Gibbs free energy problems are one of those tricky questions that will most likely be tested on your DAT exam.

Here’s a question to test your knowledge of Gibbs free energy:

Which of the following is true about a spontaneous, exothermic reaction?

A. ΔG is positive
B. ΔS is positive
C. ΔS is negative
D. ΔH is positive

Don’t stress out if you can’t answer this question right now. Once you understand the concepts given below, you will to be able to solve this problem on the DAT exam very easily.

And oh yeah, this question will most likely show up on your DAT test. So make sure you understand this concept!

So What Is Gibbs Free Energy?

This is what wikipedia says:

“In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy[1] to distinguish it from Helmholtz free energy) is a thermodynamic potential that measures the “useful” or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure (isothermal, isobaric)”

It’s something we don’t need to know. Sure if you love chemistry so much, you might want to understand this and other information on wikipedia to satisfy your appetite, but for our purposes, let’s just focus on what’s important here.

→ Gibbs free energy ΔG, is the energy that’s available to do useful work for a chemical reaction. ΔG helps us determine whether a given reaction is spontaneous or not.

Change in Gibbs Free Energy:

ΔG = ΔH – T ΔS

You must memorize this equation!

Here’s a mnemonic: Goose Hunters Take Shot Guns

If ΔG < 0, reaction is spontaneous.
If ΔG = 0, reaction is at equilibrium.
If ΔG > 0, reaction is non-spontaneous.

So how can we know when ΔG < 0 or ΔG > 0 ?

Let’s look at the equation first: ΔG = ΔH – T ΔS

Here are the different scenarios:

• If ΔH is negative and ΔS is positive, ΔG will be negative. Thus, reaction is spontaneous.
• If ΔH is positive and ΔS is negative, ΔG will be positive. Thus, reaction is non-spontaneous.
• If ΔH is positive and ΔS is positive, ΔG will be negative at high temperatures (T) and ΔG will positive at low temperatures (T). Thus, the reaction can be spontaneous or non-spontaneous depending on temperature.
• If ΔH is negative and ΔS is negative, ΔG will be positive at high temperatures (T) and ΔG will negative at low temperatures (T). Thus, the reaction can be spontaneous or non-spontaneous depending on temperature.

The chart below summarizes the points written above:

ΔH	ΔS	ΔG
Negative (-)	Positive (+)	Negative (-)
Positive (+)	Negative (-)	Positive (+)
Positive (+)	Positive (+)	Negative (-) at high T and Positive (+) at low T
Negative (-)	Negative (-)	Positive (+) at high T and Negative (-) at low T
		If ΔG < 0, then reaction is spontaneous.
		If ΔG = 0, then reaction is at equilibrium.
		If ΔG > 0, then reaction is non-spontaneous.

So let’s review the question from the beginning of this post:

Which of the following is true about a spontaneous, exothermic reaction?

A. ΔG is positive
B. ΔS is positive
C. ΔS is negative
D. ΔH is positive

By looking at the chart, we see that only possible scenario is Answer choice B. For a reaction to be a spontaneous in a exothermic reaction (ΔH < 0), ΔS must be positive.