Free energy change is the most suitable criteria for judging the spontaneity of reactions. Derive the equation for free energy change and justify the statement by providing suitable examples.

The Gibbs free energy change (ΔG) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is the most suitable criteria for judging the spontaneity of reactions because a reaction will only be spontaneous if the Gibbs free energy change is negative.

The equation for Gibbs free energy change is derived from the first and second laws of thermodynamics. The first law, ΔU = q + w, states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (q) plus the work done on the system (w). The second law, ΔS ≥ q/T, states that the change in entropy (ΔS) of a system is greater than or equal to the heat added to the system divided by the temperature (T).

Combining these two laws, we can derive the equation for Gibbs free energy change:

ΔG = ΔH - TΔS

where ΔH is the change in enthalpy, T is the absolute temperature, and ΔS is the change in entropy.

This equation tells us that a reaction will be spontaneous if the change in enthalpy is less than the product of the temperature and the change in entropy. In other words, a reaction will be spontaneous if it results in a decrease in free energy.

For example, consider the reaction of hydrogen and oxygen to form water:

2H2(g) + O2(g) → 2H2O(l)

The enthalpy change (ΔH) for this reaction is -571.6 kJ/mol, the entropy change (ΔS) is -197.0 J/(mol·K), and the temperature (T) is 298 K. Substituting these values into the Gibbs free energy change equation gives:

ΔG = -571.6 kJ/mol - (298 K)(-197.0 J/(mol·K))

= -571.6 kJ/mol + 58.7 kJ/mol

= -512.9 kJ/mol

Since ΔG is negative, this reaction is spontaneous under these conditions.

The Gibbs free energy change (ΔG) is a thermodynamic potential that measures the maximum reversible work that a system can perform at constant temperature and pressure. It is the most suitable criteria for judging the spontaneity of reactions because a negative ΔG indicates a spontaneous process, while a positive ΔG indicates a non-spontaneous process.

The equation for Gibbs free energy change is derived from the second law of thermodynamics. It is given by:

ΔG = ΔH - TΔS

where: ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy (heat content), T is the absolute temperature (in Kelvin), and ΔS is the change in entropy (disorder).

The equation essentially states that the change in free energy of a system at constant temperature and pressure is equal to the change in enthalpy minus the product of the absolute temperature and the change in entropy.

To justify this statement, let's consider the example of ice melting into water at 0°C and 1 atm pressure. The enthalpy change (ΔH) for this process is positive because heat is absorbed. However, the entropy change (ΔS) is also positive because the disorder increases when solid ice turns into liquid water. Since the temperature is above absolute zero, the TΔS term is positive and larger than ΔH, making ΔG negative. Therefore, the process is spontaneous.

On the other hand, if we consider the reverse process (water freezing into ice), ΔH is negative because heat is released. But ΔS is also negative because the disorder decreases when liquid water turns into solid ice. In this case, the TΔS term is negative and smaller in magnitude than ΔH, making ΔG positive. Therefore, the process is non-spontaneous under the same conditions.

These examples demonstrate that the Gibbs free energy change is indeed a suitable criterion for judging the spontaneity of reactions.