Question

Are ${S_N}1$ reactions faster in polar solvents?

Answer 1

As we know that ${S_N}1$ reaction is an organic nucleophilic substitution reaction. In this reaction , a carbocation intermediates form. In this question we have to find out if ${S_N}1$ reacts faster in polar solvents or not. So we will first understand the mechanism of the typical ${S_N}1$ reaction and then we will solve this.

Complete Step By Step Answer:
As we know that ${S_N}1$ reaction proceeds by carbocation formation, so the stability of carbocation will favour the ${S_N}1$ mechanism.
We can write the mechanism of typical ${S_N}1$ reaction as:
${\left( {C{H_3}C{H_2}} \right)_3}C - Br\xrightarrow{{}}{\left( {C{H_3}C{H_2}} \right)_3}{C^ + } + B{r^ - }$ (slow)
${\left( {C{H_3}C{H_2}} \right)_3}{C^ + } + O{H^ - }\xrightarrow{{}}{\left( {C{H_3}C{H_2}} \right)_3}C - OH$ (Fast)
Now we know that a polar solvent favours the ${S_N}1$ reaction because polar solvents has the following properties:
It stabilizes the carbocation intermediate.
Polar solvents act like permanent dipoles which means that partial negative charge on the molecule will have the dipole- dipole interactions with the carbocation by stabilizing it.
We know that they lower the energy of both the transition states and starting material, this lowers the activation energy and so the reaction goes faster.
We can show the transition state for the slow step as follow:
\ \left[ \ {H_3}C{H_2}C\,\,\,\,\,\, \searrow \\\ {H_3}C{H_2}C\,\,\,\,\, \to \,{C^{\delta + }} - - - B{r^{\delta - }} \\\ {H_3}C{H_2}C\,\,\,\,\, \nearrow \\\ \ \right] \\\ \\\ \
It changes to the below:
\ {H_3}C{H_2}C\,\,\,\,\,\, \searrow \\\ {H_3}C{H_2}C\,\,\,\,\, \to \,{C^ + }\,\,\,\, + \,\,\,\,\,B{r^ - } \\\ {H_3}C{H_2}C\,\,\,\,\, \nearrow \\\ \
Hence we can say that yes, ${S_N}1$ reactions faster in polar solvents.

Note:
We should note the $C\,\,\, - \,\,Br$ bond is somewhat polar in the starting material. It is even more polar in the transition states and the products are completely ionic. We should know that dielectric constant of a solvent is a rough measure of the solvent’s polarity. A dielectric constant below $15$ is non polar. Here in the above solution we have shown the typical rate order for the same reaction in their different solvents. Typical polar solvents include water, alcohols and carboxylic acids.