Thermodynamics and Entropy Worksheet – Guided Study

Q1. Which of the following will have the greatest standard molar entropy (S°)?

Background

Topic: Entropy and States of Matter

This question tests your understanding of how entropy varies with the physical state (gas, liquid, solid) and molecular complexity.

Key Terms:

• Standard molar entropy (S°): The entropy content of one mole of a substance under standard conditions (usually 1 bar, 25°C).

• Entropy (S): A measure of disorder or randomness in a system. Gases generally have higher entropy than liquids or solids.

Step-by-Step Guidance

1. Recall that entropy increases in the order: solid < liquid < gas.

2. Compare the physical states of each substance listed (g = gas, l = liquid, s = solid).

3. For substances in the same state, consider molecular complexity (more atoms = higher entropy).

4. Identify which option is a gas and has the most atoms or complexity.

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Q2. Indicate which of the following has the lowest standard molar entropy (S°).

Background

Topic: Entropy and States of Matter

This question asks you to identify the substance with the lowest entropy, considering both physical state and molecular complexity.

Key Terms:

• Standard molar entropy (S°): See above.

• Solids generally have lower entropy than liquids or gases.

Step-by-Step Guidance

1. List the physical state of each substance (g, l, s).

2. Recall that solids have the lowest entropy, followed by liquids, then gases.

3. Among the solids, compare molecular complexity if needed.

4. Identify the substance that is a solid and least complex.

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Q3. Indicate which one of the following reactions result in a positive ΔSsys.

Background

Topic: Entropy Change in Chemical Reactions

This question tests your ability to predict whether the entropy of the system increases (ΔSsys > 0) during a reaction.

Key Terms:

• ΔSsys: Change in entropy of the system.

• Formation of gases increases entropy; formation of solids decreases entropy.

Step-by-Step Guidance

1. For each reaction, count the number of moles of gas on both sides.

2. Identify if gases are produced or consumed.

3. Look for reactions where the number of gas molecules increases or a solid decomposes to gases.

4. Choose the reaction where entropy increases (more disorder).

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Q4. Indicate which one of the following reactions results in a negative ΔSsys.

Background

Topic: Entropy Change in Chemical Reactions

This question asks you to identify a reaction where the system's entropy decreases (ΔSsys < 0).

Key Terms:

• ΔSsys: See above.

• Formation of solids or fewer gas molecules usually means a decrease in entropy.

Step-by-Step Guidance

1. For each reaction, compare the number of gas molecules before and after the reaction.

2. Identify if gases are being converted to solids or liquids.

3. Look for reactions where the system becomes more ordered (less random).

4. Select the reaction with a decrease in entropy.

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Q5. Which of the processes A–D will lead to a positive change in the entropy of the system?

Background

Topic: Entropy Changes in Physical Processes

This question tests your understanding of how different physical processes affect the entropy of a system.

Key Terms:

• Entropy (S): See above.

• Processes that increase disorder (e.g., melting, evaporation, gas expansion) increase entropy.

Step-by-Step Guidance

1. For each process, decide if the system becomes more or less ordered.

2. Identify which processes involve a transition to a more disordered state (e.g., solid to liquid, liquid to gas).

3. Eliminate processes that decrease entropy (e.g., freezing, crystallization).

4. Choose the correct option based on your analysis.

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Q6. Which of the following processes will lead to a decrease in the entropy of the system?

Background

Topic: Entropy Changes in Physical and Chemical Processes

This question asks you to identify a process where the system's entropy decreases.

Key Terms:

• Decrease in entropy: Occurs when a system becomes more ordered (e.g., gas to solid, formation of a compound from elements).

Step-by-Step Guidance

1. For each process, determine if the system becomes more ordered or disordered.

2. Identify processes where a gas becomes a solid or liquid, or where a compound forms from simpler substances.

3. Eliminate processes that increase entropy (e.g., melting, dissolving, gas expansion).

4. Select the process that leads to a decrease in entropy.

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Q7. Determine ΔS for H2(g) + I2(g) → 2HI(g) given the following information.

Background

Topic: Calculating Entropy Change for a Reaction

This question tests your ability to calculate the standard entropy change (ΔS°) for a reaction using standard molar entropy values.

Key Formula:

$\Delta S^\circ = \sum n S^\circ_{\text{products}} - \sum n S^\circ_{\text{reactants}}$

Where:

• $n$ = number of moles

• $S^\circ$ = standard molar entropy (J/mol·K)

Step-by-Step Guidance

1. Write the balanced chemical equation: $\mathrm{H_2(g) + I_2(g) \rightarrow 2HI(g)}$

2. List the standard molar entropy values for each substance:

   • $S^\circ_{\mathrm{H_2(g)}} = 130.58$ J/mol·K

   • $S^\circ_{\mathrm{I_2(g)}} = 116.73$ J/mol·K

   • $S^\circ_{\mathrm{HI(g)}} = 206.3$ J/mol·K

3. Apply the formula for $\Delta S^\circ$:

   $\Delta S^\circ = [2 \times S^\circ_{\mathrm{HI(g)}}] - [S^\circ_{\mathrm{H_2(g)}} + S^\circ_{\mathrm{I_2(g)}}]$

4. Set up the calculation by plugging in the values, but do not compute the final result yet.

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Q8. If 3.500 g of Ni (58.69 g/mol) are reacted with excess oxygen to form nickel oxide (NiO) under standard state conditions, what is the entropy change for the reaction?

Background

Topic: Calculating Entropy Change for a Reaction with Mass Given

This question tests your ability to calculate the entropy change for a reaction, starting from a given mass of reactant.

Key Formula:

$\Delta S = \sum n S^\circ_{\text{products}} - \sum n S^\circ_{\text{reactants}}$

Where:

• $n$ = number of moles (you'll need to convert grams to moles)

• $S^\circ$ = standard molar entropy (J/mol·K)

Step-by-Step Guidance

1. Write the balanced equation: $2\mathrm{Ni(s)} + \mathrm{O_2(g)} \rightarrow 2\mathrm{NiO(s)}$

2. Calculate the number of moles of Ni used: $n = \frac{3.500\ \mathrm{g}}{58.69\ \mathrm{g/mol}}$

3. Determine the moles of NiO produced (based on stoichiometry: 2 mol Ni → 2 mol NiO).

4. Apply the entropy formula for the reaction, using the given S° values and the number of moles calculated.

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Q9. What is the entropy change if 4.500 g of CaCO3(s) is placed in a container and allowed to decompose to CaO(s) and CO2(g)?

Background

Topic: Calculating Entropy Change for a Decomposition Reaction

This question tests your ability to calculate the entropy change for a reaction, starting from a given mass of reactant.

Key Formula:

$\Delta S = \sum n S^\circ_{\text{products}} - \sum n S^\circ_{\text{reactants}}$

Where:

• $n$ = number of moles (convert grams to moles)

• $S^\circ$ = standard molar entropy (J/mol·K)

Step-by-Step Guidance

1. Write the balanced equation: $\mathrm{CaCO_3(s) \rightarrow CaO(s) + CO_2(g)}$

2. Calculate the number of moles of CaCO3 used: $n = \frac{4.500\ \mathrm{g}}{\text{molar mass of CaCO}_3}$

3. Determine the moles of products formed (1:1:1 ratio in this reaction).

4. Apply the entropy formula using the S° values and the number of moles calculated.

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Q10. Processes are always spontaneous, regardless of temperature, when __________ (H and S refer to the system).

Background

Topic: Spontaneity and Gibbs Free Energy

This question tests your understanding of the relationship between enthalpy (ΔH), entropy (ΔS), and spontaneity.

Key Formula:

$\Delta G = \Delta H - T\Delta S$

Where:

• $\Delta G$ = change in Gibbs free energy

• $\Delta H$ = change in enthalpy

• $T$ = temperature in Kelvin

• $\Delta S$ = change in entropy

Step-by-Step Guidance

1. Recall that a process is spontaneous when $\Delta G < 0$.

2. Analyze the formula to determine which combinations of ΔH and ΔS always make ΔG negative, regardless of T.

3. Consider the sign of each term and how temperature affects the outcome.

4. Identify the correct combination of ΔH and ΔS for spontaneity at all temperatures.

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Q11. What is the ΔGrxn for the reaction: CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)?

Background

Topic: Calculating Gibbs Free Energy Change for a Reaction

This question tests your ability to calculate the standard Gibbs free energy change (ΔG°) for a reaction using standard free energies of formation.

Key Formula:

$\Delta G^\circ_{\text{rxn}} = \sum n \Delta G^\circ_{\text{f, products}} - \sum n \Delta G^\circ_{\text{f, reactants}}$

Where:

• $n$ = number of moles

• $\Delta G^\circ_{\text{f}}$ = standard free energy of formation (kJ/mol)

Step-by-Step Guidance

1. Write the balanced equation: $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

2. List the ΔGf values for each substance (O2 is an element in its standard state, so ΔGf = 0).

3. Apply the formula for ΔGrxn using the stoichiometric coefficients and the given values.

4. Set up the calculation, but do not compute the final result yet.

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Q12. Hydrogen reacts with nitrogen to form ammonia (NH3): 3H2(g) + N2(g) → 2NH3(g). The value of ΔH° is –92.38 kJ/mol, and that of ΔS° is –198.2 J/mol·K. Determine ΔG° at 25°C.

Background

Topic: Calculating Gibbs Free Energy Change from ΔH and ΔS

This question tests your ability to calculate ΔG° using ΔH°, ΔS°, and temperature.

Key Formula:

$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

Where:

• $\Delta H^\circ$ = standard enthalpy change (kJ/mol)

• $\Delta S^\circ$ = standard entropy change (J/mol·K; convert to kJ/mol·K if needed)

• $T$ = temperature in Kelvin (add 273.15 to °C)

Step-by-Step Guidance

1. Convert ΔS° from J/mol·K to kJ/mol·K by dividing by 1000.

2. Convert 25°C to Kelvin: $T = 25 + 273.15$

3. Plug the values into the formula: $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

4. Set up the calculation, but do not compute the final result yet.

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Q13. A reaction with a low enthalpy of reaction value is not spontaneous at low temperature but becomes spontaneous at high temperature. What are the signs for ΔH° and ΔS°, respectively?

Background

Topic: Temperature Dependence of Spontaneity

This question tests your understanding of how the signs of ΔH° and ΔS° affect spontaneity as temperature changes.

Key Formula:

$\Delta G = \Delta H - T\Delta S$

Key Concepts:

• If ΔH is positive and ΔS is positive, the reaction can become spontaneous at high T.

• If ΔH is negative and ΔS is negative, the reaction is spontaneous at low T.

Step-by-Step Guidance

1. Recall the formula and how T affects ΔG depending on the signs of ΔH and ΔS.

2. Analyze which sign combination makes ΔG negative only at high temperature.

3. Match this reasoning to the answer choices provided.

Try solving on your own before revealing the answer!