Practice Test 2-1: Thermodynamics, Calorimetry, and Entropy Guidance

Q1. Which statement is true of the internal energy of a system and its surroundings during an energy exchange with a positive value of ∆Usystem?

Background

Topic: Thermodynamics – Internal Energy

This question tests your understanding of how energy is transferred between a system and its surroundings, specifically when the internal energy of the system increases (∆Usystem > 0).

Key Terms:

• System: The part of the universe being studied.

• Surroundings: Everything outside the system.

• Internal Energy (U): The total energy contained within the system.

• ∆U: Change in internal energy.

Step-by-Step Guidance

1. Recall that the internal energy of the system increases when energy is added to it (∆Usystem > 0).

2. Consider the law of conservation of energy: energy lost by the surroundings is gained by the system.

3. Think about whether both system and surroundings can increase or decrease together, or if one increases while the other decreases.

4. Review the answer choices and match them to your reasoning about energy transfer.

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Q2. A gas is compressed from an initial volume of 5.55 L to a final volume of 0.700 L by an external pressure of 1.00 atm. During the compression the gas releases |224.0 J| of heat. What is the change in internal energy of the gas?

Background

Topic: Thermodynamics – First Law

This question tests your ability to apply the first law of thermodynamics to calculate the change in internal energy (∆U) during a process involving work and heat transfer.

Key Terms and Formulas:

• First Law of Thermodynamics: $\Delta U = q + w$

• q = heat exchanged (J)

• w = work done on/by the system (J)

• Work for constant external pressure: $w = -P_{ext} \Delta V$

• 1 L·atm = 101.3 J (unit conversion)

Step-by-Step Guidance

1. Calculate the change in volume: $\Delta V = V_{final} - V_{initial}$

2. Calculate the work done on the gas: $w = -P_{ext} \Delta V$ (convert to J using 1 L·atm = 101.3 J)

3. Determine the sign and value of q (heat released means q is negative).

4. Set up the first law equation: $\Delta U = q + w$

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Q3. A 25.0-L sample of gas is compressed by a constant pressure of 1.267 × 105 Pa. If 328 J of work was done on the gas, what will be the final volume of the gas?

Background

Topic: Thermodynamics – Work and Pressure-Volume Changes

This question tests your understanding of how to relate work, pressure, and volume changes for a gas.

Key Terms and Formulas:

• Work at constant pressure: $w = -P \Delta V$

• 1 L·atm = 101.3 J; 101 kPa = 1 atm

• Pressure in Pa must be converted to atm or J as needed.

Step-by-Step Guidance

1. Convert the pressure from Pa to atm if needed.

2. Set up the equation for work: $w = -P (V_{final} - V_{initial})$

3. Rearrange to solve for $V_{final}$ given the work and initial volume.

4. Check unit consistency (work in J, pressure in atm or Pa, volume in L).

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Q4. Which statement is always true of the internal energy of a system and its surroundings during an energy exchange with an endothermic value of ∆Usystem?

Background

Topic: Thermodynamics – Endothermic Processes

This question tests your understanding of energy flow during endothermic reactions, where the system absorbs energy.

Key Terms:

• Endothermic: Process where the system absorbs heat (∆H > 0).

• Internal energy: Total energy within the system.

Step-by-Step Guidance

1. Recall that in an endothermic process, the system absorbs energy from the surroundings.

2. Consider how this affects the internal energy of both the system and surroundings.

3. Review the answer choices and match them to your understanding of energy transfer.

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Q5. Calculate the value of ∆H˚rxn for the reaction: Na2SO4(aq) + Pb(NO3)2(aq) ⟶ PbSO4(s) + 2 NaNO3(aq), given the calorimeter data.

Background

Topic: Calorimetry – Enthalpy of Reaction

This question tests your ability to use calorimeter data to calculate the enthalpy change for a reaction.

Key Terms and Formulas:

• Heat capacity (C): Amount of heat required to raise temperature by 1 K.

• q = C × ∆T

• ∆Hrxn: Enthalpy change per mole of reaction.

Step-by-Step Guidance

1. Calculate the total heat absorbed/released: $q = C \times \Delta T$

2. Determine the limiting reactant to find the number of moles reacting.

3. Calculate ∆Hrxn per mole using $\Delta H_{rxn} = \frac{q}{\text{moles}}$

4. Convert units as needed (J to kJ).

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Q6. Calculate the expected final temperature of water when 26.4 grams of an insoluble material at 98.56 °C is added to 80.0 grams of water at 20.00 °C.

Background

Topic: Calorimetry – Heat Exchange

This question tests your ability to use the concept of heat transfer between two substances to find the final equilibrium temperature.

Key Terms and Formulas:

• Specific heat (c): Amount of heat required to raise 1 g of substance by 1 °C.

• Heat lost = Heat gained: $m_1 c_1 (T_{final} - T_{initial,1}) = -m_2 c_2 (T_{final} - T_{initial,2})$

Step-by-Step Guidance

1. Set up the heat balance equation for the two substances.

2. Plug in the masses, specific heats, and initial temperatures.

3. Combine terms to solve for $T_{final}$.

4. Check that the final temperature is between the two initial temperatures.

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Q7. Determine the number of gummy bears that must be burned in a bomb calorimeter with a total heat capacity of 29.8 kJ·K–1 to raise the temperature by 8.4 °C.

Background

Topic: Calorimetry – Energy Content of Food

This question tests your ability to relate the energy released from burning food to the temperature change in a calorimeter.

Key Terms and Formulas:

• Calorimeter heat capacity (C): $q = C \times \Delta T$

• Energy per gummy bear: 10 nutritional Calories = 10,000 calories = 41,840 J

• 1 calorie = 4.184 J

Step-by-Step Guidance

1. Calculate the total energy required: $q = C \times \Delta T$ (convert kJ to J if needed).

2. Calculate the energy provided by one gummy bear.

3. Set up the equation: (number of gummy bears) × (energy per bear) = total energy required.

4. Solve for the number of gummy bears.

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Q8. What is the specific heat capacity of a substance that requires 6.0 Joules of energy to heat 10.0 grams of the material by 2.4 °C?

Background

Topic: Calorimetry – Specific Heat

This question tests your ability to use the formula for specific heat capacity to solve for c.

Key Terms and Formulas:

• Specific heat formula: $q = m c \Delta T$

• q = heat absorbed (J)

• m = mass (g)

• c = specific heat (J·g–1·°C–1)

• ∆T = temperature change (°C)

Step-by-Step Guidance

1. Write the formula: $q = m c \Delta T$

2. Rearrange to solve for c: $c = \frac{q}{m \Delta T}$

3. Plug in the values for q, m, and ∆T.

4. Check the units to ensure the answer is in J·g–1·°C–1.

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Q9. Calculate the standard enthalpy of reaction for 2 C(graphite) + 3 H2(g) ⟶ C2H6(g) given standard enthalpy of combustion data.

Background

Topic: Thermochemistry – Hess's Law

This question tests your ability to use Hess's Law and enthalpy of combustion data to calculate the enthalpy of formation for a compound.

Key Terms and Formulas:

• Hess's Law: The enthalpy change for a reaction is the sum of enthalpy changes for individual steps.

• Standard enthalpy of combustion: ∆H˚comb

• Standard enthalpy of formation: ∆H˚f

Step-by-Step Guidance

1. Write the target reaction and the given combustion reactions.

2. Manipulate the given equations (reverse, multiply) to sum to the target reaction.

3. Add or subtract the enthalpy values accordingly.

4. Check that the final equation matches the target reaction.

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Q10. Calculate the enthalpy of reaction for B(s) + 3/2 H2(g) ⟶ ½ B2H6(g) using the provided data.

Background

Topic: Thermochemistry – Hess's Law

This question tests your ability to use multiple reactions and their enthalpy changes to find the enthalpy of a target reaction.

Key Terms and Formulas:

• Hess's Law: Combine reactions to get the target reaction, sum enthalpy changes.

• Enthalpy (∆H): Heat change at constant pressure.

Step-by-Step Guidance

1. Write the target reaction and all provided reactions.

2. Manipulate (reverse, multiply) the provided reactions to sum to the target reaction.

3. Add or subtract the enthalpy values as you manipulate the equations.

4. Check that the final equation matches the target reaction.

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Q11. If the standard enthalpy of combustion of CH3COOH(l) at 298 K is –875 kJ/mol, estimate the standard enthalpy of formation of CH3COOH(l).

Background

Topic: Thermochemistry – Enthalpy of Formation

This question tests your ability to use enthalpy of combustion and formation data to estimate the enthalpy of formation for a compound.

Key Terms and Formulas:

• Enthalpy of combustion: ∆H˚comb

• Enthalpy of formation: ∆H˚f

• Hess's Law: Combine reactions to get the desired enthalpy.

Step-by-Step Guidance

1. Write the combustion reaction for acetic acid.

2. Write the formation reactions for CO2(g) and H2O(l).

3. Set up the enthalpy cycle using Hess's Law.

4. Plug in the given enthalpy values and solve for ∆H˚f of acetic acid.

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Q12. How many of the following have a ∆H˚f of zero: Br2(g), Hg(l), Mo(l), F2(g), I2(g), H(g), Mg(s)?

Background

Topic: Thermochemistry – Standard Enthalpy of Formation

This question tests your knowledge of which elements have a standard enthalpy of formation of zero.

Key Terms:

• Standard enthalpy of formation (∆H˚f): Zero for elements in their standard state.

• Standard state: Most stable form of an element at 1 atm and 25°C.

Step-by-Step Guidance

1. Identify the standard state for each element listed.

2. Determine which are in their standard state and thus have ∆H˚f = 0.

3. Count the number of elements meeting this criterion.

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Q13. Use average molar bond energies to estimate ∆H˚rxn for 2CH3CH2OH(g) + 2Cl2(g) ⟶ 2CH3CH2OCl(g) + 2HCl(g).

Background

Topic: Thermochemistry – Bond Enthalpy

This question tests your ability to estimate the enthalpy change of a reaction using average bond energies.

Key Terms and Formulas:

• Bond enthalpy: Energy required to break a bond.

• ∆H˚rxn = (sum of bonds broken) – (sum of bonds formed)

Step-by-Step Guidance

1. Write out all bonds broken and formed in the reaction.

2. Sum the bond energies for all bonds broken (reactants).

3. Sum the bond energies for all bonds formed (products).

4. Calculate ∆H˚rxn using the formula above.

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Q14. Estimate the heat of reaction at 298 K for Br2(g) + 3F2(g) ⟶ 2BrF3(g) using bond enthalpies.

Background

Topic: Thermochemistry – Bond Enthalpy

This question tests your ability to estimate the enthalpy change of a reaction using bond energies.

Key Terms and Formulas:

• Bond enthalpy: Energy required to break a bond.

• ∆H˚rxn = (sum of bonds broken) – (sum of bonds formed)

Step-by-Step Guidance

1. List all bonds broken in reactants and all bonds formed in products.

2. Sum the bond energies for bonds broken and formed.

3. Calculate ∆H˚rxn using the formula above.

4. Check your calculation for sign and magnitude.

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Q15. For how many of the following does the entropy decrease: mixing sugar into tea, condensation of a gas, dissolving O2(g) into H2O(l), shuffling a deck of cards, C(s) + ½ O2(g) ⟶ CO(g), sublimation of CO2(s)?

Background

Topic: Thermodynamics – Entropy

This question tests your understanding of entropy changes in various physical and chemical processes.

Key Terms:

• Entropy (S): Measure of disorder or randomness.

• Processes that decrease entropy: typically involve going from more disordered to more ordered states.

Step-by-Step Guidance

1. Analyze each process to determine if entropy increases or decreases.

2. Count the number of processes where entropy decreases.

3. Review your reasoning for each process.

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Q16. How many of the following isothermal reactions have a positive change in entropy?

Background

Topic: Thermodynamics – Entropy

This question tests your ability to identify processes with positive entropy change.

Key Terms:

• Positive entropy change: Increase in disorder.

• Isothermal: Constant temperature.

Step-by-Step Guidance

1. Analyze each reaction or process for entropy change.

2. Count the number of processes with positive entropy change.

3. Review your reasoning for each process.

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Q17. When MnSO4 is dissolved in 25°C water, the solution becomes hotter. What happens to the solubility of MnSO4 if the temperature is raised?

Background

Topic: Thermodynamics – Solubility and Enthalpy

This question tests your understanding of how temperature affects solubility based on whether dissolution is exothermic or endothermic.

Key Terms:

• Exothermic dissolution: Releases heat, solution gets hotter.

• Solubility: Amount of solute that dissolves in solvent.

Step-by-Step Guidance

1. Recall that exothermic dissolution means heat is released.

2. Consider Le Chatelier's principle: increasing temperature favors the reverse (endothermic) process.

3. Predict how solubility changes with temperature for exothermic processes.

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Q18. When NH4NO3 is dissolved in 25°C water, the solution becomes colder. What happens to the solubility of NH4NO3 if the temperature is lowered?

Background

Topic: Thermodynamics – Solubility and Enthalpy

This question tests your understanding of how temperature affects solubility for endothermic dissolution.

Key Terms:

• Endothermic dissolution: Absorbs heat, solution gets colder.

• Solubility: Amount of solute that dissolves in solvent.

Step-by-Step Guidance

1. Recall that endothermic dissolution means heat is absorbed.

2. Consider Le Chatelier's principle: lowering temperature favors the exothermic direction.

3. Predict how solubility changes with temperature for endothermic processes.

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Q19. For which of the following could you expect both the solubility in H2O to decrease with increasing temperature and a negative entropy of solution (∆Ssol < 0): N2, K2SO4, CH3CH2OH, C6H12?

Background

Topic: Thermodynamics – Solubility and Entropy

This question tests your understanding of how solubility and entropy change for different types of solutes.

Key Terms:

• ∆Ssol: Entropy change upon dissolution.

• Solubility: How much solute dissolves in solvent.

Step-by-Step Guidance

1. Consider the nature of each solute (gas, ionic, organic).

2. Recall that gas solubility typically decreases with increasing temperature and often has negative entropy change.

3. Analyze each solute for the criteria given.

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Q20. How many of the following processes are driven by an increase in entropy only (not driven by enthalpy)? NaCl dissolving in water; O2 dissolving in water; freezing of water; boiling of water.

Background

Topic: Thermodynamics – Entropy vs. Enthalpy

This question tests your ability to distinguish between processes driven by entropy and those driven by enthalpy.

Key Terms:

• Entropy-driven: Process occurs because disorder increases.

• Enthalpy-driven: Process occurs because heat is released or absorbed.

Step-by-Step Guidance

1. Analyze each process to determine if it is primarily driven by entropy.

2. Count the number of processes meeting the criterion.

3. Review your reasoning for each process.

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