Understanding Reaction Rate and Substituent Effects

This question involves determining which substituent Z makes the nucleophilic substitution reaction fastest. The reaction is:

$C{H}_{3}C{H}_{2}OCOC{H}_2-Z+O_H-\stackrel{H2O}{\to }C{H}_{3}C{H}_{2}OCOC{H}_2-OH+Z-$

This is a nucleophilic substitution reaction (likely S_N2) where OH⁻ attacks the carbon attached to Z.

Step 1: Identify the Reaction Mechanism

The nucleophile (OH⁻) is attacking a primary carbon (CH₂−Z). Primary carbons typically undergo S_N2 reactions. The rate of an S_N2 reaction is highly dependent on the nature of the leaving group (Z).

Step 2: Understand the Role of the Leaving Group (Z)

In S_N2 reactions, a better leaving group increases the reaction rate. A good leaving group is one that is stable and weak after it departs (i.e., it is the conjugate base of a strong acid).

The general rule is: The weaker the base, the better the leaving group.

Step 3: Analyze the Basicity of the Potential Leaving Groups

Let's compare the basicity of the conjugate bases of the options for Z.

• If Z = OC₂H₅, the leaving group is ethoxide ion (C₂H₅O⁻). It is a strong base and a very poor leaving group.
• If Z = H, the leaving group is hydride ion (H⁻). It is an extremely strong base and a very poor leaving group.
• If Z = CH₃, the leaving group is methyl carbanion (CH₃⁻). It is also an extremely strong base and a very poor leaving group.
• If Z = Cl, the leaving group is chloride ion (Cl⁻). Cl⁻ is the conjugate base of a strong acid (HCl), making it a weak base and an excellent leaving group.

Step 4: Determine the Fastest Reaction

Since the S_N2 rate is fastest with the best leaving group, and Cl⁻ is by far the best leaving group among the options, the reaction will be fastest when Z is Cl.

Final Answer

The reaction is fastest when Z is Cl.

Related Topics

• Nucleophilic Substitution Reactions: Reactions where a nucleophile replaces a leaving group in a molecule. The two main mechanisms are S_N1 (unimolecular) and S_N2 (bimolecular).
• Leaving Group Ability: The capacity of an atom or group to depart with the bonding electrons. It is inversely related to the basicity of the group.
• Basicity: The tendency of a species to donate electrons or accept a proton. pK_a of the conjugate acid is a common measure; lower pK_a means stronger acid and weaker conjugate base (better leaving group).

Key Formulae and Theory

Relationship between Leaving Group Ability and Basicity:

A leaving group (LG) is good if its conjugate acid (H-LG) is a strong acid.

$Ka\propto \frac{1}{p{K}_a}\propto \text{Leaving Group Ability}$

For example:

• HCl (pK_a ≈ -7) is a strong acid → Cl⁻ is a weak base and excellent LG.
• H₂O (pK_a ≈ 15.7) is a weak acid → HO⁻ is a strong base and poor LG.
• Alkoxides (RO⁻) and carbanions (R⁻) are very strong bases and terrible leaving groups.

S_N2 Rate Law:

$\text{Rate}=k\left[\text{Substrate}\right]\left[\text{Nucleophile}\right]$

The rate depends on the concentration of both the substrate and the nucleophile, as well as the nature of the leaving group and the substrate's steric hindrance.