Question

Write out the equation for the change in Gibbs free energy. Briefly describe the meaning of this equation.

Short answer

Answer: The equation for the change in Gibbs free energy is ∆G = ∆H - T∆S, where ∆G is the change in Gibbs free energy, ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy. This equation provides a measure of the spontaneity of a process by taking into account both the changes in enthalpy (∆H) and entropy (∆S) during the process. If ∆G is negative, the process is spontaneous, while if ∆G is positive, the process is non-spontaneous, and an external source of energy would be needed to drive the process. When ∆G is equal to zero, the process is at equilibrium.

Step-by-step solution

Writing the equation for the change in Gibbs free energy

The equation for the change in Gibbs free energy (∆G) is given as follows: ∆G = ∆H - T∆S where ∆G is the change in Gibbs free energy, ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy.

Briefly describe the meaning of the equation

The equation for the change in Gibbs free energy provides a measure of the spontaneity of a process, taking into account both the changes in enthalpy (∆H) and entropy (∆S) during the process. The change in enthalpy (∆H) represents the amount of heat absorbed or released in a process, effectively measuring the difference in bond energies between the reactants and products. A negative ∆H indicates an exothermic reaction, and a positive ∆H indicates an endothermic reaction. The change in entropy (∆S) represents the degree of random motion or disorder in a system. An increase in entropy (positive ∆S) occurs when there's a greater degree of disorder, while a decrease in entropy (negative ∆S) occurs when the system becomes more ordered. Temperature (T) has a significant effect on the spontaneity of a reaction, as it affects the balance between enthalpy and entropy. For example, at high temperatures, the entropy term can dominate, leading to a more spontaneous reaction. The Gibbs free energy equation combines these factors to determine whether a process is spontaneous or not. If ∆G is negative, the process is spontaneous, while if ∆G is positive, the process is non-spontaneous, and an external source of energy would be needed to drive the process. In the particular case when ∆G is equal to zero, the process is at equilibrium.

Key concepts

Enthalpy Change

Enthalpy change (∆H) is a measure of the total heat content of a system. It's an essential concept in thermodynamics, especially when discussing chemical reactions. During a reaction, bonds between atoms are either broken or formed, and this process either absorbs or releases energy, typically in the form of heat. An exothermic reaction, where ∆H is negative, releases heat to the surroundings, making the temperature of the surroundings increase. Conversely, an endothermic reaction absorbs heat, resulting in a positive ∆H, and decreases the temperature around the system.

• Exothermic reaction: ∆H < 0 (Releases heat)
• Endothermic reaction: ∆H > 0 (Absorbs heat)

To better understand enthalpy change, one could think of it as the energetic difference between reactants and products. In a chemical reaction, the outcome often depends on whether energy is put in or taken out. Thus, evaluating ∆H gives insights into the energy requirements or energy release of the reaction.

Entropy Change

Entropy change (∆S) quantifies the change in disorder or randomness within a system during a chemical reaction or physical process. Entropy is a core concept within the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. A positive ∆S implies an increase in disorder. For instance, when a solid melts into a liquid, there's more randomness in the movement of molecules, hence the entropy increases.

Examples of Entropy Change

• Solid to liquid: ∆S > 0 (Increase in entropy)
• Liquid to gas: ∆S > 0 (Further increase in entropy)
• Gas to solid: ∆S < 0 (Decrease in entropy)

These changes suggest that entropy can also be related to the phases of matter. Higher entropy in gases makes sense, as molecules have the most freedom of movement. Transitions that restrict movement, like condensation or freezing, lead to a decrease in entropy.

Thermodynamics

Thermodynamics is a field of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. The core idea behind thermodynamics is the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

Thermodynamics involves several key principles or 'laws.' The first law, as mentioned, concerns the conservation of energy. The second law focuses on the concept of entropy, stating that entropy of an isolated system always increases. The third law states that as the temperature approaches absolute zero, the entropy of a perfect crystal approaches zero. Within this field, we find useful applications in understanding the transfer of energy during chemical reactions and the conditions under which these reactions will proceed spontaneously.

Spontaneity of Reactions

The spontaneity of a reaction refers to whether a chemical reaction will occur without needing an external energy source. Essentially, it's about whether a reaction is 'self-driving' or not. Gibbs free energy (∆G), enthalpy (∆H), entropy (∆S), and temperature (T in Kelvin) all play a significant role in determining this.

If the Gibbs free energy change (∆G) for a reaction is negative, it indicates that the process can happen on its own; it's spontaneous. If ∆G is positive, the process requires energy input to occur, hence it is non-spontaneous. At equilibrium, where the forward and reverse reactions occur at the same rate, ∆G is zero. Factors such as temperature can shift this balance, making some reactions spontaneous at higher temperatures due to the increased role of entropy.

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This balance means that the concentrations of the reactants and products remain constant over time, though not necessarily equal. It's important to note that reaching equilibrium doesn't mean the reactions have stopped; they are still occurring but at equal and opposite rates.

At equilibrium, the Gibbs free energy (∆G) is zero, indicating no net change in the system's energy. This state is dynamic, meaning that external changes such as temperature or pressure can shift the equilibrium position by favoring either the forward or reverse reaction according to Le Chatelier's principle.