Question

For a reaction taking place at constant \(p\) and \(\mathrm{T}\), why can we say that the \(\Delta \mathrm{G}^{0}\) remains constant, but we cannot say the same for \(\Delta G\) ?

Short answer

Answer: The standard Gibbs free energy change (\(\Delta \mathrm{G}^{0}\)) remains constant because it depends only on the standard state properties of reactants and products. In contrast, the actual Gibbs free energy change (\(\Delta G\)) does not remain constant, as it is influenced by the changing concentrations of reactants and products throughout the reaction, even at constant pressure and temperature.

Step-by-step solution

Understand the equation for Gibbs free energy change of a reaction

Gibbs free energy change (\(\Delta G\)) is a thermodynamic property, which is used to determine the spontaneity of a chemical reaction at a constant temperature and pressure. The equation for Gibbs free energy change is: \(\Delta G = \Delta H - \mathrm{T} \Delta S\) Where, \(\Delta G\) = Gibbs free energy change \(\Delta H\) = Enthalpy change of the reaction \(\mathrm{T}\) = Absolute temperature (in Kelvin) \(\Delta S\) = Entropy change of the reaction It is essential to note that \(\Delta G\) depends on the changes in enthalpy and entropy of the reaction, as well as the temperature.

Define standard Gibbs free energy change of a reaction

Standard Gibbs free energy change (\(\Delta \mathrm{G}^{0}\)) is the change in Gibbs free energy at standard conditions, namely 1 bar pressure and a specific temperature (\(\mathrm{T}\)). For the calculation, all the components in the reaction are considered to be in their standard states. The relation between \(\Delta G\) and \(\Delta \mathrm{G}^{0}\) can be expressed by the following equation: \(\Delta G = \Delta \mathrm{G}^{0} + RT \ln Q\) Where, \(\Delta G\) = Gibbs free energy change \(\Delta \mathrm{G}^{0}\) = Standard Gibbs free energy change \(R\) = Universal gas constant \(\mathrm{T}\) = Absolute temperature (in Kelvin) \(Q\) = Reaction quotient

Standard Gibbs free energy change remains constant at constant \(\mathrm{T}\) and \(p\)

The standard Gibbs free energy change is calculated at standard conditions of pressure and temperature, where all reactants and products are in their standard states. Thus, at a constant pressure (\(p\)) and temperature (\(\mathrm{T}\)), \(\Delta \mathrm{G}^{0}\) remains constant because it only depends on the properties of the reactants and products in their standard states.

Gibbs free energy change does not remain constant at constant \(\mathrm{T}\) and \(p\)

On the contrary, the actual Gibbs free energy change (\(\Delta G\)) depends on the concentration of reactants and products, which varies throughout the course of the reaction. As the reaction proceeds, the concentration of reactants decreases, while the concentration of products increases. From the equation \( \Delta G = \Delta \mathrm{G}^{0} + RT \ln Q \), we can see that the value of \(\Delta G\) will change, given that the reaction quotient (\(Q\)) is affected by the changing concentrations of the reactants and products. Therefore, even at a constant pressure (\(p\)) and temperature (\(\mathrm{T}\)), \(\Delta G\) does not remain constant. In conclusion, during a reaction at constant pressure and temperature, standard Gibbs free energy change (\(\Delta \mathrm{G}^{0}\)) remains constant because it depends only on the standard state properties of reactants and products. However, the actual Gibbs free energy change (\(\Delta G\)) does not remain constant, as it is influenced by the changing concentrations of reactants and products in the system.

Key concepts

Thermodynamic Properties

Thermodynamic properties are essential concepts in chemistry that help us understand the behavior of substances under different conditions. Two important thermodynamic properties are enthalpy and entropy. These properties give insight into the energy changes and disorder associated with chemical reactions.

• Enthalpy (\(\Delta H\)): This is a measure of the total energy of a thermodynamic system. It encompasses the internal energy and the energy required for a system to expand against the surrounding pressure. It helps to define if a reaction releases heat (exothermic) or absorbs heat (endothermic).


• Entropy (\(\Delta S\)): Entropy is a measure of the disorder or randomness within a system. A positive \(\Delta S\) indicates an increase in disorder, while a negative value suggests a decrease in disorder. Entropy is significant in determining the spontaneity of a reaction.

Understanding these properties is crucial when evaluating the Gibbs free energy, which combines both enthalpy and entropy to predict the direction and feasibility of a chemical reaction.

Reaction Spontaneity

The spontaneity of a chemical reaction is determined by Gibbs free energy change (\(\Delta G\)). A reaction is considered spontaneous if it occurs naturally without needing additional external energy. The \(\Delta G\) helps to predict this spontaneous behavior.

• A negative \(\Delta G\) indicates that the reaction is spontaneous. This means that the total energy of the products is lower than that of the reactants, implying a release of free energy.


• A positive \(\Delta G\) means that the reaction is non-spontaneous and requires external energy to proceed. This suggests that the reactants' energy is higher than that of the products.


• If \(\Delta G = 0\), the system is at equilibrium, and there is no net change occurring.

Therefore, the sign and magnitude of \(\Delta G\) are pivotal in determining whether a reaction will occur spontaneously.

Enthalpy and Entropy Changes

In thermodynamics, both enthalpy and entropy play a critical role in defining the Gibbs free energy, represented by the equation \(\Delta G = \Delta H - T \Delta S\). This expression shows how these properties influence the feasibility of chemical reactions.

Influence of Enthalpy Change

If a reaction has a negative \(\Delta H\), it is generally favorable, as it releases energy (exothermic). This can greatly contribute to a negative \(\Delta G\), hence promoting spontaneity.
If \(\Delta H\) is positive, the reaction absorbs energy (endothermic), often resisting spontaneous change unless there is a compensating increase in entropy.

Impact of Entropy Change

A positive \(\Delta S\) contributes to making \(\Delta G\) more negative, which aids in reaction spontaneity by increasing the system's disorder.On the other hand, a negative \(\Delta S\) may hinder spontaneity by leading to a more organized system, often offset by a favorable \(\Delta H\).Understanding these changes allows chemists to tailor conditions that optimize reaction favorability.

Standard Conditions in Thermodynamics

Standard conditions in thermodynamics refer to a set of defined conditions used to compute specific properties like standard Gibbs free energy change (\(\Delta G^0\)). These conditions allow for the comparison of reactions under a consistent framework.

• Standard Pressure: Usually 1 bar or 1 atm. This consistency enables the comparison of different reactions' thermodynamic properties.


• Specific Temperature: Often 298.15 K (25°C). This is the standard temperature commonly used to assess reactions.


• Standard States: Reactants and products are in their most stable forms at 1 bar for substances in a gaseous state or as pure liquids or solids.

Under these conditions, \(\Delta G^0\) remains constant for a given reaction as it relies solely on intrinsic properties of reactants and products in their standard states. It is not influenced by variations in concentration like the actual Gibbs free energy change (\(\Delta G\)), providing a valuable reference point for understanding reaction dynamics.