Which sample has the highest entropy under the stated conditions?

• A. $H_{2}O$(aq) at $25°C$ and $1\mathrm{atm}$
• B. $H_{2}O$(l) at $25°C$ and $1\mathrm{atm}$
• C. $H_{2}O$(s) at $25°C$ and $1\mathrm{atm}$
• D. $H_{2}O$(g) at $25°C$ and $1\mathrm{atm}$

Answer: (D)

Verified step by step guidance

1. Understand that entropy (S) is a measure of the disorder or randomness in a system. Generally, gases have higher entropy than liquids, and liquids have higher entropy than solids under the same conditions.
2. Identify the physical states of the samples given: aqueous (H2O(aq)), liquid (H2O(l)), and solid (H2O(s)) all at 25°C and 1 atm. Note that the problem's correct answer includes gaseous water (H2O(g)) at the same conditions, which is not listed among the initial samples but is mentioned as the highest entropy state.
3. Recall the typical order of entropy for a substance at the same temperature and pressure: solid < liquid < aqueous solution < gas. This is because molecules in the gas phase have more freedom of movement and more accessible microstates, leading to higher entropy.
4. Compare the entropy values conceptually: H2O(s) has the lowest entropy due to its ordered crystal structure; H2O(l) has higher entropy because molecules move more freely; H2O(aq) can have entropy influenced by solute interactions but generally is between liquid and gas; H2O(g) has the highest entropy due to maximum molecular freedom.
5. Conclude that among the given states, gaseous water (H2O(g)) at 25°C and 1 atm has the highest entropy because gas molecules have the greatest randomness and number of accessible microstates.