Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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**Gibbs Free Energy: Spontaneity**

Gibbs free energy is a measure of the spontaneity of a chemical reaction. It is the chemical potential for a reaction and is minimized at equilibrium. The change in Gibbs free energy can be calculated by:

\[
\Delta G^\circ_{\text{rxn}} = \Delta H^\circ_{\text{rxn}} - T\Delta S^\circ_{\text{rxn}}
\]

where \(\Delta G^\circ_{\text{rxn}}\) is the standard Gibbs free energy change for a reaction, \(\Delta H^\circ_{\text{rxn}}\) is the standard enthalpy change for a reaction, \(T\) is the temperature in kelvins, and \(\Delta S^\circ_{\text{rxn}}\) is the standard entropy change for a reaction.

For a reaction at equilibrium, \(\Delta G^\circ_{\text{rxn}}\) is equal to zero. For negative values, the reaction is spontaneous, and for positive values, the reaction is nonspontaneous.

**Elemental Carbon Forms**

Elemental carbon usually exists in one of two forms: graphite or diamond. It is generally believed that diamonds last forever. The table shows the standard enthalpy of formation \((\Delta H^\circ_f)\) and the standard molar entropy \((S^\circ)\) values for diamond and graphite.

| Substance   | \(\Delta H^\circ_f\) (kJ/mol) | \(S^\circ\) (J/mol·K) |
|-------------|-------------------------------|-----------------------|
| \(C_{\text{graphite}}\) | 0                              | 5.740                 |
| \(C_{\text{diamond}}\)  | 1.897                          | 2.38                  |

**Part A**

What is the standard Gibbs free energy for the transformation of diamond to graphite at 298 K?

\[ C_{\text{diamond}} \rightarrow C_{\text{graphite}} \]

Express your answer to three significant figures and include the appropriate units.

- **Answer Box:**  
  \(\Delta G^\circ_{\text{rxn}} = [ \text{Value} \quad \text{Units} ]\)

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Transcribed Image Text:**Gibbs Free Energy: Spontaneity** Gibbs free energy is a measure of the spontaneity of a chemical reaction. It is the chemical potential for a reaction and is minimized at equilibrium. The change in Gibbs free energy can be calculated by: \[ \Delta G^\circ_{\text{rxn}} = \Delta H^\circ_{\text{rxn}} - T\Delta S^\circ_{\text{rxn}} \] where \(\Delta G^\circ_{\text{rxn}}\) is the standard Gibbs free energy change for a reaction, \(\Delta H^\circ_{\text{rxn}}\) is the standard enthalpy change for a reaction, \(T\) is the temperature in kelvins, and \(\Delta S^\circ_{\text{rxn}}\) is the standard entropy change for a reaction. For a reaction at equilibrium, \(\Delta G^\circ_{\text{rxn}}\) is equal to zero. For negative values, the reaction is spontaneous, and for positive values, the reaction is nonspontaneous. **Elemental Carbon Forms** Elemental carbon usually exists in one of two forms: graphite or diamond. It is generally believed that diamonds last forever. The table shows the standard enthalpy of formation \((\Delta H^\circ_f)\) and the standard molar entropy \((S^\circ)\) values for diamond and graphite. | Substance | \(\Delta H^\circ_f\) (kJ/mol) | \(S^\circ\) (J/mol·K) | |-------------|-------------------------------|-----------------------| | \(C_{\text{graphite}}\) | 0 | 5.740 | | \(C_{\text{diamond}}\) | 1.897 | 2.38 | **Part A** What is the standard Gibbs free energy for the transformation of diamond to graphite at 298 K? \[ C_{\text{diamond}} \rightarrow C_{\text{graphite}} \] Express your answer to three significant figures and include the appropriate units. - **Answer Box:** \(\Delta G^\circ_{\text{rxn}} = [ \text{Value} \quad \text{Units} ]\) - **Submit Button**: Submit - **Feedback**: Incorrect; Try Again, 5 attempts remaining For hints and templates, click "View Available
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