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Δrg for The Following Reaction Is Calculate E

Reviewed by Calculator Editorial Team

The change in Gibbs free energy (δrg) is a fundamental concept in thermodynamics that measures the energy available to do work in a chemical reaction. This calculator helps you determine δrg for any given reaction using standard Gibbs free energy values.

What is δrg?

Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work a system can perform at constant temperature and pressure. The change in Gibbs free energy (δrg) for a reaction is calculated as the difference between the Gibbs free energies of the products and reactants.

δrg = ΣGproducts - ΣGreactants

The sign of δrg indicates the spontaneity of the reaction:

  • If δrg < 0, the reaction is spontaneous under standard conditions
  • If δrg > 0, the reaction is non-spontaneous under standard conditions
  • If δrg = 0, the reaction is at equilibrium

Gibbs free energy is typically measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).

How to calculate δrg

To calculate δrg, you need the standard Gibbs free energy values for all reactants and products in the reaction. These values are typically found in thermodynamic tables or databases.

Step-by-step calculation

  1. Write the balanced chemical equation for the reaction
  2. Look up the standard Gibbs free energy values for each reactant and product
  3. Multiply each Gibbs free energy value by its stoichiometric coefficient
  4. Sum the Gibbs free energy values for all products
  5. Sum the Gibbs free energy values for all reactants
  6. Calculate δrg as the difference between the product sum and reactant sum

Example calculation

For the reaction: C6H12O6 + 6O2 → 6CO2 + 6H2O

Compound ΔG°f (kJ/mol) Stoichiometric Coefficient Total ΔG°f
Glucose (C6H12O6) -1273.3 1 -1273.3
Oxygen (O2) 0 6 0
Carbon dioxide (CO2) -394.4 6 -2366.4
Water (H2O) -237.2 6 -1423.2
Total for products -3789.6
Total for reactants -1273.3
Δrg -2516.3 kJ/mol

In this example, the reaction is spontaneous (δrg < 0) because the products have a lower Gibbs free energy than the reactants.

Note: Standard Gibbs free energy values are typically measured at 25°C and 1 atm pressure. For reactions at different temperatures or pressures, additional calculations are needed.

Interpreting the result

The value of δrg provides several important pieces of information about the reaction:

Spontaneity

  • Negative δrg: The reaction is spontaneous and will proceed in the forward direction
  • Positive δrg: The reaction is non-spontaneous and will proceed in the reverse direction
  • Zero δrg: The reaction is at equilibrium

Energy requirements

The magnitude of δrg indicates the energy available to do work. A more negative δrg means the reaction releases more energy.

Temperature dependence

δrg is temperature-dependent. For reactions where the entropy change (δs) is positive, the reaction becomes more spontaneous at higher temperatures.

δrg = δh - Tδs

Where:

  • δh = change in enthalpy
  • T = temperature in Kelvin
  • δs = change in entropy

FAQ

What is the difference between δrg and δh?

δrg (Gibbs free energy change) measures the energy available to do work, while δh (enthalpy change) measures the total heat content of the system. δrg accounts for both heat and entropy changes, while δh only considers heat.

How do I find standard Gibbs free energy values?

Standard Gibbs free energy values can be found in thermodynamic tables, chemistry textbooks, or online databases like the NIST Chemistry WebBook or the CRC Handbook of Chemistry and Physics.

What units are used for δrg?

δrg is typically measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol).

Can δrg be negative?

Yes, a negative δrg indicates a spontaneous reaction where the products have lower Gibbs free energy than the reactants.