Question

How is Gibbs free energy related to enthalpy and entropy?

Answer 1

Hint The Gibbs Helmholtz equation defines the relation between Gibbs free energy, enthalpy and entropy. The term entropy is denoted as S and the term enthalpy is represented as H.

Complete step by step solution:
In the question it is asked how the Gibbs free energy, enthalpy and entropy is related to each other. We are very familiar with these terms as we have heard these while studying about the thermodynamic systems in Physical chemistry. Let’s briefly discuss each term so that we could just brush up the concepts and approach the question with more clarity. The three important terms mentioned in the question are Gibbs energy, enthalpy and entropy. We know that the Gibbs energy or Gibbs free energy can be defined as a parameter which is used to measure the useful work done in a thermodynamic system ,when the temperature and pressure of the system is taken as constant and free energy is represented as G and measured in joules or kilojoules.
Enthalpy- is the measure of the quantity of heat absorbed or emitted during a chemical reaction, if heat is absorbed it is called as the endothermic reaction and if heat is evolved it is called as the exothermic reaction. The enthalpy is denoted as H. The sign of H for the exothermic reaction is negative since negative change in enthalpy occurs and for endothermic its positive since positive change occurs.
Entropy –is the disorderness of a system. The system will always tend to increase its entropy in a chemical reaction and is represented as S.
Now let’s relate these three terms. The Gibbs-Helmholtz equation related these three terms.
The equation states that the Gibbs free energy is equal to the change in enthalpy subtracted from the product of temperature and change in entropy.
The equation is $\text{ }\\!\\!\Delta\\!\\!\text{ G= }\\!\\!\Delta\\!\\!\text{ H-T }\\!\\!\Delta\\!\\!\text{ S}$
And we could tell whether the reaction will be spontaneous or not by comparing the value of $\text{ }\\!\\!\Delta\\!\\!\text{ G}$ if we are provided with adequate data.
If $\text{ }\\!\\!\Delta\\!\\!\text{ G}$ is negative i.e.$\Delta G\langle 0$, then the reaction will be spontaneous reaction
If $\text{ }\\!\\!\Delta\\!\\!\text{ G}$ is positive i.e.$\Delta G\rangle 0$, then the reaction will be non-spontaneous reaction
If $\Delta G=0$, the reaction is at equilibrium.

Note: We can predict if the reaction will be spontaneous or not by having the values like $\Delta H$and$\Delta S$ comparing these values with the Gibbs-Helmholtz equation, we could tell if the value of $\Delta G$ will be negative or positive.
If $\Delta H\langle 0,\Delta S\rangle 0$, then the value of $\Delta G$ will be negative, $\Delta G\langle 0$ and the reaction will be spontaneous at all temperatures.
If $\Delta H\rangle 0,\Delta S\langle 0$, the value of $\Delta G$ will be positive i.e. $\Delta G\rangle 0$ and the reaction will not be spontaneous at any temperature.
If $\Delta H\rangle 0,\Delta S\rangle 0$, the reaction will be spontaneous at higher temperatures, for higher value of $T\Delta S$
If $\Delta H\langle 0,\Delta S\langle 0$, the reaction will be spontaneous at lower temperature if the value of $T\Delta S$ is less.