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Calculating [tex] \Delta G_{ \text{rxn} } [/tex]

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

[tex]\[
\begin{array}{l}
CaCO_3(s) \rightarrow CaO(s) + CO_2(g) \\
\Delta G_{ \text{f}, \, CaCO_3} = -1,128.76 \, \text{kJ/mol} \\
\Delta G_{ \text{f}, \, CaO } = -604.17 \, \text{kJ/mol} \\
\Delta G_{ \text{f}, \, CO_2} = -394.4 \, \text{kJ/mol} \\
\Delta G_{ \text{rxn} } = \square \, \text{kJ}
\end{array}
\][/tex]

Note: The formatting issues and extra text have been corrected and unnecessary elements have been removed.

Sagot :

GinnyAnsweridn
To find the standard Gibbs free energy change for the reaction [tex]\( \Delta G_{ \text{rxn} } \)[/tex], we need to use the Gibbs free energies of formation of the reactants and products. The reaction given is:

[tex]\[ \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \][/tex]

The given Gibbs free energies of formation ([tex]\( \Delta G_{f} \)[/tex]) are:
- [tex]\( \Delta G_{f,\text{CaCO}_3} = -1128.76 \, \text{kJ/mol} \)[/tex]
- [tex]\( \Delta G_{f,\text{CaO}} = -604.17 \, \text{kJ/mol} \)[/tex]
- [tex]\( \Delta G_{f,\text{CO}_2} = -394.4 \, \text{kJ/mol} \)[/tex]

The standard Gibbs free energy change for the reaction ([tex]\( \Delta G_{ \text{rxn} } \)[/tex]) can be calculated using the following formula:

[tex]\[ \Delta G_{ \text{rxn} } = \Delta G_{ \text{products} } - \Delta G_{ \text{reactants} } \][/tex]

In this case:
[tex]\[ \Delta G_{ \text{products} } = \Delta G_{f,\text{CaO}} + \Delta G_{f,\text{CO}_2} \][/tex]

[tex]\[ \Delta G_{ \text{reactants} } = \Delta G_{f,\text{CaCO}_3} \][/tex]

Substituting the given values:

[tex]\[ \Delta G_{ \text{products} } = (-604.17) + (-394.4) \][/tex]

[tex]\[ \Delta G_{ \text{products} } = -998.57 \, \text{kJ/mol} \][/tex]

Now, we calculate [tex]\( \Delta G_{ \text{rxn} } \)[/tex]:

[tex]\[ \Delta G_{ \text{rxn} } = -998.57 - (-1128.76) \][/tex]

[tex]\[ \Delta G_{ \text{rxn} } = -998.57 + 1128.76 \][/tex]

[tex]\[ \Delta G_{ \text{rxn} } = 130.19 \, \text{kJ/mol} \][/tex]

Lastly, we round the answer to the nearest whole number:

[tex]\[ \Delta G_{ \text{rxn} } \approx 130 \, \text{kJ/mol} \][/tex]

Thus, the standard Gibbs free energy change for the reaction, [tex]\( \Delta G_{ \text{rxn} } \)[/tex], is [tex]\( 130 \, \text{kJ/mol} \)[/tex].
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