Chemistry 30

3.3 Gibbs Free Energy Equation

So, both enthalpy and entropy changes are important in determining whether a reaction will occur or not. A relationship between these two factors can be expressed by a new thermodynamic term known as Gibbs Free Energy (named after the American physicist Josiah Willard Gibbs [1839-1903]). What can we conclude about spontaneity, once we've calculated ΔG? IF   ΔG < 0   The reaction is spontaneous   ΔG > 0   The reaction is nonspontaneous   ΔG = 0   The reaction is at equilibrium. Free energy change is the net driving force of a chemical reaction— whether the reaction will be spontaneous or not

Gibbs Free Energy Equation ΔG = ΔH - TΔS where ΔG = Gibbs Free Energy, in kJ ΔH = enthalpy change T = temperature, in Kelvin ΔS = entropy change (in kJ · K-1) Key items to note Temperature must be expressed in Kelvin. To convert a celsius temperature to Kelvin: K = 273 + °C ΔS must be expressed in kJ · K-1. When you calculated it before, the units were J · K-1. Divide by 1,000 to convert joules to kilojoules.

Notice the case where ΔG = 0. Equilibrium is a concept we will be discussing in depth in another module.

Generally you will find that most exothermic reactions are spontaneous, even if entropy decreases (becomes more ordered), because enthalpy contributes more to ΔG than does entropy. The exceptions are reactions occurring at high temperatures.

Example.

Calculate ΔG for the following reaction at 25°C. Will the reaction occur (be spontaneous)? How do you know?

NH₃(g) + HCl(g) → NH₄Cl(s)

Also given for this reaction:

ΔH = -176.0 kJ

ΔS = -284.8 J·K-1

Solution

We will calculate ΔG using the formula

ΔG = ΔH - TΔS

but first we need to convert units for ΔS and temperature to Kelvin:

ΔS = -284.8 J·K-1 = -0.2848 kJ·K-1

K = 273 + °C = 273 + 25 = 298 K

Now we can solve our equation:

ΔG = -176.0 - (298)(-0.2848)

ΔG = -176.0 - (-84.9)

ΔG = -91.1 kJ

Since ΔG < 0 the reaction will be spontaneous.

Here's the solution again, with the units included. You should see that ΔG will have the units kJ because the unit "K" cancels out. To simplify these web pages, units won't always be shown - it's certainly not because they aren't important (they are!) but they will be harder to show clearly on these web pages.

ΔG	=	ΔH	-	T		ΔS
	=	-176.0 kJ 1	-	298 K 1	×	-0.2848 kJ K
	=	-91.1 kJ

 

Another Method

ΔG can also be calculated using a Table of Thermochemical Data and our familiar formula

ΔG = ΣΔG^° _products - ΣΔG^° _reactants

Just as the heat of formation, ΔH^°_f for pure elements was equal to 0 kJ
(see Section 2-2), the free energy of formation, ΔG^°_f for pure elements is also
equal to 0 kJ.

Let's try the previous example again, this time using ΔG^°_f values from the Table of Thermochemical Data:

		NH3	+	HCl	→	NH4Cl
ΔG	:	-16.5	+	-95.3		-202.9
		-111.8				-202.9
ΔG	=	ΣΔG°f products - ΣΔG°f reactants
	=	-202.9 - (-111.8)
ΔG	=	-91.1 kJ				answer

 

NOTE: The values given in the Table of Thermochemical Data are for temperatures of 25°C (273 K); therefore the values are really only valid for that temperature. If the reaction occurs at some other temperature, the formula ΔG = ΔH - TΔS should be used instead.