Question

Is Gibbs Free Energy Always Negative?

Answer 1

Hint: In this question first we will analyse the properties of Gibb’s Free Energy using change in enthalpy and change in entropy as measuring factors. Also, Gibb’s Free Energy is used to describe the spontaneity of a reaction. Thus, its sign will imply the type of reaction undergone in a process.

Complete step by step solution:
Gibbs Free Energy is a thermodynamic potential which is used to measure the maximum amount of work done in a system when temperature and pressure are kept constant. Gibbs free energy is a state function and is independent of the path followed in a reaction.
At a constant temperature, the change in Gibbs energy is given by the Gibbs Helmholtz equation:
$\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$
Here, $\mathrm{\Delta }H$ is change in enthalpy and $\mathrm{\Delta }S$ is change in entropy. Enthalpy refers to the amount of heat involved in a reaction and entropy is the measure of disorder in a system. Now, according to the equation, the sign of Gibb’s free energy depends on the sign of enthalpy,$\mathrm{\Delta }H$ and entropy, $\mathrm{\Delta }S$. Following are the cases:
If $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are either positive or negative then the sign of $\mathrm{\Delta }G$ depends on the sign of temperature, T. Temperature can be both negative as well as positive. So, the spontaneity of the reaction depends on temperature. If $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are positive, then the reaction is spontaneous at high temperature and if $\mathrm{\Delta }H$ and $\mathrm{\Delta }S$ are both negative then the reaction is spontaneous at low temperature.
If $\mathrm{\Delta }H$ is negative and $\mathrm{\Delta }S$ is positive, then $\mathrm{\Delta }G$ will always be negative. In this case, the reaction will be spontaneous and exergonic (i.e. there is flow of energy from the system to the surrounding. In other words releasing energy in the form of work).
If $\mathrm{\Delta }H$ is positive and $\mathrm{\Delta }S$ is negative, then $\mathrm{\Delta }G$ will always be positive. Hence the reaction will be non-spontaneous and endergonic (i.e. energy is absorbed in order to start the reaction).
If $\mathrm{\Delta }G=0$, then the system is in equilibrium.
Thus, the sign of Gibbs Free Energy depends on the enthalpy, entropy and temperature.

Note: Entropy can never be positive or negative. It is the change in entropy that can be positive or negative. Negative change of entropy means that the system is less disorder. For example, when water freezes and forms ice. Positive change of entropy means the system is highly disorder. Here signs only signifies the process being followed by a system.