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Calculate Δg Rxn for The Following Reaction

Reviewed by Calculator Editorial Team

Calculating the Gibbs free energy change (ΔG rxn) for a chemical reaction is essential in thermodynamics and chemical engineering. This value determines whether a reaction is spontaneous, the direction of equilibrium, and the energy requirements. Our calculator provides a quick and accurate way to compute ΔG rxn using standard thermodynamic data.

What is ΔG rxn?

The Gibbs free energy change (ΔG rxn) is a thermodynamic property that measures the maximum amount of reversible work a system can perform at constant temperature and pressure. It is calculated using the following formula:

ΔG rxn = ΔH rxn - TΔS rxn

Where:

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

The sign of ΔG rxn indicates the spontaneity of the reaction:

  • ΔG rxn < 0: Spontaneous reaction
  • ΔG rxn = 0: Reaction at equilibrium
  • ΔG rxn > 0: Non-spontaneous reaction

Note: ΔG rxn is temperature-dependent because it includes the entropy term (ΔS rxn). For accurate calculations, use the exact temperature of the reaction.

How to Calculate ΔG rxn

To calculate ΔG rxn, you need the following data:

  1. Standard enthalpy change (ΔH° rxn)
  2. Standard entropy change (ΔS° rxn)
  3. Temperature of the reaction (T)

These values can be obtained from thermodynamic tables or experimental data. Once you have these values, you can use the formula above to calculate ΔG rxn.

Step-by-Step Calculation

  1. Determine the standard enthalpy change (ΔH° rxn) for the reaction.
  2. Determine the standard entropy change (ΔS° rxn) for the reaction.
  3. Convert the temperature to Kelvin (K) if it is given in Celsius.
  4. Plug the values into the ΔG rxn formula.
  5. Calculate the result.

Tip: Always ensure that the units are consistent (kJ/mol for ΔH rxn and J/mol·K for ΔS rxn) to avoid calculation errors.

Interpreting the Results

The value of ΔG rxn provides important information about the reaction:

  • If ΔG rxn is negative, the reaction is spontaneous under the given conditions.
  • If ΔG rxn is positive, the reaction is non-spontaneous and requires an input of energy to proceed.
  • If ΔG rxn is zero, the reaction is at equilibrium.

Understanding ΔG rxn helps in predicting the feasibility of a reaction, designing reaction conditions, and optimizing industrial processes.

Caution: ΔG rxn is a theoretical value under standard conditions. Real-world reactions may have different ΔG values due to factors like concentration, pressure, and catalyst effects.

Example Calculation

Let's calculate ΔG rxn for the following reaction at 298 K:

C(s) + O₂(g) → CO₂(g)

Given:

  • ΔH° rxn = -393.5 kJ/mol
  • ΔS° rxn = -197.7 J/mol·K
  • T = 298 K

Using the formula:

ΔG rxn = ΔH rxn - TΔS rxn

Plugging in the values:

ΔG rxn = (-393.5 kJ/mol) - (298 K)(-197.7 J/mol·K)

First, convert ΔS rxn to kJ/mol·K:

-197.7 J/mol·K = -0.1977 kJ/mol·K

Now calculate:

ΔG rxn = -393.5 - (298)(-0.1977) = -393.5 + 59.1 ≈ -334.4 kJ/mol

The result shows that the reaction is spontaneous (ΔG rxn < 0) under standard conditions.

FAQ

What is the difference between ΔG rxn and ΔH rxn?

ΔG rxn (Gibbs free energy change) considers both enthalpy and entropy changes, while ΔH rxn (enthalpy change) only considers the heat content change. ΔG rxn is more comprehensive for predicting reaction spontaneity.

How does temperature affect ΔG rxn?

ΔG rxn is temperature-dependent because it includes the entropy term (ΔS rxn). Higher temperatures can make non-spontaneous reactions (ΔG rxn > 0) more favorable by reducing the entropy term's negative impact.

Can ΔG rxn be negative for an endothermic reaction?

Yes, if the entropy change (ΔS rxn) is sufficiently positive, an endothermic reaction (ΔH rxn > 0) can have a negative ΔG rxn, making it spontaneous.