Calculate Delta G for The Following Reaction H20 1 2o2

The Gibbs free energy change (ΔG) is a fundamental concept in thermodynamics that helps predict whether a chemical reaction will occur spontaneously. For the reaction H₂O → 2H₂ + O₂, we can calculate ΔG using standard thermodynamic data.

Introduction to Gibbs Free Energy

Gibbs free energy (G) is defined as:

G = H - TS

where:

G = Gibbs free energy (J/mol)
H = Enthalpy (J/mol)
T = Absolute temperature (K)
S = Entropy (J/mol·K)

The change in Gibbs free energy (ΔG) for a reaction is calculated as the difference between the products and reactants:

ΔG = ΣG(products) - ΣG(reactants)

For standard conditions (298 K, 1 atm), we use standard Gibbs free energy of formation (ΔG°f) values.

How to Calculate ΔG

Step 1: Find Standard Gibbs Free Energy Values

We need ΔG°f values for:

Water (H₂O)
Hydrogen gas (H₂)
Oxygen gas (O₂)

These values are typically found in thermodynamic tables or databases.

Step 2: Apply the Reaction Stoichiometry

The balanced reaction is:

H₂O → 2H₂ + O₂

We multiply the ΔG°f values by their stoichiometric coefficients:

ΔG° = [2 × ΔG°f(H₂) + ΔG°f(O₂)] - ΔG°f(H₂O)

Step 3: Calculate at Non-Standard Conditions

If the reaction occurs at different temperature or pressure, we use:

ΔG = ΔG° + RT ln(Q)

where:

R = Gas constant (8.314 J/mol·K)
T = Temperature (K)
Q = Reaction quotient

Worked Example

Let's calculate ΔG° for the reaction at standard conditions using these standard Gibbs free energy values:

ΔG°f(H₂O) = -237.1 kJ/mol
ΔG°f(H₂) = 0 kJ/mol
ΔG°f(O₂) = 0 kJ/mol

Calculation:

ΔG° = [2 × 0 + 0] - (-237.1) = 237.1 kJ/mol

This positive value indicates the reaction is non-spontaneous under standard conditions.

Interpreting Results

The sign of ΔG tells us about reaction spontaneity:

ΔG < 0: Reaction is spontaneous
ΔG = 0: Reaction is at equilibrium
ΔG > 0: Reaction is non-spontaneous

For our example, ΔG° = +237.1 kJ/mol means:

The reaction requires energy input to proceed
Water decomposition is not thermodynamically favorable
This matches experimental observations

Note: In reality, water decomposition requires catalysts and high temperatures to occur, as the activation energy barrier is very high.

Frequently Asked Questions

What is the difference between ΔG and ΔG°?: ΔG° refers to the Gibbs free energy change under standard conditions (298 K, 1 atm). ΔG is the actual free energy change at the conditions of interest, which may differ from ΔG°.
Can ΔG be negative for this reaction?: Under standard conditions, ΔG° is positive for this reaction, meaning it's non-spontaneous. However, at very high temperatures or with catalysts, ΔG can become negative.
Why is ΔG°f for H₂ and O₂ zero?: By definition, the standard Gibbs free energy of formation for pure elements in their standard states (H₂ gas at 1 atm, O₂ gas at 1 atm) is zero.
How does pressure affect ΔG?: For gases, ΔG changes with pressure because the reaction quotient Q includes partial pressures. Higher pressures can make non-spontaneous reactions more favorable.
What units should I use for ΔG?: ΔG is typically expressed in kilojoules per mole (kJ/mol) or joules per mole (J/mol). Always ensure units are consistent when performing calculations.