Question

Which of the following has the highest enthalpy content, and which the lowest at a given temperature: \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s}), \mathrm{H}_{2} \mathrm{O}(l)\), or \(\mathrm{H}_{2} \mathrm{O}(g) ?\) Explain.

Short answer

\(\mathrm{H}_2\mathrm{O}(g)\) has the highest enthalpy; \(\mathrm{H}_2\mathrm{O}(s)\) has the lowest.

Step-by-step solution

Understand the Problem

We need to determine the enthalpy content of water in its three different states: solid (ice, \(\mathrm{H}_2\mathrm{O}(s)\)), liquid (water, \(\mathrm{H}_2\mathrm{O}(l)\)), and gas (vapor, \(\mathrm{H}_2\mathrm{O}(g)\)). Enthalpy changes with phase transitions due to energy absorption or release.

Recognize State Enthalpy

In general, for a given substance, the enthalpy increases from solid to liquid to gas. This is because energy is required to overcome intermolecular forces: \(\mathrm{H}_2\mathrm{O}(s) \to \mathrm{H}_2\mathrm{O}(l)\) absorbs energy (melting), and \(\mathrm{H}_2\mathrm{O}(l) \to \mathrm{H}_2\mathrm{O}(g)\) requires even more energy (vaporization).

Rank the Enthalpy Content

Among the states of \(\mathrm{H}_2\mathrm{O}\), the gaseous state \(\mathrm{H}_2\mathrm{O}(g)\) has the highest enthalpy content because it requires the most energy for molecules to escape intermolecular attractions. Conversely, the solid state \(\mathrm{H}_2\mathrm{O}(s)\) has the lowest enthalpy as it involves less energy than other states.

Conclusion

Therefore, at a given temperature, \(\mathrm{H}_2\mathrm{O}(g)\) has the highest enthalpy content, while \(\mathrm{H}_2\mathrm{O}(s)\) has the lowest. This conclusion is based on the energy required to transition between different states of matter.

Key concepts

Phase Transitions

Phase transitions occur when a substance changes from one state of matter to another. For water, these transitions can be from solid (\(\mathrm{H}_2\mathrm{O}(s)\) or ice) to liquid (\(\mathrm{H}_2\mathrm{O}(l)\) or water), and then to gas (\(\mathrm{H}_2\mathrm{O}(g)\) or vapor).
During each of these transitions, energy is either absorbed or released, which affects the enthalpy content.

• Solid to Liquid: known as melting, it absorbs energy.
• Liquid to Gas: known as vaporization, it absorbs even more energy.
• Gas to Liquid: known as condensation, releases energy.
• Liquid to Solid: known as freezing, releases energy.

These energy changes are crucial for the enthalpy comparison between states.

State of Matter

The state of matter is a distinct form that different phases of matter take on. Common states include solid, liquid, and gas. Water is a great example as it naturally exists in all three states depending on the temperature and pressure conditions.

• Solid: In the case of water, this is ice. Molecules are tightly packed and vibrate in place.
• Liquid: Water is in its liquid form, with molecules free to move around but still moderately attracted to each other.
• Gas: Water vapor, where molecules move freely and are far apart.

Moving from one state to another involves overcoming or reducing intermolecular forces, which impacts enthalpy.

Energy Absorption

Energy absorption is a key process during phase transitions. When a substance absorbs energy, its temperature or state can change.

• Melting: When ice (\(\mathrm{H}_2\mathrm{O}(s)\)) absorbs heat, it turns into water (\(\mathrm{H}_2\mathrm{O}(l)\)).
• Vaporization: When water (\(\mathrm{H}_2\mathrm{O}(l)\)) absorbs sufficient heat, it becomes steam (\(\mathrm{H}_2\mathrm{O}(g)\)).
• This absorbed energy is stored as potential energy in molecular movements and is reflected in higher enthalpy.

Energy absorption facilitates the transition from a lower to a higher state of matter, increasing the enthalpy of the substance.

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together in different states of matter. These include hydrogen bonds, dipole-dipole interactions, and van der Waals forces, varying in strength and consequences.

• Solid: Strong intermolecular forces keep molecules closely packed, resulting in low enthalpy.
• Liquid: Forces are moderate, allowing some freedom of movement, and therefore intermediate enthalpy.
• Gas: Very weak forces as molecules move independently, leading to the highest enthalpy.

To transition from solid to liquid to gas, energy must be input to overcome these forces, explaining why gaseous states have a higher enthalpy content.