Problem 53 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system? (b) For a certain process that occurs at constant \(T\) and \(P\), the value of \(\Delta G\) is positive. Is the process spontaneous? (c) If \(\Delta G\) for a process is large, is the rate at which it occurs fast?

Step-by-Step Solution

Answer

(a) The change in Gibbs free energy (ΔG) does depend on changes in the enthalpy (ΔH) and entropy (ΔS) of the system, as described by the equation: \(ΔG = ΔH - TΔS\), where the process occurs at constant temperature (T). (b) A process with a positive ΔG at constant T and P is considered non-spontaneous, as ΔG should be negative for a process to be spontaneous. (c) A large ΔG value indicates a more significant thermodynamic driving force for the process but doesn't necessarily mean the rate of the process is fast. The rate is determined by reaction kinetics, which are governed by activation energy and the reaction mechanism.

Step 1: (a) Relationship of ΔG with ΔH and ΔS at constant temperature

The Gibbs free energy change (ΔG) is related to the enthalpy change (ΔH) and entropy change (ΔS) according to the equation: \[ ΔG = ΔH - TΔS \] In this case, the process occurs at constant temperature (T). Thus, the change in Gibbs free energy (ΔG) does depend on changes in the enthalpy (ΔH) and entropy (ΔS) of the system.

Step 2: (b) Spontaneity of process with positive ΔG

A process with positive ΔG is considered to be non-spontaneous at constant T and P. This is because, according to the equation: \[ ΔG = ΔH - TΔS \] when ΔG is positive, it indicates unfavorable thermodynamic conditions for the process to be spontaneous. Remember that for a process to be spontaneous, ΔG should be negative.

Step 3: (c) Relationship of ΔG magnitude with the rate of the process

The magnitude of ΔG doesn't determine the rate at which the process occurs, but rather the thermodynamic favorability or feasibility of the reaction. A large ΔG value indicates a more significant thermodynamic driving force for the process in either the forward or reverse direction (based on the sign of ΔG). To determine the rate of the process, we need to consider the reaction kinetics, which are governed by the activation energy and the reaction mechanism. So, having a large (positive or negative) ΔG doesn't necessarily mean the rate of the process is fast.

Key Concepts

Enthalpy Change

Enthalpy change, denoted as ΔH, is a measure of the total heat content in a chemical system. It represents the energy absorbed or released in a reaction, especially under constant pressure. When we look at reactions, if the enthalpy change is positive, the system absorbs heat from its surroundings. This is known as an endothermic reaction. On the other hand, if ΔH is negative, it releases heat and is called an exothermic reaction.
Enthalpy change plays a crucial role in determining the Gibbs free energy change (ΔG) of a system, as seen in the equation:\[ΔG = ΔH - TΔS\]This relationship implies that how much heat is taken in or given out affects the spontaneity of the reaction. It's important because it helps predict whether a process needs energy input to proceed, or if it will release energy as it progresses.

Entropy Change

Entropy, often represented as ΔS, is a measure of disorder or randomness in a system. A positive ΔS indicates that a system becomes more disordered during the reaction, while a negative ΔS suggests a decrease in disorder.
Entropy change is a key factor in the formula for Gibbs free energy:\[ΔG = ΔH - TΔS\]This equation highlights that as temperature (T) increases, the impact of the entropy change on ΔG becomes more significant. Entropy change is vital in processes, as greater disorder in a system often leads to increased spontaneity. This is because systems naturally tend to progress towards states with higher entropy, or more randomness.

Spontaneity

Spontaneity in chemical reactions indicates whether a process can occur without external intervention. For a process to be spontaneous, the change in Gibbs free energy (ΔG) must be negative. The equation:\[ΔG = ΔH - TΔS\]highlights the balance between enthalpy and entropy changes that affect spontaneity.

• If ΔG is negative, the process can proceed and release free energy.
• A positive ΔG means the process is non-spontaneous and requires energy input.
• A ΔG of zero suggests the system is in equilibrium, with no net change occurring.

Understanding spontaneity helps predict whether reactions favor products or reactants under certain conditions.

Reaction Rate

The reaction rate refers to how quickly a chemical reaction proceeds. Unlike spontaneity, which is governed by ΔG, reaction rate depends on kinetic factors, particularly the activation energy. This is the minimum energy needed to initiate a reaction.

• Lower activation energy usually results in a faster reaction rate.
• Higher temperatures can increase reaction rates by providing more kinetic energy to molecules.
• Concentration of reactants can also influence how fast the reaction occurs.

So while ΔG determines if and how reactions can happen thermodynamically, the actual speed of these reactions is determined by kinetic parameters like activation energy.

Activation Energy

Activation energy is the energy barrier that must be overcome for a chemical reaction to start. It influences the rate at which a reaction occurs but does not affect whether the reaction is thermodynamically favorable or spontaneous.
Reactions with lower activation energies tend to occur more quickly because it's easier for reactants to reach the energy level needed for reaction. This relates to the reaction rate, which is primarily driven by kinetics rather than thermodynamics.
Though critical for reaction speed, activation energy doesn't appear in the Gibbs free energy equation but is crucial for understanding how reactions proceed in real-world scenarios, especially when comparing the effects of different catalysts that lower this barrier.