Question

The $\mathrm{\Delta }G$ in the process of melting of ice at $-{15}^{\circ }\mathrm{C}$ : is (1) $\mathrm{\Delta }\mathrm{G}<0$ (2) $\mathrm{\Delta }G>0$ (3) $\mathrm{\Delta }\mathrm{G}=0$ (4) All

Short answer

$\mathrm{\Delta }G>0$. Melting ice at -15°C is non-spontaneous.

Step-by-step solution

Understanding the Concept of $\mathrm{\Delta }G$

The Gibbs free energy change ($\mathrm{\Delta }G$) determines whether a process is spontaneous. If $\mathrm{\Delta }G<0$, the process is spontaneous. If $\mathrm{\Delta }G>0$, the process is non-spontaneous. At equilibrium, $\mathrm{\Delta }G=0$.

Relationship Between Temperature and State Changes

Melting of ice involves a phase change from solid to liquid. The melting point of ice is 0°C. At temperatures below 0°C, such as -15°C, ice does not spontaneously melt because the energy required for melting is not freely available from the surroundings.

Determining $\mathrm{\Delta }G$ at -15°C

Since the process of melting ice at -15°C is non-spontaneous, the Gibbs free energy change ($\mathrm{\Delta }G$) will be positive. This indicates that external energy would be necessary to melt the ice at this temperature.

Conclusion

Based on the analysis, the correct answer to the question is (2) $\mathrm{\Delta }G>0$.

Key concepts

spontaneous processes

A spontaneous process is a self-driven event that occurs without external intervention. In thermodynamics, whether a process is spontaneous is determined by the Gibbs free energy change ( $\mathrm{\Delta }G$). If $\mathrm{\Delta }G\text{<}0$, the process happens spontaneously. This means the system naturally tends to a lower free energy state. For example, rusting of iron in a moist environment and the expansion of a gas into a vacuum are spontaneous processes.
Mature wineries practice non-spontaneous processes too! For non-spontaneous processes, like electrolyzing water to get hydrogen and oxygen, $\mathrm{\Delta }G0$. This indicates that these processes require an input of energy to proceed.

phase changes

Phase changes involve transformations between solid, liquid, and gaseous states. Examples are melting, freezing, and boiling. The transition from ice to water (melting) is a familiar phase change. At 0°C, this occurs spontaneously, so $\mathrm{\Delta }G=0$ because the system is in equilibrium. However, at temperatures below 0°C, such as -15°C, ice will not melt spontaneously because the energy from the surroundings is insufficient to drive the process. Thus, $\mathrm{\Delta }G0$ under these conditions. This is why ice remains solid in a freezer!
Conversely, think about warm butter melting on a sunny day – that's a phase change propelled by spontaneous Gibbs free energy.

thermodynamics

Thermodynamics studies energy transformations in physical and chemical processes. It comprises laws that govern these energy changes. The second law of thermodynamics is crucial for understanding entropy and spontaneous processes. According to this law, the total entropy of an isolated system can never decrease over time. Gibbs free energy ( $\mathrm{\Delta }G$ ) is derived from this concept and is defined as $\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$, where $\mathrm{\Delta }H$ is the enthalpy change, $T$ is the temperature, and $\mathrm{\Delta }S$ is the entropy change.
Understanding these laws helps explain why some reactions or processes require energy while others release it.