Which of the following has the greatest entropy, S?

• A. 1.00 mole of liquid water at 30° C
• B. 1.00 mole of water vapor at 30° C
• C. 1.00 mole of regular ice at -10° C
• D. 1.00 mole of 'dry ice' (solid CO₂) at -10° C
• E. 1.00 mole of water under 10 atm of pressure at -10° C

Answer: (B)

Verified step by step guidance

1. Understand the concept of entropy: 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 due to the increased freedom of movement of particles.
2. Identify the states of matter for each option: Liquid water, water vapor (gas), regular ice (solid), dry ice (solid CO2), and water under high pressure (liquid).
3. Compare the entropy of different states: Gases have the highest entropy, followed by liquids, and then solids. Therefore, water vapor, being a gas, will have the highest entropy among the given options.
4. Consider the effect of temperature and pressure: Higher temperatures generally increase entropy as particles move more vigorously. However, in this problem, all substances are at similar temperatures, so the state of matter is the primary factor.
5. Conclude based on the analysis: Since water vapor is in the gaseous state at 30°C, it has the greatest entropy compared to the other substances listed, which are either in liquid or solid states.