Calculate G At 298 K For The Reaction CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g) Based On These
Understanding how to calculate the Gibbs free energy change (ΔG) at a specific temperature, such as 298 K, is fundamental in thermodynamics, especially when analyzing chemical reactions. The reaction:
CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g)
involves both gaseous and liquid reactants and products, and determining ΔG at 298 K helps predict whether the reaction is spontaneous under standard conditions. This comprehensive guide will walk you through the necessary steps, concepts, and calculations involved in determining ΔG for this reaction at 298 K.
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Introduction to Gibbs Free Energy (ΔG)
What is Gibbs Free Energy?
Gibbs free energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is expressed as:\[ G = H - TS \]
where:
- H is enthalpy,
- T is temperature (in Kelvin),
- S is entropy.
The change in Gibbs free energy (ΔG) during a reaction indicates whether the process is spontaneous:
- ΔG < 0: reaction is spontaneous,
- ΔG = 0: reaction is at equilibrium,
- ΔG > 0: reaction is non-spontaneous.
Why Calculate ΔG at 298 K?
298 K (about 25°C) is standard room temperature, making it a common reference point for thermodynamic calculations. Calculating ΔG at this temperature helps determine if the reaction occurs naturally under standard conditions.
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Gathering Necessary Data
Standard Thermodynamic Data
To calculate ΔG at 298 K, you need standard thermodynamic data for each species involved:- Standard Gibbs free energy of formation (ΔG°f)
- Standard enthalpy of formation (ΔH°f)
- Standard entropy (S°)
Data for Reactants and Products
| Species | ΔG°f (kJ/mol) | ΔH°f (kJ/mol) | S° (J/mol·K) | |-------------|----------------|----------------|--------------| | CS₂(l) | –119.0 | –89.4 | 213.8 | | O₂(g) | 0 | 0 | 205.0 | | CO₂(g) | –394.4 | –393.5 | 213.7 | | SO₂(g) | –300.2 | –296.8 | 248.0 |Note: These are approximate standard values; actual values may vary slightly depending on the source.
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Calculating ΔG° for the Reaction
Step 1: Write the Reaction in Terms of Standard Data
The reaction:CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g)
requires calculating the standard Gibbs free energy change (ΔG°) using:
\[ \Delta G^\circ{\text{reaction}} = \sum \nui \Delta G^\circ_{f,i} \]
where:
- νi is the stoichiometric coefficient (positive for products, negative for reactants),
- ΔG°f,i is the standard Gibbs free energy of formation for each species.
Step 2: Apply the Formula
\[ \Delta G^\circ{\text{reaction}} = [\Delta G^\circ{f,\mathrm{CO}2} + 2 \times \Delta G^\circ{f,\mathrm{SO}2}] - [\Delta G^\circ{f,\mathrm{CS}2} + 3 \times \Delta G^\circ{f,\mathrm{O}_2}] \]
Plugging in the numbers:
\[ \Delta G^\circ_{\text{reaction}} = [(-394.4) + 2 \times (-300.2)] - [(-119.0) + 3 \times 0] \]
Calculations:
\[ \Delta G^\circ_{\text{reaction}} = (-394.4 - 600.4) - (-119.0) \]
\[ \Delta G^\circ_{\text{reaction}} = -994.8 + 119.0 \]
\[ \Delta G^\circ_{\text{reaction}} = -875.8\, \text{kJ/mol} \]
This indicates the reaction is thermodynamically favorable under standard conditions.
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Calculating ΔH° for the Reaction
Similarly, to find the enthalpy change:
\[ \Delta H^\circ{\text{reaction}} = \sum \nui \Delta H^\circ_{f,i} \]
Using the data:
\[ \Delta H^\circ_{\text{reaction}} = [–393.5 + 2 \times (–296.8)] - [–89.4 + 3 \times 0] \]
\[ \Delta H^\circ_{\text{reaction}} = (–393.5 – 593.6) – (–89.4) \]
\[ \Delta H^\circ_{\text{reaction}} = –987.1 + 89.4 \]
\[ \Delta H^\circ_{\text{reaction}} = –897.7\, \text{kJ/mol} \]
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Calculating ΔS° for the Reaction
The standard entropy change:
\[ \Delta S^\circ{\text{reaction}} = \sum \nui S^\circ_i \]
Calculations:
\[ \Delta S^\circ{\text{reaction}} = [S^\circ{\mathrm{CO}2} + 2 \times S^\circ{\mathrm{SO}2}] - [S^\circ{\mathrm{CS}2} + 3 \times S^\circ{\mathrm{O}_2}] \]
\[ \Delta S^\circ_{\text{reaction}} = (213.7 + 2 \times 248.0) - (213.8 + 3 \times 205.0) \]
\[ \Delta S^\circ_{\text{reaction}} = (213.7 + 496.0) - (213.8 + 615.0) \]
\[ \Delta S^\circ_{\text{reaction}} = 709.7 – 828.8 \]
\[ \Delta S^\circ_{\text{reaction}} = -119.1\, \text{J/mol·K} \]
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Calculating ΔG at 298 K
Step 1: Convert ΔS° to kJ/mol·K
Since ΔG°, ΔH°, and ΔS° are in different units, convert entropy to kJ:\[ \Delta S^\circ = -119.1\, \text{J/mol·K} = -0.1191\, \text{kJ/mol·K} \]
Step 2: Use the Gibbs Free Energy Equation
The temperature (T) is 298 K. Apply:\[ \Delta G = \Delta H - T \Delta S \]
\[ \Delta G_{298\,K} = –897.7\, \text{kJ/mol} – 298\, \text{K} \times (–0.1191\, \text{kJ/mol·K}) \]
\[ \Delta G_{298\,K} = –897.7 + 35.5 \]
\[ \Delta G_{298\,K} = –862.2\, \text{kJ/mol} \]
This negative value confirms that the reaction proceeds spontaneously at 298 K under standard conditions.
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Interpreting the Results
The calculated ΔG at 298 K is approximately –862.2 kJ/mol, indicating a highly spontaneous reaction. The negative Gibbs free energy change confirms that, under standard conditions, the reaction between CS₂ and oxygen produces CO₂ and SO₂ gases spontaneously at room temperature.
Additionally, the large magnitude of ΔG suggests the reaction is thermodynamically favorable and will likely proceed readily without requiring external energy input.
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Additional Considerations and Practical Applications
Factors Influencing ΔG
While thermodynamic calculations predict spontaneity, actual reaction rates depend on kinetics and other factors such as:- Temperature variations,
- Pressure conditions,
- Catalysts,
- Concentrations.
Industrial Relevance
Understanding ΔG for this reaction is essential in:- Sulfur compound processing,
- Combustion analysis,
- Environmental impact assessments, especially regarding sulfur dioxide emissions.
Environmental Implications
The formation of SO₂ is a concern due to its role in acid rain. Calculations confirming the spontaneity can aid in designing better pollution control strategies.---
Summary
Calculating Gibbs free energy change at 298 K involves:
- Collecting standard thermodynamic data for all species involved,
- Calculating ΔG°, ΔH°, and ΔS° for the reaction,
- Applying the Gibbs free energy equation at the
