To calculate the change in Gibbs free energy (ΔG) for the given reaction, we need to follow these steps:
1. Identify the Gibbs free energies of formation (ΔG_f) for the reactants and products:
- ΔG_f for [tex]\( CaCO_3(s) \)[/tex] = -1128.76 kJ/mol
- ΔG_f for [tex]\( CaO(s) \)[/tex] = -604.17 kJ/mol
- ΔG_f for [tex]\( CO_2(g) \)[/tex] = -394.4 kJ/mol
2. Write down the balanced chemical equation:
[tex]\[ CaCO_3(s) \rightarrow CaO(s) + CO_2(g) \][/tex]
3. Use the formula to calculate the change in Gibbs free energy (ΔG_rxn):
The formula for the change in Gibbs free energy for the reaction is:
[tex]\[
\Delta G_{rxn} = \sum \Delta G_f (\text{products}) - \sum \Delta G_f (\text{reactants})
\][/tex]
For our reaction:
[tex]\[
\Delta G_{rxn} = [\Delta G_f (CaO(s)) + \Delta G_f (CO_2(g))] - [\Delta G_f (CaCO_3(s))]
\][/tex]
4. Substitute the values into the formula:
[tex]\[
\Delta G_{rxn} = [(-604.17) + (-394.4)] - (-1128.76)
\][/tex]
5. Perform the arithmetic:
- Calculate the sum of the Gibbs free energies of the products:
[tex]\[
\Delta G_f (\text{products}) = -604.17 + (-394.4) = -998.57 \text{ kJ/mol}
\][/tex]
- Calculate the change in Gibbs free energy for the reaction:
[tex]\[
\Delta G_{rxn} = -998.57 - (-1128.76) = -998.57 + 1128.76 = 130.19 \text{ kJ/mol}
\][/tex]
6. Round the result to the nearest whole number:
[tex]\[
\Delta G_{rxn} \approx 130 \text{ kJ/mol}
\][/tex]
Therefore, the change in Gibbs free energy (ΔG_rxn) for the given reaction, rounded to the nearest whole number, is 130 kJ/mol.
