Calculate Δg for The Following Reactions at 25 C

What is ΔG?

The Gibbs free energy change (ΔG) is a thermodynamic property that measures the maximum amount of reversible work that a system can perform at constant temperature and pressure. It's a key concept in chemical thermodynamics that helps predict whether a reaction will occur spontaneously.

ΔG is calculated using the following formula:

Where:

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

The sign of ΔG determines the spontaneity of the reaction:

• ΔG < 0: Reaction is spontaneous and will occur as written
• ΔG = 0: Reaction is at equilibrium
• ΔG > 0: Reaction is non-spontaneous as written

How to calculate ΔG

To calculate ΔG for a reaction at 25°C (298.15 K), you'll need to know the enthalpy change (ΔH) and entropy change (ΔS) for the reaction. These values can be found in thermodynamic tables or calculated from standard thermodynamic properties of the reactants and products.

Step-by-step calculation

1. Convert the temperature from Celsius to Kelvin: T = 25°C + 273.15 = 298.15 K
2. Find the standard enthalpy change (ΔH°) for the reaction from thermodynamic tables
3. Find the standard entropy change (ΔS°) for the reaction from thermodynamic tables
4. Calculate ΔG using the formula: ΔG = ΔH - TΔS

Example calculations

Let's look at two example reactions to demonstrate how to calculate ΔG.

Example 1: Formation of water

Reaction: 2H₂(g) + O₂(g) → 2H₂O(g)

Given:

• ΔH° = -483.6 kJ/mol
• ΔS° = -10.4 J/mol·K

Calculation:

Interpretation: The positive ΔG indicates this reaction is non-spontaneous as written.

Example 2: Dissolution of sodium chloride

Reaction: NaCl(s) → Na⁺(aq) + Cl⁻(aq)

Given:

• ΔH° = 3.87 kJ/mol
• ΔS° = 35.9 J/mol·K

Calculation:

Interpretation: The negative ΔG indicates this reaction is spontaneous and will occur as written.

Interpreting ΔG results

Understanding the meaning of ΔG values is crucial for predicting reaction behavior:

• ΔG < 0: The reaction is thermodynamically favorable and will occur spontaneously under standard conditions.
• ΔG = 0: The reaction is at equilibrium, meaning the forward and reverse reactions occur at the same rate.
• ΔG > 0: The reaction is thermodynamically unfavorable under standard conditions, though kinetic factors might still allow it to proceed.

Remember that ΔG provides information about the thermodynamic favorability of a reaction, but it doesn't account for reaction rates or kinetic factors that might affect whether a reaction actually occurs.