update : Found potential energy graphs for suphonation and nitration and it does seem like protonation either becomes the rate determining step or just smaller than carbocation hill, but why in sulphonation, the deprotonation curve was high is still a mystery.

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    $\begingroup$ The slow step is electrophilic attack. Deprotonation after electrophilic attack is likely not the slow stop in any of those cases. $\endgroup$ – SendersReagent Feb 5 '16 at 20:09
  • $\begingroup$ -----Update---- $\endgroup$ – Mrigank Feb 6 '16 at 15:45
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In general, deprotonation of a C-D bond would require more energy then C-H because the zero point vibrational energy of the bond is lowered. By referring to our harmonic oscillator zero point energy equation,

$E_0 = \frac{1}{2}h \nu$

where frequency is,

$\nu = \frac{1}{2 \pi} \sqrt{\frac{k}{\mu}}$

and the reduced mass ($\mu$) being,

$\mu = \frac{m_1m_2}{m_1 + m_2}$

we see that as the mass for either atom increases, the zero point energy decreases, therefore, the bond is relatively more stable then its lighter isotopologue. However, swapping out isotopes in a molecule does not change the potential energy surface for the reaction [1]

1.) Sulphonation

Changes in the rate determining step may arise from the type of sulfuric acid used. Since fuming sulfuric acid has a higher concentration of $SO_3$ (the electrophile) then more dilute forms of $H_2SO_4$, the rate limiting step is no longer forming the bond between benzene and $SO_3$, rather, it is re-forming the aromatic ring through deprotonation. Ergo, if you did a KIE study with different concentrations of sulfuric acid, you may see that only fuming $H_2SO_4$ shows significant values of $\frac{K_H}{K_D}$.

2.) Iodination

This article [2] studied the iodination of benzene with the source of iodine being generated through the "oxidation of 0.5 g of $I_2$ in acetonitrile-tetraethylammonium perchlorate to 2.4 faradays/mol."

enter image description here

The article reported that the secondary kinetic isotope effect for $k_1$ and $k_{-1}$ is negligible, however, $\frac{K_H}{K_D} = 2.25$ for $k_2$.

Here is a thesis I found that discusses the iodination of aromatic rings [3]

The thesis, in short, suggests that whether the deprotonation is rate limiting has to do with the concentration of the reactants, along with the transition state of the molecule. The transition state is affected by the strength of the base, since a higher $pk_b$ may give a transition state where the hydrogen is partially bound to both the ring and the base, making this step in the reaction faster (therefore, not rate limiting). However, it did only investigate substituted aromatic rings, where substituents can play a significant role in the transition state, making the reaction with benzene a little less comparable.

3.) Nitration

This article reports no KIE observed in nitration of benzene [4].

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