The following condition is not possible:

This is because if enthalpy is positive, and entropy is negative, the negative sign in front of the temperature term in the formula becomes positive. Addition of 2 positive numbers can not be negative. Plugging in arbitrary numbers into the other conditions can show they are all possible.

Take the following condition:

Then Gibbs free energy  can either be positive or negative, depending on the magnitude of enthalpy, entropy, and temperature. (If enthalpy is much larger than entropy and temperature, then the difference will be positive, but if entropy *  is greater than the enthalpy, then the difference will be negative).

Condition I is always true. Condition II is never true, as Gibbs free energy cannot be negative if enthalpy is positive and entropy is negative. Condition III may be true if temperature is very high (this is the scenario when the  term dominates the  term. Condition IV is not possible because  and we were given a system with a Gibbs free Energy that is  (we were told the system was spontaneous). 

Gibbs free energy of a system can be solved using the following equation.

where  is change in Gibbs free energy,  is change in enthalpy,  is temperature in Kelvins and  is change in entropy. To solve for  we need all three of the variables. We are not given the temperature; therefore, we cannot solve for Gibbs free energy.

Exergonic reaction suggests that the Gibbs free energy is negative. Since the change in Gibbs free energy is defined as Gibbs free energy of products - Gibbs free energy of reactants, a negative change in Gibbs free energy suggests that the products have a lower Gibbs free energy than reactants. A reaction is spontaneous if it has negative Gibbs free energy; therefore, exergonic reactions are always spontaneous. This is because the reaction is producing a more stable product (lower energy) from a less stable reactant (higher energy).

Enthalpy is the amount of internal energy contained in a compound whereas entropy is the amount of intrinsic disorder within the compound. Enthalpy is zero for elemental compounds such hydrogen gas and oxygen gas; therefore, enthalpy is nonzero for water (regardless of phase). Entropy, or the amount of disorder, is always highest for gases and lowest for solids. This is because gas molecules are widely spread out and, therefore, are more disordered than solids and liquids. Hydrogen gas will have a higher entropy than liquid water.

The first law of thermodynamics states that the energy of the universe is always constant, which implies that energy cannot be created or destroyed. The energy lost by a system is gained by surroundings and vice versa; however, the total energy of the universe is always constant. The second law of thermodynamics states that the entropy, or the amount of disorder in the universe, is always increasing. This suggests that the universe is always going towards a more disordered state. Based on these two laws, we can determine that statement I and statement II are false. Note that these two statements are talking about the system, rather than the universe. The energy (in the form of enthalpy) and entropy can increase or decrease in a system. The surroundings will compensate accordingly to keep the energy of universe constant and increase the entropy. Absolute entropy of a system, surroundings or the universe can never be negative because it isn’t possible to have negative disorder (this is due to the definition of entropy; just remember that entropy can never be negative). Note that the change in entropy can, however, be negative.

The Third Law of Thermodynamics states that a pure crystalline substance at absolute zero has an entropy of . Mathematically, this formula is expressed as:

where  is the Boltzmann constant  and W is the number of microstates of a gaseous atom in the system. Because microstates are used to describe this gaseous atom, there has to be at least one or more. 

If only one microstate exists for the system, then the entropy is zero , and can only increase from this point. It is therefore mathematically impossible for any element to have a negative standard entropy. 

Remark: keep in mind that entropy changes can be negative, but the entropy of pure compounds cannot be negative. 

The First Law of thermodynamics states that for a system that only exchanges energy by heat or work: 

Work is done by the system, therefore

The First Law of thermodynamics states that for a system that only exchanges energy by heat or work: 

The heat is given off by the system, so . Similarly, work is being done by the system, so 
 

The First Law of thermodynamics states that for a system that only exchanges energy by heat or work: 

Heat is absorbed by the system, therefore 

So 

 done by the system.