Change in Gibbs free energy is _____ related to interfacial energy and _____ related to radius of precipitate.
directly, inversely
inversely, directly
directly, directly
inversely, inversely
Directly, inversely
The change in Gibbs free energy is directly related to interfacial energy and inversely related to the radius of precipitate.
To understand this relationship, let's start with the definition of Gibbs free energy. Gibbs free energy (ΔG) is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and pressure. It is expressed as the sum of enthalpy (ΔH) minus the product of temperature (T) and entropy (ΔS): ΔG = ΔH - TΔS.
When a precipitate forms, it creates an interface between the precipitate and the surrounding medium. This interface has an interfacial energy associated with it. Interfacial energy refers to the energy required to create or maintain the interface between two phases.
Now, let's consider the process of precipitate formation. When a solute in a solution reaches its solubility limit, it can form a solid precipitate. This process typically involves a reduction in the entropy of the system since the solute molecules are transitioning from a more disordered state in the solution to a more ordered state in the solid precipitate. Therefore, ΔS is usually negative.
Since the change in Gibbs free energy is directly related to interfacial energy, as the interfacial energy increases, the change in Gibbs free energy also increases. This is because it requires more energy to create or maintain a large interface. Conversely, as the interfacial energy decreases, the change in Gibbs free energy decreases.
On the other hand, ΔG is inversely related to the radius of precipitate. As the radius of the precipitate increases, the total interfacial area between the precipitate and the surrounding medium also increases. Since interfacial energy is directly related to the area of the interface, a larger interface area leads to a higher interfacial energy. Consequently, the change in Gibbs free energy increases.
Therefore, the change in Gibbs free energy is directly related to interfacial energy and inversely related to the radius of precipitate.