Step 1 : Understanding the Question:
This question asks us to identify the compound with the highest boiling point among the given options. The boiling point of a molecular substance is primarily determined by the strength of its intermolecular forces, which hold the molecules together in the liquid phase. Stronger intermolecular interactions require more energy to break, leading to higher boiling points.
Step 2 : Key Formulas and Approach:
Hydrogen bonding is the strongest type of intermolecular dipole-dipole attraction. It occurs when hydrogen is covalently bonded to a highly electronegative atom:
\[
\text{F}, \text{O}, \text{ or } \text{N}
\]
We will analyze each given molecule to check for the presence of hydrogen bonding and compare their relative strengths.
Step 3 : Detailed Solution:
Analyze \( \text{CH}_4 \): Carbon has low electronegativity, resulting in non-polar molecules held together only by weak London dispersion forces.
Analyze \( \text{H}_2\text{S} \): Sulfur is not sufficiently electronegative to form hydrogen bonds, meaning it only experiences weak dipole-dipole attractions.
Analyze \( \text{HCl} \): Chlorine is electronegative, but its large size prevents the formation of strong hydrogen bonds.
Analyze \( \text{H}_2\text{O} \): Oxygen is highly electronegative and small, allowing for extensive and strong intermolecular hydrogen bonding networks.
Conclude that because water molecules form a strong network of hydrogen bonds, a substantial amount of thermal energy is required to boil it.
Step 4 : Final Answer:
The compound with the highest boiling point is \( \text{H}_2\text{O} \), which corresponds to option (A).
\[
\boxed{\text{H}_2\text{O}}
\]