Total Number of Compounds Soluble in Aqueous NaOH

To determine the total number of compounds soluble in aqueous $\text{NaOH}$, we must consider the acidity of the functional groups present in each structure:

1. Criterion for Solubility in Aqueous $\text{NaOH}$:
   A compound is soluble in aqueous sodium hydroxide ($\text{NaOH}$) if it contains functional groups that are acidic enough ($pK_a \lesssim 10$) to undergo an acid-base neutralization reaction with $\text{OH}^-$. This deprotonation converts the organic compound into a water-soluble ionic salt (e.g., sodium carboxylates or sodium phenoxides).
   • Carboxylic acids ($-\text{COOH}$, $pK_a \sim 3-5$) and phenols ($\text{Ar-OH}$, $pK_a \sim 10$) are acidic enough to react with aqueous $\text{NaOH}$ and dissolve.
   • Aliphatic alcohols ($-\text{CH}_2\text{OH}$, $pK_a \sim 15-17$), amines, ethers, hydrocarbons, and neutral aromatic compounds (such as nitrobenzene) do not react significantly with $\text{NaOH}$ and remain insoluble.

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1. Analysis of the Given Compounds:

   • Compound 1: $N,N$-Dimethylaniline ($\text{C}_6\text{H}_5\text{N(CH}_3\text{)}_2$)

     • Functional group: Tertiary aromatic amine (basic).
     • Acidity: Contains no acidic protons to react with $\text{NaOH}$.
     • Solubility: Insoluble in aqueous $\text{NaOH}$.

   • Compound 2: Cyclohexanecarboxylic acid ($\text{C}_6\text{H}_{11}\text{COOH}$)

     • Functional group: Carboxylic acid ($pK_a \approx 4.8$).
     • Reaction: $\text{C}_6\text{H}_{11}\text{COOH} + \text{NaOH} \rightarrow \text{C}_6\text{H}_{11}\text{COO}^-\text{Na}^+ + \text{H}_2\text{O}$
     • Solubility: Soluble due to salt formation.

   • Compound 3: 2-Ethoxybenzyl alcohol ($o\text{-EtO-C}_6\text{H}_4\text{-CH}_2\text{OH}$)

     • Functional group: Ether and benzylic (aliphatic) alcohol ($pK_a \approx 15$).
     • Acidity: Benzylic alcohols are not acidic enough to react with $\text{NaOH}$.
     • Solubility: Insoluble in aqueous $\text{NaOH}$.

   • Compound 4: Phenol ($\text{C}_6\text{H}_5\text{OH}$)

     • Functional group: Phenolic hydroxyl group ($pK_a \approx 10$).
     • Reaction: $\text{C}_6\text{H}_5\text{OH} + \text{NaOH} \rightarrow \text{C}_6\text{H}_5\text{O}^-\text{Na}^+ + \text{H}_2\text{O}$
     • Solubility: Soluble due to formation of sodium phenoxide.

   • Compound 5: Nitrobenzene ($\text{C}_6\text{H}_5\text{NO}_2$)

     • Functional group: Nitro group attached to benzene ring.
     • Acidity: Neutral compound, no acidic protons.
     • Solubility: Insoluble in aqueous $\text{NaOH}$.

   • Compound 6: 4-(Dimethylamino)phenol ($p\text{-Me}_2\text{N-C}_6\text{H}_4\text{-OH}$)

     • Functional group: Phenolic hydroxyl group ($pK_a \approx 10$) and tertiary amine.
     • Reaction: The phenolic $-\text{OH}$ group reacts with $\text{NaOH}$ to yield a soluble phenoxide salt:
       $p\text{-Me}_2\text{N-C}_6\text{H}_4\text{-OH} + \text{NaOH} \rightarrow p\text{-Me}_2\text{N-C}_6\text{H}_4\text{-O}^-\text{Na}^+ + \text{H}_2\text{O}$
     • Solubility: Soluble.

   • Compound 7: 1,2-Diethylbenzene ($\text{C}_6\text{H}_4(\text{C}_2\text{H}_5)_2$)

     • Functional group: Aromatic hydrocarbon.
     • Acidity: Non-acidic.
     • Solubility: Insoluble in aqueous $\text{NaOH}$.

   • Compound 8: 1-Naphthoic acid ($\text{C}_{10}\text{H}_7\text{COOH}$)

     • Functional group: Carboxylic acid ($pK_a \approx 3.7$).
     • Reaction: $\text{C}_{10}\text{H}_7\text{COOH} + \text{NaOH} \rightarrow \text{C}_{10}\text{H}_7\text{COO}^-\text{Na}^+ + \text{H}_2\text{O}$
     • Solubility: Soluble due to salt formation.

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1. Conclusion:

The compounds soluble in aqueous $\text{NaOH}$ are:

1. Cyclohexanecarboxylic acid
2. Phenol
3. 4-(Dimethylamino)phenol
4. 1-Naphthoic acid

Thus, the total number of compounds soluble in aqueous $\text{NaOH}$ is 4.