Identify the reaction type

The question asks: "Rate of the reaction is fastest when $Z$ is ..." with substituents $Z = OC_2H_5,\, NH_2,\, Cl,\, OCOCH_3$

This standard type of question in basic organic chemistry usually refers to electrophilic aromatic substitution on an aromatic ring, where the substituent $Z$ already present on the ring affects the reaction rate.

Recall the effect of substituents on ring activation/deactivation

In electrophilic aromatic substitution:

• Electron-donating groups activate the ring and increase the rate.
• Electron-withdrawing groups deactivate the ring and decrease the rate.

Compare the given groups:

• $-NH_2$ : very strong $+M$ (resonance donation), strongly activating
• $-OC_2H_5$ : strong $+M$, activating
• $-OCOCH_3$ : oxygen is attached to ring, but its lone pair is partly tied up with the carbonyl; still o/p-directing but less activating than alkoxy/amino
• $-Cl$ : has lone-pair resonance donation, but strong $-I$ effect dominates; overall deactivating

Order of activation

The approximate reactivity order is $NH_2 > OR > OCOCH_3 > Cl$

Therefore, the aromatic ring reacts fastest when $Z = NH_2$

Check each option

• A: $OC_2H_5$ — activating, but not the strongest
• B: $NH_2$ — strongest activator among the options ✅
• C: $Cl$ — deactivating, so not fastest
• D: $OCOCH_3$ — weaker activator than $OR$ and $NH_2$

Derived answer

Hence, the rate is fastest for $\boxed{NH_2}$

Comparison with stored correct answer

Stored correct answer is C ($Cl$).

This does not match the standard substituent effect in electrophilic aromatic substitution. Unless the missing reaction scheme is of some unusual type where $Cl$ specifically accelerates the reaction, the chemically correct answer from the given substituent effects is B ($NH_2$).