In lecture I suggested that ethanol, as well as ethoxide, could act as a nucleophile for SN2 substitution because the reaction proceeds, albeit slowly, in the absence of added ethoxide salt.

Ben Kass raised the great question of whether, in the absence of added ethoxide, the nucleophile might instead be the small amount of ethoxide in equilibrium with pure ethanol:

There are numbers on page 59 in the textbook that allow one to address this kind of question approximately for closely related solvents.

The text tells us that the second-order rate constant for reaction of CH₃Cl with OH^- in methanol at 25°C is

The same reaction in water would probably be somewhat slower, because charge is being dispersed in the transition state and water is a more polar solvent than methanol, and thus more reluctant to allow charge dispersal in the SN2 transition state.

In neutral water the concentration of OH^- (like that of H⁺) is 10^-7 M (pH = 7). So the pseudo-first-order rate constant for reaction of CH₃Cl with OH^- in pure water should be

Page 59 also tells us that the pseudo-first-order rate constant for reaction of CH₃Cl in pure water at 25°C is

The fraction of reaction that involves OH^- must be the ratio of the OH^- rate to the total rate:

Thus more than 99.8% of the reaction of CH₃Cl with water must involve a nucleophile other than OH^-, namely water itself. The situation should be similar for ethoxide/ethanol.

Note that since pure water is 55 M, the second-order rate constant for reaction with water must be

This means that OH^- is somewhat less than 6 x 10^-6 / 6 x 10^-12 = 10⁶ faster as a nucleophile than water is. A study in 1953 suggested that for reaction with CH₃Br in water, OH^- is about 20,000 times more reactive that HOH.

The negative charge is worth a lot in nucleophilicity (rate of attack on carbon). It is worth even more in equilibrium basicity; the pKa difference between H₂O (15.7) and H₃O⁺ (-1.7) is 17.4, close to a million million million fold!

There is another objection to OH^- being the predominant nucleophile in pure water. As the reaction proceeds, the other product (HCl) builds up. As it does so, the concentration of OH^- at equilibrium plummets, so even less of the reaction would involve OH^-. Consider that reaction of only 10^-4 M of the chloride would generate 10^-4 M H⁺ , lowering [OH^-] from 10^-7 M to 10^-10 M! By contrast, the concentration of water hardly changes at all.