Gibbs Free Energy and Spontaneity in Chemical Reactions

Gibbs Free Energy and Spontaneity

Definition and Importance of Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic quantity that measures the amount of energy available to do work during a chemical or physical process at constant temperature and pressure. It is crucial for predicting whether a reaction will occur spontaneously.

• ΔG determines the spontaneity of a reaction.

• If ΔG is negative, the process is spontaneous.

• If ΔG is positive, the process is nonspontaneous.

• If ΔG is zero, the system is at equilibrium.

Sign of ΔG	Spontaneity of Reaction
ΔG < 0	spontaneous
ΔG > 0	nonspontaneous
ΔG = 0	at equilibrium

Example:

If ΔG is small and positive, which of the following statements is true?

• a) The forward reaction is spontaneous and system is far from equilibrium

• b) The forward reaction is spontaneous and system is near equilibrium

• c) The reverse reaction is spontaneous and system is far from equilibrium

• d) The reverse reaction is spontaneous and system is near equilibrium

Predicting Spontaneity Using ΔH and ΔS

When the sign of ΔG is unknown, spontaneity can be predicted from the signs of Enthalpy (ΔH) and Entropy (ΔS):

	+ΔS	-ΔS
+ΔH	Spontaneous at high T	Never spontaneous
-ΔH	Always spontaneous	Spontaneous at low T

Example:

For the reaction: PCl5(g) ⇌ PCl3(g) + Cl2(g), ΔH = 92.50 kJ at 25°C. Which of the following statements is/are true?

• a) This is an endothermic reaction.

• b) If the temperature is increased, the ratio of [PCl3][Cl2] / [PCl5] will increase.

Practice Problems: Signs of ΔH, ΔS, and ΔG

• Practice: What are the signs of ΔH, ΔS, and ΔG for the spontaneous conversion of a solid into gas?

• Practice: You calculate the value of ΔG for a chemical reaction and get a positive value. Which would be the most accurate way to interpret this result?

  • a) If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more reactant than product.

  • b) If a mixture of reactants and products is created, we cannot say anything about its composition at equilibrium but we can say it will reach equilibrium very rapidly.

  • c) The reaction will not occur under any circumstances.

  • d) If a mixture of reactants and products is created and left to equilibrate, the equilibrium mixture will contain more product than reactant.

• Practice: Consider the combustion of butane gas and predict the signs of ΔS, ΔH, and ΔG for the reaction:

  • C4H10(g) + 13/2 O2(g) → 4 CO2(g) + 5 H2O(g)

  • 13 + 2 = 15 (moles of gas on reactant side)

  • 13 - 2 = 11 (moles of gas on product side)

Calculations of Gibbs Free Energy

Gibbs Free Energy Formula

The Gibbs Free Energy formula allows us to calculate the value of ΔG (in kJ) by using ΔH (kJ), ΔS (J/K), and T (K) values:

$\Delta G = \Delta H - T\Delta S$

• ΔH: Enthalpy change (kJ)

• ΔS: Entropy change (J/K)

• T: Temperature (K)

• Note: ΔS must be converted to kJ/K if ΔH is in kJ.

Example:

For a particular reaction, ΔH = -111.4 kJ and ΔS = -25.0 J/K. Calculate ΔG for this reaction at 298 K. What can be said about the spontaneity of the reaction at 298 K?

• a) The system is at equilibrium

• b) The system is at equilibrium

• c) The system is spontaneous in the reverse direction

• d) The system is spontaneous as written

Practice Problems: Calculating ΔG and Spontaneity

• Practice: A particular reaction has ΔG = -350 kJ and ΔS = -350 J/K at 24°C. How much heat will be released/absorbed?

  • Answer: 2,940,000 J

• Practice: For a reaction in which ΔH = 125 kJ and ΔS = 325 J/K, determine the temperature in Celsius above which the reaction is spontaneous.

  • a) 385°C

  • b) 273°C

  • c) 112°C

  • d) 405°C

  • e) 25°C

Summary Table: Spontaneity Based on ΔH and ΔS

ΔH	ΔS	Spontaneity
-	+	Always spontaneous
+	-	Never spontaneous
-	-	Spontaneous at low T
+	+	Spontaneous at high T

Key Terms: Gibbs Free Energy, spontaneity, enthalpy, entropy, equilibrium, endothermic, exothermic.

Additional info: The notes and questions are focused on the thermodynamic criteria for spontaneity, the calculation and interpretation of Gibbs Free Energy, and the relationship between enthalpy, entropy, and temperature in determining reaction spontaneity. These are core topics in GOB Chemistry.