1. Write the Balanced Chemical Equation:
The synthesis of carbon disulfide from its elements is:
C(s) + 2S(s) → CS₂(l)
2. Gather Standard Gibbs Free Energy of Formation Values:
You'll need the standard Gibbs free energy of formation (ΔG°f) for each component in the reaction. These values are typically found in thermodynamic tables. Here's a common set of values:
* ΔG°f [C(s)] = 0 kJ/mol (by definition, the standard state of an element is 0)
* ΔG°f [S(s)] = 0 kJ/mol (same as above)
* ΔG°f [CS₂(l)] = +65.3 kJ/mol
3. Apply the Gibbs Free Energy Equation:
The Gibbs free energy change for a reaction (ΔG°) is calculated as:
ΔG° = ΣnΔG°f(products) - ΣmΔG°f(reactants)
where:
* n and m are the stoichiometric coefficients in the balanced equation
* ΔG°f is the standard Gibbs free energy of formation
4. Substitute Values and Calculate:
ΔG° = (1 * ΔG°f[CS₂(l)]) - (1 * ΔG°f[C(s)] + 2 * ΔG°f[S(s)])
ΔG° = (1 * 65.3 kJ/mol) - (1 * 0 kJ/mol + 2 * 0 kJ/mol)
ΔG° = 65.3 kJ/mol
Therefore, the change in Gibbs free energy for the synthesis of carbon disulfide at 25°C is +65.3 kJ/mol.
Interpretation:
* Positive ΔG°: This indicates that the reaction is non-spontaneous under standard conditions (25°C and 1 atm). In other words, energy input is required to drive the reaction forward.
Important Notes:
* The Gibbs free energy equation assumes standard conditions (25°C and 1 atm). For other conditions, you would need to use the Gibbs free energy equation with the appropriate temperature and pressure values.
* The actual spontaneity of a reaction can be influenced by factors like concentration, pressure, and temperature. The Gibbs free energy equation provides a good starting point but may need adjustments for specific conditions.
