Problem 15 - Chemistry The Central Science In Si Units

Question

Consider the melting of ice (solid water) to liquid water at a pressure of \(101.3 \mathrm{kPa}\). (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

Step-by-Step Solution

Answer

(a) Endothermic; (b) Above 0°C (273.15 K); (c) Below 0°C (273.15 K); (d) 0°C (273.15 K)

Step 1: Understanding Endothermic and Exothermic Processes

An endothermic process is one that absorbs energy (heat) from its surroundings. During the melting of ice, heat is absorbed from the surroundings to break the hydrogen bonds between water molecules, converting ice into liquid water. Therefore, this process is endothermic.

Step 2: Defining Spontaneity of Processes

A spontaneous process occurs naturally without needing external energy under given conditions. For the phase change of ice melting, it is spontaneous at temperatures above 0°C (273.15 K) at 1 atmospheric pressure (or 101.3 kPa). In this range, the Gibbs free energy change is negative, making the process spontaneous.

Step 3: Identifying Nonspontaneous Range

A nonspontaneous process is one that cannot occur without external energy. Below 0°C (273.15 K), the melting of ice is nonspontaneous, as ice does not melt on its own under these conditions. Here, the Gibbs free energy change is positive.

Step 4: Equilibrium Temperature for Phase Change

At equilibrium between solid and liquid phases, the temperature is exactly 0°C or 273.15 K for pure water at 101.3 kPa. At this temperature, ice and water coexist, with the Gibbs free energy change equal to zero.

Key Concepts

Endothermic Process

In thermodynamics, an endothermic process is characterized by the absorption of heat from the surroundings. When ice melts to form liquid water, it absorbs heat to break the hydrogen bonds between the water molecules. This heat absorption makes the process endothermic.

Understanding endothermic processes helps us appreciate how energy is required to overcome intermolecular forces. Unlike exothermic processes, which release energy, endothermic processes are often observed in physical changes like melting. Whether it's ice turning to water or other substances changing phases, the absorption of heat is the defining feature of an endothermic process.

Spontaneous Process

A spontaneous process is one that occurs naturally under given conditions without requiring continuous energy input from the surroundings. When considering the melting of ice, spontaneity occurs when ice converts to liquid water in a natural progression at temperatures above 0°C (273.15 K) at standard atmospheric pressure.

For a process to be spontaneous, the Gibbs free energy change must be negative. This means the system moves towards a state of decreased free energy, indicating that the process can proceed on its own. Understanding spontaneity helps in predicting whether a reaction or phase change is likely to occur under specified conditions.

Gibbs Free Energy

Gibbs free energy (G) is a thermodynamic potential that helps to predict the direction of a process and the condition for spontaneity. It combines the enthalpy and entropy of a system, formulated as \(G = H - TS\).

- **H** represents enthalpy, or the total energy of the system.- **T** is the temperature in Kelvin.- **S** stands for entropy, which measures the disorder within the system.

When Gibbs free energy (G) of a process is negative, the process is spontaneous. A G value of zero indicates system equilibrium, where no net change occurs. Conversely, a positive G signals a nonspontaneous process that requires energy input.

This concept is crucial in understanding phase changes, chemical reactions, and the feasibility of processes under specified conditions.

Phase Equilibrium

Phase equilibrium refers to the state where two phases of a substance coexist at equilibrium. For water, at a temperature of 0°C (273.15 K) and a pressure of 101.3 kPa, both ice and liquid water exist together without any net change in the amount of either phase.

At this equilibrium point, the Gibbs free energy change is zero (G=0), indicating no drive for the change to proceed in any direction. This equilibrium condition is crucial for understanding the stability and transitions between various states of matter.

Recognizing phase equilibrium helps in processes that require careful temperature and pressure control to maintain specific material properties, such as in metallurgy or food processing. Understanding these principles can aid in controlling and optimizing industrial processes and natural phenomena.