Problem 99 - Chemistry Matter and Change

Question

What is the sign of the free energy change, \(\Delta G^{\circ}\) system for a spontaneous reaction? (Chapter 15\()\)

Step-by-Step Solution

Answer

The sign of the free energy change, \(\Delta G^{\circ}\), for a spontaneous reaction is negative.

Step 1: Definition of Free Energy Change

The Gibbs free energy change, denoted by \(\Delta G^{\circ}\), is a thermodynamic potential that represents the maximum reversible work that may be performed by a system at a constant temperature and pressure. It is defined as the energy available to do useful work in a system, such as performing a chemical reaction.

Step 2: Relation between Free Energy Change and Spontaneity of a Reaction

A reaction is considered to be spontaneous when it occurs without the need for external influence, such as applying heat or pressure. In thermodynamics, a spontaneous process is characterized by a negative free energy change, meaning that the system loses energy in the form of work. Conversely, a non-spontaneous process has a positive free energy change, indicating that the system gains energy.

Step 3: Determining the Sign of \(\Delta G^{\circ}\) for a Spontaneous Reaction

Based on the relationship between free energy change and spontaneity of a reaction discussed in Step 2, we can conclude that for a spontaneous reaction, the sign of the free energy change \(\Delta G^{\circ}\) must be negative. This means that the system is releasing energy in the form of work, enabling the reaction to proceed without the need for external influence. So, the answer is: The sign of the free energy change, \(\Delta G^{\circ}\), for a spontaneous reaction is negative.

Key Concepts

Spontaneity of Reaction

A spontaneous reaction happens when a process occurs naturally without any outside force prompting it, such as adding heat or pressure. This doesn't mean the reaction happens immediately or quickly. Rather, it indicates that the process can proceed on its own in a given set of conditions. To determine if a reaction is spontaneous, we look at the Gibbs free energy change, \(\Delta G^{\circ}\). Spontaneity is indicated by:

• Negative \(\Delta G^{\circ}\): Shows the reaction is spontaneous and will release energy, often as work.
• Positive \(\Delta G^{\circ}\): The reaction is non-spontaneous, meaning it requires energy input to occur.

Consider a falling ball; it naturally falls due to gravity. Similarly, chemicals with a negative \(\Delta G^{\circ}\) spontaneously undergo changes without any additional help.

Gibbs Free Energy

Gibbs free energy is a measure that helps us predict the direction of chemical reactions and processes. It is a thermodynamic quantity combining enthalpy and entropy to gauge the spontaneity of a reaction under constant temperature and pressure. Gibbs free energy is represented by:\[ \Delta G = \Delta H - T\Delta S \]Where:

• \(\Delta G\) is the change in free energy, indicative of a process’s spontaneity.
• \(\Delta H\) is the change in enthalpy, or total energy change of a system.
• \(T\) is the temperature in Kelvin.
• \(\Delta S\) is the change in entropy, reflecting disorder within the system.

If \(\Delta G\) is negative, the reaction is spontaneous. If it's zero, the system is in equilibrium, and if it's positive, the process is not spontaneous.

Thermodynamic Potential

Thermodynamic potential relates to energy that a system can use to do work. The Gibbs free energy is a type of thermodynamic potential that tells us about the energy changes during a process, especially at constant pressure and temperature. Energy in the universe has different types of thermodynamic potentials, which include:

• Gibbs free energy (\(G\)): Relevant in reactions and processes occurring in open systems at constant pressure and temperature.
• Helmholtz free energy (\(F\)): Useful in processes at constant volume and temperature.
• Enthalpy (\(H\)) and internal energy (\(U\)): Understanding these aids in making energy calculations related to heat transfer and work.

Gibbs free energy, as a thermodynamic potential, helps us figure out if a reaction will occur on its own. By examining potential energy, scientists predict if reactions are favorable or if they need additional energy input.