Question

Explain why water spontaneously freezes to form ice below \(0^{\circ} \mathrm{C}\) even though the entropy of the water decreases during the state transition. Why is the freezing of water not spontaneous above \(0^{\circ} \mathrm{C} ?\)

Short answer

Water freezes spontaneously below \(0^\circ\mathrm{C}\) because the Gibbs free energy change, \( \Delta G \), is negative, indicating spontaneity even though entropy decreases. Above \(0^\circ\mathrm{C}\), freezing is non-spontaneous due to a positive \( \Delta G \), making the process thermodynamically unfavored.

Step-by-step solution

Understanding Entropy and System Spontaneity

To understand the freezing of water, it's important to recognize the role of entropy in spontaneous processes. Entropy measures the disorder within a system; generally, processes where the entropy increases are spontaneous. However, a decrease in entropy, as seen when water freezes, doesn't necessarily preclude spontaneity. To assess the spontaneity of the process, we must consider the Gibbs free energy change, not just entropy.

Introducing Gibbs Free Energy

The Gibbs free energy, denoted by \( G \), determines the spontaneity of a process. The change in Gibbs free energy, \( \Delta G \), is given by the equation \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the enthalpy change, \( T \) is the temperature (in Kelvin), and \( \Delta S \) is the entropy change. A negative \( \Delta G \) indicates that the process is spontaneous.

Analyzing the Freezing of Water Below 0°C

When water freezes below \(0^\circ\mathrm{C}\), there's an exothermic enthalpy change (it releases heat, so \( \Delta H < 0 \)), and the entropy decreases (\( \Delta S < 0 \)). Despite the decrease in entropy, the negative enthalpy change can result in a negative \( \Delta G \), making the process spontaneous due to the thermodynamic favorability of heat release.

Explaining the Lack of Spontaneity Above 0°C

Above \(0^\circ\mathrm{C}\), the enthalpy change linked with the freezing of water does not sufficiently compensate for the decrease in entropy; thus, the Gibbs free energy change, \( \Delta G \), would be positive. This indicates that the freezing process is non-spontaneous at temperatures above \(0^\circ\mathrm{C}\) because it is not thermodynamically favored.

Key concepts

Entropy

Entropy, symbolized as 'S', is a measure of disorder or randomness in a thermodynamic system. It's a fundamental concept in understanding why certain processes occur spontaneously. Entropy can be thought of as the number of ways a system's particles can be arranged while still maintaining the same overall energy.
When water freezes below 0°C, the entropy of the system decreases because the molecules in ice are more ordered than in liquid water. At first glance, this seems counterintuitive since spontaneous processes typically increase entropy. One might wonder then, why does water freeze spontaneously if it leads to decreased entropy? The answer lies in the fact that while entropy is crucial, it's not the sole determinant of spontaneity. This leads us to consider the Gibbs free energy, which combines both enthalpy and entropy to determine a process's spontaneity.

Gibbs Free Energy

The Gibbs free energy, denoted as 'G', is essential to predicting whether a process will occur spontaneously. It integrates both enthalpy and entropy changes within a system under constant pressure and temperature. The formula for the change in Gibbs free energy is
\[\begin{equation} \Delta G = \Delta H - T\Delta S \end{equation}\]
where \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) represents the enthalpy change, \( T \) is the absolute temperature, and \( \Delta S \) is the change in entropy. A negative \( \Delta G \) value implies a spontaneous process.
In the case of water freezing below 0°C, even though the entropy decreases (\( \Delta S < 0 \)), the enthalpy change is exothermic (\( \Delta H < 0 \)) and significant enough to ensure that the overall \( \Delta G \) is negative, favoring a spontaneous freeze. However, above 0°C, where the enthalpy change isn't sufficiently negative to offset the entropy decrease, \( \Delta G \) turns positive, and water freezing becomes non-spontaneous.

Enthalpy Change

Enthalpy change, represented by \( \Delta H \), refers to the total heat content change in a system at constant pressure. It is an essential aspect of thermodynamics because it helps us understand how much energy is released or absorbed during a process.
During the freezing of water, the process is exothermic. This means that the water releases heat to the surroundings; mathematically, we represent this by saying \( \Delta H < 0 \). The release of heat, in this context, is a crucial factor for the spontaneity of freezing because it contributes to a negative \( \Delta G \), competing against the tendency of the entropy decrease that disfavors spontaneity.
If the temperature is above freezing, the enthalpy change is not substantial enough to drive the spontaneity against the entropic cost, and thus, freezing does not occur. This tells us that for spontaneity, not only the sign of \( \Delta H \) is important, but also its magnitude in relation to the temperature and entropy change.