Determine the standard free energy (DG) of the reaction C2H5OH (g) ( => C2H5OH (C) The vapor pressure of C₂H5OH (g) at 95°c is mmitte and K = 8.31 JIK)

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### Determining the Standard Free Energy (ΔG⁰) of the Reaction

**Reaction:**
\[ \text{C}_2\text{H}_5\text{OH (g)} \rightarrow \text{C}_2\text{H}_5\text{OH (l)} \]

**Given Data:**
- The vapor pressure of \(\text{C}_2\text{H}_5\text{OH (g)}\) at 95°C is 5 mmHg.
- \(R\) (the universal gas constant) = 8.31 J/K·mol

In order to determine the standard free energy of the reaction at the given temperature, we can utilize the following formula:

\[ \Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ} \]

However, additional thermodynamic data might be required such as the enthalpy change \((\Delta H^{\circ})\) and the entropy change \((\Delta S^{\circ})\) at the specific temperature, which are not provided in the given text. 

Given only the vapor pressure and the universal gas constant, one would typically need to apply the Clausius-Clapeyron equation or other similar equations to find the necessary thermodynamic quantities before calculating \(\Delta G^{\circ}\).

### Explanation:

In this context:
- \(\text{C}_2\text{H}_5\text{OH}\) is Ethanol.
- Vapor pressure signifies the equilibrium pressure exerted by the vapor in contact with its liquid.
- The temperature \(95^{\circ}C\) is the condition under which the vapor pressure measurement is provided.
- \(R\), the universal gas constant, is used in thermodynamic equations to relate energy scales to temperature.

### Graphs/Diagrams:

No graphs or diagrams are provided within this image. If graphs or diagrams depicting changes in vapor pressure with temperature, or phase diagrams, were provided or needed, they would typically illustrate:
- The vapor pressure versus temperature plot to show at what vapor pressure equilibrium is achieved at a specific temperature.
- A phase diagram denoting the phase transitions (solid, liquid, gas) and the respective triple and critical points.

Understanding how vapor pressure changes with temperature is fundamental to determining thermodynamic properties like Gibbs Free Energy, which helps in predicting the direction of the reaction and the extent to which the
Transcribed Image Text:### Determining the Standard Free Energy (ΔG⁰) of the Reaction **Reaction:** \[ \text{C}_2\text{H}_5\text{OH (g)} \rightarrow \text{C}_2\text{H}_5\text{OH (l)} \] **Given Data:** - The vapor pressure of \(\text{C}_2\text{H}_5\text{OH (g)}\) at 95°C is 5 mmHg. - \(R\) (the universal gas constant) = 8.31 J/K·mol In order to determine the standard free energy of the reaction at the given temperature, we can utilize the following formula: \[ \Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ} \] However, additional thermodynamic data might be required such as the enthalpy change \((\Delta H^{\circ})\) and the entropy change \((\Delta S^{\circ})\) at the specific temperature, which are not provided in the given text. Given only the vapor pressure and the universal gas constant, one would typically need to apply the Clausius-Clapeyron equation or other similar equations to find the necessary thermodynamic quantities before calculating \(\Delta G^{\circ}\). ### Explanation: In this context: - \(\text{C}_2\text{H}_5\text{OH}\) is Ethanol. - Vapor pressure signifies the equilibrium pressure exerted by the vapor in contact with its liquid. - The temperature \(95^{\circ}C\) is the condition under which the vapor pressure measurement is provided. - \(R\), the universal gas constant, is used in thermodynamic equations to relate energy scales to temperature. ### Graphs/Diagrams: No graphs or diagrams are provided within this image. If graphs or diagrams depicting changes in vapor pressure with temperature, or phase diagrams, were provided or needed, they would typically illustrate: - The vapor pressure versus temperature plot to show at what vapor pressure equilibrium is achieved at a specific temperature. - A phase diagram denoting the phase transitions (solid, liquid, gas) and the respective triple and critical points. Understanding how vapor pressure changes with temperature is fundamental to determining thermodynamic properties like Gibbs Free Energy, which helps in predicting the direction of the reaction and the extent to which the
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