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Calculate Grxn for The Following Process at 25.0

Reviewed by Calculator Editorial Team

The Gibbs free energy change (GRxN) is a fundamental concept in thermodynamics that helps predict the spontaneity of chemical reactions. This calculator allows you to compute GRxN for a given process at 25.0°C using standard thermodynamic data.

What is GRxN?

The Gibbs free energy change (ΔG) for a reaction (GRxN) is a thermodynamic quantity that measures the maximum amount of useful work that can be obtained from a chemical reaction at constant temperature and pressure. It combines the enthalpy change (ΔH) and entropy change (ΔS) of the reaction according to the equation:

ΔG = ΔH - TΔS

Where:

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

At 25.0°C (298.15 K), the equation becomes:

ΔG = ΔH - 298.15ΔS

The sign of ΔG determines the spontaneity of the reaction:

  • ΔG < 0: The reaction is spontaneous as written
  • ΔG = 0: The reaction is at equilibrium
  • ΔG > 0: The reaction is non-spontaneous as written

How to Calculate GRxN

To calculate GRxN for a chemical reaction at 25.0°C, follow these steps:

  1. Determine the standard enthalpy change (ΔH°) for the reaction from thermodynamic tables or literature sources.
  2. Determine the standard entropy change (ΔS°) for the reaction from thermodynamic tables or literature sources.
  3. Convert ΔS° from J/mol·K to kJ/mol·K by dividing by 1000.
  4. Calculate ΔG using the formula: ΔG = ΔH° - 298.15ΔS°.

Note: These calculations assume standard conditions (25.0°C and 1 atm pressure). For non-standard conditions, additional corrections may be needed.

Example Calculation

Let's calculate GRxN for the following reaction at 25.0°C:

2H₂(g) + O₂(g) → 2H₂O(g)

From thermodynamic tables:

  • ΔH° = -483.6 kJ/mol
  • ΔS° = -188.8 J/mol·K

Convert ΔS° to kJ/mol·K:

ΔS° = -188.8 J/mol·K ÷ 1000 = -0.1888 kJ/mol·K

Calculate ΔG:

ΔG = ΔH° - 298.15ΔS°

ΔG = -483.6 - (298.15 × -0.1888)

ΔG = -483.6 + 56.3

ΔG = -427.3 kJ/mol

The negative value indicates the reaction is spontaneous under standard conditions.

Interpretation of Results

The calculated GRxN value provides several important insights:

  1. Spontaneity: A negative ΔG indicates the reaction will proceed spontaneously as written.
  2. Energy Requirements: The magnitude of ΔG indicates the energy available to do work.
  3. Equilibrium Position: The closer ΔG is to zero, the closer the reaction is to equilibrium.

Remember that GRxN calculations are based on standard conditions. For real-world applications, consider factors like concentration, pressure, and catalyst effects.

FAQ

What is the difference between ΔG and ΔH?

ΔG (Gibbs free energy change) represents the energy available to do useful work, while ΔH (enthalpy change) represents the total heat content change. ΔG accounts for both heat and entropy changes.

Why is temperature important in GRxN calculations?

Temperature affects the entropy term in the Gibbs free energy equation. At higher temperatures, the entropy term becomes more significant, potentially changing the spontaneity of reactions.

Can GRxN be negative for an endothermic reaction?

Yes, if the entropy increase is large enough to overcome the endothermic enthalpy change, the reaction can have a negative ΔG and be spontaneous.