Question

Molar heat capacity of water in equilibrium with ice at constant pressure is (a) zero (b) infinity (c) \(40.45 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) (d) \(75.48 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)

Short answer

(b) infinity

Step-by-step solution

Understanding the Concept

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Kelvin. When water is in equilibrium with ice, both phases exist together without any temperature change as long as pressure and temperature remain constant.

Phase Equilibrium Condition

When ice and water are in equilibrium at constant pressure, the temperature remains fixed at the melting point. Therefore, any heat added does not cause a change in temperature but only a phase change.

Calculating Heat Capacity at Phase Transition

At the phase transition between ice and water, the heat capacity is calculated based on the fact that it requires energy to convert phase instead of raising temperature. This causes the heat capacity to approach infinity because any finite amount of heat does not change the temperature.

Conclusion

Given that the temperature does not increase with added heat because of the phase transition, the molar heat capacity becomes infinitely large during this phase equilibrium.

Key concepts

Phase Transition

Phase transitions occur when a substance changes from one state of matter to another, like from solid to liquid or liquid to gas. During a phase transition, the added energy does not increase the temperature of the substance.
Instead, the energy is used to change the state. A common example of phase transition is when ice melts to become water.
For ice, this phase transition occurs at 0°C (273.15 K). The temperature remains constant during this change, even as energy is added.

• Temperature does not increase until the transition is complete.
• The added heat is used entirely in altering the molecular structure from solid to liquid.

Understanding phase transitions is crucial because they explain why heat added during these processes does not raise temperature.

Equilibrium of Ice and Water

The equilibrium of ice and water is a delicate balance where both ice and water coexist at the melting point. At this stage, any heat added to the system goes into the phase change rather than increasing temperature.
This balance is pivotal because:

• Both phases exist simultaneously at the same temperature.
• The system remains at 0°C or 273.15 K under standard atmospheric pressure.
• This state ensures the molar heat capacity approaches infinity because heat input does not affect temperature.

In essence, during ice and water equilibrium, energy added does not warm the system but shifts the equilibrium towards more liquid water.

Constant Pressure Conditions

Constant pressure conditions mean the pressure in the system does not change even as the phase transition occurs. This is significant in understanding molar heat capacity because both temperature and pressure affect how substances absorb heat.
Under constant pressure, as in melting ice, any added heat causes phase transitions rather than temperature changes.

• The system remains at a homogeneous pressure level, typically atmospheric pressure.
• This constancy ensures equilibrium conditions are unaltered during the energy input process.

Therefore, constant pressure conditions help ensure the phase transition progresses smoothly without external pressure fluctuations impacting the balance of its phases.