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Calculate [tex]\Delta G_{\text{rxn}}[/tex] for this equation, rounding your answer to the nearest whole number.

[tex]\[
\begin{array}{l}
CaCO_3(s) \rightarrow CaO(s) + CO_2(g) \\
\Delta G_{f, CaCO_3} = -1128.76 \text{ kJ/mol} \\
\Delta G_{f, CaO} = -604.17 \text{ kJ/mol} \\
\Delta G_{f, CO_2} = -394.4 \text{ kJ/mol} \\
\Delta G_{\text{rxn}} = \square \text{ kJ} \\
\end{array}
\][/tex]



Answer :

GinnyAnswer
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.

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