19.6 – 19.7 Student Notes

IV. Free Energy and Equilibrium Constants

A. Relating ΔG° to the Equilibrium Constant

1. Thermodynamic equilibrium constant – K –

2. Liquid solution K à K_c

Gases K à K_p

3. Writing the Expression for a Thermodynamic Equilibrium Constant

Write expressions for the thermodynamic equilibrium constants for each of the following reactions:

a. 2 NH₃ (g) + CO₂ (g) ¯ NH₂CONH₂ (aq) + H₂O (l)

b. AgCl (s) ¯ Ag⁺ (aq) + Cl^- (aq)

4. ΔG =

Q – reaction quotient – [products] / [reactants]

ΔG° =

5. Calculating K from the Standard Free-Energy Change (Molecular Equation)

Find the value of the equilibrium constant K at 25° C (298 K) for the reaction

2 NH₃ (g) + CO₂ (g) ¯ NH₂CONH₂ (aq) + H₂O (l)

The standard free-energy change, ΔG°, at 25° C equals – 13.6 kJ.

5. Calculating K from the Standard Free-Energy Change (Net Ionic Equation)

Calculate the equilibrium constant K_sp at 25° C for the reaction

AgCl (s) ¯ Ag⁺ (aq) + Cl^- (aq)

using standard free energies of formation.

6. Criterion for Spontaneity

a. When equilibrium constant is greater than 1,

b. When equilibrium constant is less than 1,

c. When K is between 0.018 and 57,

7. Concept Check

The following reaction is spontaneous in the direction give.

A (g) + B (g) à C (g) + D (g)

Suppose you are given a vessel containing an equilibrium mixture of A, B, C, and D, and you increase the concentration of C by increasing its partial pressure.

a. How is the value of ΔG° affected by the addition of C to the vessel?

b. How is the value of ΔG affected by the addition of C to the vessel?

B. Change of Free Energy with Temperature

1. ΔG°_T = ΔH° - T ΔS° (approximation for ΔG°_T)

2. Spontaneity and Temperature Change

ΔH°	ΔS°	ΔG°	Description
-	+	-
+	-	+
-	-	+ or -
+	+	+ or -

1. Concept Check

Consider the decomposition of dinitrogen tetroxide, N₂O₄, to nitrogen dioxide, NO₂.

N₂O₄ (g) à 2 NO₂ (g)

How would you expect the spontaneity of the reaction to behave with temperature change?

2. Calculation of ΔG° at Various Temperatures

a. What is ΔG° at 1000° C for the following reaction?

CaCO₃ (s) ¯ CaO (s) + CO₂ (g)

Is this reaction spontaneous at 1000° C and 1 atm?

c. What is the value of K_p at 1000° C for this reaction? What is the partial pressure of CO₂?