# Physical Chemistry : Gibbs Free Energy

## Example Questions

### Example Question #1 : Gibbs Free Energy

For Constant Temperature, Gibbs Free Energy is defined as:

Where ,  is the change in Gibbs Free Energy,  is the change in enthalpy,  is temperature, and  is the change in entropy.

Which of the following scenarios is not possible?

Explanation:

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).

### Example Question #2 : Gibbs Free Energy

For constant temperature, Gibbs free energy is defined as:

Where ,  is the change in Gibbs free energy,  is the change in enthalpy,  is temperature, and  is the change in entropy.

Given that a system is spontaneous, which of the following states are possible?

I.

II.

III.

IV.

II and III

I and III

I, II, and III

I, II, III, and IV

IV only

I and III

Explanation:

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).

### Example Question #3 : Gibbs Free Energy

The enthalpy of a reaction is  and the entropy of a reaction is . Which of the following is the Gibbs free energy (in ) of this reaction?

Cannot be determined from the given information

Cannot be determined from the given information

Explanation:

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.

### Example Question #4 : Gibbs Free Energy

In an exergonic reaction, products will have __________ Gibbs free energy and the reaction is __________.

lower . . . nonspontaneous

higher . . . nonspontaneous

lower . . . spontaneous

higher . . . spontaneous