Thermodynamics: Entropy, Free Energy, and Equilibrium – Guided Study Notes

Q1. What does freezing water (liquid to solid) do to the entropy and enthalpy of the system, the entropy of the surroundings, and the entropy of the universe? Is the process spontaneous? Why?

Background

Topic: Thermodynamics – Entropy, Enthalpy, and Spontaneity

This question tests your understanding of how phase changes affect entropy ($S$), enthalpy ($H$), and spontaneity, as well as the relationship between the system, surroundings, and universe.

Key Terms and Formulas:

• Entropy ($S$): A measure of disorder or randomness in a system.

• Enthalpy ($H$): The heat content of a system at constant pressure.

• Spontaneity: A process is spontaneous if it occurs without outside intervention, often determined by the sign of $\Delta G$ (Gibbs Free Energy).

• Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

Step-by-Step Guidance

1. Consider what happens to the entropy of the system when water freezes (liquid to solid). Does the system become more ordered or disordered?

2. Think about the enthalpy change ($\Delta H$) for freezing. Is heat released or absorbed by the system?

3. Analyze the entropy of the surroundings. If the system releases heat, what happens to the surroundings' entropy?

4. Combine the changes in entropy for the system and surroundings to determine the entropy change of the universe ($\Delta S_{univ}$).

5. Use the relationship between $\Delta S_{univ}$ and spontaneity to discuss whether freezing is spontaneous under typical conditions, and what extra information (if any) you might need.

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Q2. What is Gibbs Free Energy and why is it important?

Background

Topic: Gibbs Free Energy

This question is about understanding the definition and significance of Gibbs Free Energy in predicting the spontaneity of chemical processes.

Key Terms and Formulas:

• Gibbs Free Energy ($G$): A thermodynamic quantity that combines enthalpy and entropy to predict spontaneity.

• Formula: $\Delta G = \Delta H - T\Delta S$

Step-by-Step Guidance

1. Recall the definition of Gibbs Free Energy and what each term in the formula represents.

2. Explain how the sign of $\Delta G$ determines whether a process is spontaneous ($\Delta G < 0$), nonspontaneous ($\Delta G > 0$), or at equilibrium ($\Delta G = 0$).

3. Discuss why Gibbs Free Energy is useful for chemists and how it relates to real-world chemical reactions.

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Q3. What is the 3rd law of thermodynamics? Order the following from least to most entropy: H2O (l), H2O (s), H2O2 (l), C (s, diamond), D2O (l)

Background

Topic: Third Law of Thermodynamics and Entropy Trends

This question tests your understanding of the third law of thermodynamics and how molecular structure and phase affect entropy.

Key Terms and Formulas:

• Third Law of Thermodynamics: The entropy of a perfect crystal at absolute zero is zero.

• Entropy Trends: Entropy increases with increasing molecular complexity, disorder, and phase (solid < liquid < gas).

Step-by-Step Guidance

1. Recall the third law of thermodynamics and its implications for entropy values at 0 K.

2. Compare the phases of the substances (solid vs. liquid) and predict which has higher entropy.

3. Consider molecular complexity (number of atoms, mass) when comparing entropy values for similar phases.

4. Arrange the substances in order from least to most entropy based on your analysis.

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Q4. Use the standard free energies of formation to determine ΔGrxn for the reaction: CH4(g) + 0.5 O2(g) → CO2(g) + 2 H2O(g) + O3(g) at 25°C.

Background

Topic: Calculating Standard Free Energy Change

This question tests your ability to use standard free energies of formation ($\Delta G_f^\circ$) to calculate the standard free energy change for a reaction.

Key Terms and Formulas:

• Standard Free Energy of Formation ($\Delta G_f^\circ$): The free energy change when 1 mole of a compound forms from its elements in their standard states.

• Formula: $\Delta G_{rxn}^\circ = \sum n_p \Delta G_f^\circ (products) - \sum n_r \Delta G_f^\circ (reactants)$

Step-by-Step Guidance

1. Write out the balanced chemical equation and identify the number of moles of each reactant and product.

2. List the $\Delta G_f^\circ$ values for each substance from the provided table.

3. Multiply each $\Delta G_f^\circ$ value by the number of moles for that substance in the reaction.

4. Set up the equation for $\Delta G_{rxn}^\circ$ using the formula above, but do not calculate the final value yet.

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Q5. Find ΔGrxn for the reaction: 3 C(s) + 4 H2(g) → C3H8(g) using the following reactions with known ΔGrxn values.

Background

Topic: Hess's Law for Gibbs Free Energy

This question tests your ability to use Hess's Law to combine reactions and their free energy changes to find the overall $\Delta G_{rxn}$ for a target reaction.

Key Terms and Formulas:

• Hess's Law: The total free energy change for a reaction is the sum of the free energy changes for the steps into which the reaction can be divided.

• Key Formula: $\Delta G_{rxn} = \sum \Delta G_{steps}$ (with appropriate manipulation of equations)

Step-by-Step Guidance

1. Write the target reaction and the given reactions with their $\Delta G_{rxn}$ values.

2. Determine how to manipulate (reverse or multiply) the given reactions so that, when added, they yield the target reaction.

3. Apply the same manipulations to the $\Delta G_{rxn}$ values (reverse sign if reaction is reversed, multiply if coefficients are changed).

4. Set up the sum of the adjusted $\Delta G_{rxn}$ values, but do not compute the final total yet.

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Q6. Calculate ΔGrxn at 25°C for SO2(g) + 0.5 O2(g) → SO3(g) and determine whether the reaction is spontaneous.

Background

Topic: Calculating ΔG from ΔH and ΔS

This question tests your ability to calculate the standard free energy change using enthalpy and entropy values, and to interpret spontaneity.

Key Terms and Formulas:

• Standard Enthalpy Change ($\Delta H^\circ$): The heat change at constant pressure for a reaction with all substances in their standard states.

• Standard Entropy Change ($\Delta S^\circ$): The entropy change for a reaction with all substances in their standard states.

• Formula: $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

Step-by-Step Guidance

1. Write the balanced chemical equation and identify the number of moles of each reactant and product.

2. List the $\Delta H^\circ$ and $S^\circ$ values for each substance from the table.

3. Calculate $\Delta H^\circ_{rxn}$ and $\Delta S^\circ_{rxn}$ using the products minus reactants method.

4. Set up the equation $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$ with your calculated values, but do not solve for the final value yet.

Try solving on your own before revealing the answer!