Question

(a) Predict the products of electrolysis in an aqueous solution of $AgN{O_3}$ with silver electrodes.
(b) Why does racemisation occur in the $S{N^1}$ mechanism?

Answer 1

Hint: Electrolysis is the process of decomposition of ionic compounds into their elements by passing a direct electric current through the compound in an aqueous solution and we also know that racemisation is conversion of optically active compounds into a mixture of enantiomers with no optical activity.

Complete Step by step answer:
(a) As we know that in an silver nitrate will decompose into its ions as \[A{g^ + }\]and $NO_3^ - $, in the aqueous solution of silver nitrate with silver electrodes two oxidation and two reduction half reactions will take place. Reduction of silver ions at cathode having the silver ions with lower discharge potential than hydrogen ions. Hence the silver ions will be deposited at cathode and not the hydrogen ions and at anode the silver anion will dissolve and help in forming the silver ions in the solution and hence hydroxide ions will get deposited at anode and silver will get oxidised more readily. We can represent it as:
At cathode: $4A{g^ + } + 4{e^ - } \to 4Ag:\;{E^\circ } = 0.80V$
At anode: $4O{H^ - } \to 2{H_2}O + {O_2} \uparrow + 4{e^ - }:\;{E^\circ } = 0.83$
Thus on electrolysis of aqueous solution of $AgN{O_3}$ with silver electrode, $Ag$ from silver anode dissolves while $A{g^ + }$ ions get deposited at cathode.

(b) We already know that in $S{N^1}$ reaction the rate limiting step is the formation of carbocation and the second step involves the attack of the nucleophile on the carbocation. So this nucleophile can attack from any face of the carbocation because the carbocation and substituents are planar but when it attacks from the rare side there is inversion of configuration of compound which results in the formation of one type of isomer and when nucleophile attacks from front there is retention of configuration leading to the formation of mirror image of the isomer. So the two isomers formed are in equal concentration as the probability of attack is $1:1$ but have opposite optical activity cancelling out one other's optical activity and make the compound optically inactive. This mixture is thus called a racemic mixture as in $S{N^1}$ the nucleophile has the ability to attack from either side.

Note: Although racemisation is involved in $S{N^1}$ but it is not $100\% $ as the carbocation formed is not stable so it is possible that nucleophile can attack from the back side of the carbocation and the front side may be shielded by the leaving group.