10. For the reaction: CH4(g) + 2 O2(g) C2(9) + 2 H20m AS = -154 J/K a. At what temperature does this reaction begin to occur spontaneously? (Hint: use the Thermodynamic Tables) b. Is the reaction spontaneous at 50°C (show your work)?

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Please answer and show all work for parts A-C, thank you!! Thermodynamics table is shown below :)
### Educational Content on Thermodynamics

#### Reaction Analysis of Methane Combustion

**Reaction:**
\[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(l) \]
**Entropy Change:**
\[ \Delta S = -154 \, \text{J/K} \]

**Questions and Solutions:**

**a. At what temperature does this reaction begin to occur spontaneously?**

*Hint:* Use the Thermodynamic Tables.

To determine the temperature at which the reaction becomes spontaneous, you should use the Gibbs Free Energy equation:
\[ \Delta G = \Delta H - T\Delta S \]
Where \(\Delta G\) must be negative for spontaneity.

**b. Is the reaction spontaneous at 50°C? Show your work.**

To check if the reaction is spontaneous at 50°C (which is 323K), calculate \(\Delta G\) using the known \(\Delta H\) and \(\Delta S\). If \(\Delta G < 0\), the reaction is spontaneous.

**c. Calculate the Joules of work done on or by the system when 1 mole of CH\(_4\) is combusted at 127°C.**

*Hint:* R = 8.31 J/mol K

To calculate the work done, analyze the system's expansion or compression work, often associated with changes in volume and pressure. You may need to determine \(\Delta G\) at 127°C (400K) and use the ideal gas constant \(R\) to find this work.

---

**Note:** Detailed calculations would involve accessing thermodynamic tables for specific values like enthalpy (\(\Delta H\)) and applying them to the formulas provided.
Transcribed Image Text:### Educational Content on Thermodynamics #### Reaction Analysis of Methane Combustion **Reaction:** \[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(l) \] **Entropy Change:** \[ \Delta S = -154 \, \text{J/K} \] **Questions and Solutions:** **a. At what temperature does this reaction begin to occur spontaneously?** *Hint:* Use the Thermodynamic Tables. To determine the temperature at which the reaction becomes spontaneous, you should use the Gibbs Free Energy equation: \[ \Delta G = \Delta H - T\Delta S \] Where \(\Delta G\) must be negative for spontaneity. **b. Is the reaction spontaneous at 50°C? Show your work.** To check if the reaction is spontaneous at 50°C (which is 323K), calculate \(\Delta G\) using the known \(\Delta H\) and \(\Delta S\). If \(\Delta G < 0\), the reaction is spontaneous. **c. Calculate the Joules of work done on or by the system when 1 mole of CH\(_4\) is combusted at 127°C.** *Hint:* R = 8.31 J/mol K To calculate the work done, analyze the system's expansion or compression work, often associated with changes in volume and pressure. You may need to determine \(\Delta G\) at 127°C (400K) and use the ideal gas constant \(R\) to find this work. --- **Note:** Detailed calculations would involve accessing thermodynamic tables for specific values like enthalpy (\(\Delta H\)) and applying them to the formulas provided.
### Thermodynamic Tables

These tables provide essential thermodynamic data for various substances, including their standard enthalpy of formation (ΔHf°) and standard free energy of formation (ΔGf°), along with atomization and bond energies.

#### Standard Enthalpy of Formation (ΔHf°) Values

| Substance   | kJ/mole  |
|-------------|----------|
| CO(g)       | -110     |
| CO₂(g)      | -394     |
| CH₃OH(l)    | -238     |
| CH₄(g)      | -75      |
| C₂H₄(g)     | +52      |
| Fe₂O₃(s)    | -824     |
| H₂O(l)      | -286     |
| H₂O(g)      | -242     |
| NaCl(s)     | -413     |
| NaOH(aq)    | -470     |
| NH₃(g)      | -46      |
| NO(g)       | +90      |
| C₂H₅OH(l)   | -485     |
| HC₂H₃O₂(l)  | -278     |

#### Standard Free Energy of Formation (ΔGf°) Values

| Substance   | kJ/mole  |
|-------------|----------|
| CO(g)       | -137     |
| CO₂(g)      | -395     |
| Fe₂O₃(s)    | -742     |
| H₂O(l)      | -237     |
| H₂O(g)      | -228     |
| NH₃(g)      | -17      |
| NO(g)       | +87      |
| NO₂(g)      | +51      |
| N₂O₄(g)     | +98      |
| C₂H₅OH(l)   | -390     |
| HC₂H₃O₂(l)  | -175     |

#### Atomization Energies

| Atom  | kJ/mole atom |
|-------|--------------|
| C(g)  | 715          |
| Cl(g) | 121          |
| H(g)  | 218          |
| I(g)  | 107          |
| Na(g) | 108          |
| O(g)  | 249          |
|
Transcribed Image Text:### Thermodynamic Tables These tables provide essential thermodynamic data for various substances, including their standard enthalpy of formation (ΔHf°) and standard free energy of formation (ΔGf°), along with atomization and bond energies. #### Standard Enthalpy of Formation (ΔHf°) Values | Substance | kJ/mole | |-------------|----------| | CO(g) | -110 | | CO₂(g) | -394 | | CH₃OH(l) | -238 | | CH₄(g) | -75 | | C₂H₄(g) | +52 | | Fe₂O₃(s) | -824 | | H₂O(l) | -286 | | H₂O(g) | -242 | | NaCl(s) | -413 | | NaOH(aq) | -470 | | NH₃(g) | -46 | | NO(g) | +90 | | C₂H₅OH(l) | -485 | | HC₂H₃O₂(l) | -278 | #### Standard Free Energy of Formation (ΔGf°) Values | Substance | kJ/mole | |-------------|----------| | CO(g) | -137 | | CO₂(g) | -395 | | Fe₂O₃(s) | -742 | | H₂O(l) | -237 | | H₂O(g) | -228 | | NH₃(g) | -17 | | NO(g) | +87 | | NO₂(g) | +51 | | N₂O₄(g) | +98 | | C₂H₅OH(l) | -390 | | HC₂H₃O₂(l) | -175 | #### Atomization Energies | Atom | kJ/mole atom | |-------|--------------| | C(g) | 715 | | Cl(g) | 121 | | H(g) | 218 | | I(g) | 107 | | Na(g) | 108 | | O(g) | 249 | |
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