Calculate Delta G for The Following Reactions at 25c

What is ΔG?

ΔG (Gibbs free energy change) is a thermodynamic quantity that measures the energy available to do useful work in a chemical reaction. It combines enthalpy (ΔH) and entropy (ΔS) changes according to the equation:

Where:

• ΔG = Gibbs free energy change (kJ/mol)
• ΔH = Enthalpy change (kJ/mol)
• T = Absolute temperature (K)
• ΔS = Entropy change (J/mol·K)

The sign of ΔG determines reaction spontaneity:

• ΔG < 0: Spontaneous reaction (energy is released)
• ΔG = 0: Reaction at equilibrium
• ΔG > 0: Non-spontaneous reaction (energy must be added)

How to Calculate ΔG

To calculate ΔG for a reaction at 25°C (298.15 K), you can use either:

1. The standard Gibbs free energy change (ΔG°) for the reaction
2. The enthalpy and entropy changes (ΔH and ΔS)

Using Standard Gibbs Free Energy Values

The most straightforward method is to use standard Gibbs free energy values (ΔG°) for the reactants and products. The change in Gibbs free energy for the reaction is the sum of the ΔG° values of the products minus the sum of the ΔG° values of the reactants.

Using Enthalpy and Entropy Changes

When ΔH and ΔS values are known, you can calculate ΔG using the Gibbs free energy equation:

For reactions at 25°C, T = 298.15 K. Remember to convert ΔS from J/mol·K to kJ/mol·K by dividing by 1000.

Standard Gibbs Free Energy Values

Standard Gibbs free energy values (ΔG°) are essential for calculating ΔG for reactions. These values represent the change in free energy when one mole of a substance is converted from its standard state to products under standard conditions (25°C, 1 atm).

Common standard Gibbs free energy values include:

For reactions involving multiple substances, sum the ΔG° values according to the stoichiometry of the reaction.

Interpreting ΔG

The value of ΔG provides important information about a chemical reaction:

Spontaneity

• ΔG < 0: The reaction is spontaneous under standard conditions
• ΔG > 0: The reaction is non-spontaneous and requires energy input

Equilibrium

When ΔG = 0, the reaction is at equilibrium. The system is in a balanced state where the forward and reverse reactions occur at the same rate.

Energy Requirements

The magnitude of ΔG indicates the amount of energy that must be supplied or released during the reaction. Larger absolute values of ΔG indicate more energy is involved in the reaction.

Example Calculations

Let's look at two example calculations to demonstrate how to determine ΔG for chemical reactions.

Example 1: Combustion of Methane

Calculate ΔG for the combustion of methane:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)

Using standard Gibbs free energy values:

• ΔG°_CH4 = -50.8 kJ/mol
• ΔG°_O2 = 0 kJ/mol
• ΔG°_CO2 = -394.4 kJ/mol
• ΔG°_H2O = -237.1 kJ/mol

Calculation:

Interpretation: The negative ΔG indicates this exothermic reaction is spontaneous under standard conditions.

Example 2: Formation of Water

Calculate ΔG for the formation of water:

2H₂(g) + O₂(g) → 2H₂O(l)

Using standard Gibbs free energy values:

• ΔG°_H2 = 0 kJ/mol
• ΔG°_O2 = 0 kJ/mol
• ΔG°_H2O = -237.1 kJ/mol

Calculation:

Interpretation: This highly exothermic reaction is spontaneous, releasing significant energy when water forms.