Medium Enthalpy Change Practice Questions

Concept Explanation

Enthalpy change (ΔH) is the amount of heat energy absorbed or released by a system during a chemical reaction at constant pressure. This thermodynamic property indicates whether a process is exothermic (releasing heat, negative ΔH) or endothermic (absorbing heat, positive ΔH). To calculate enthalpy change, chemists often use calorimetry data, standard enthalpies of formation, or bond enthalpies. According to the First Law of Thermodynamics, energy cannot be created or destroyed; therefore, the heat lost by a reaction is gained by the surroundings, typically measured as a temperature change in water or a solution. Understanding these energy shifts is critical for industrial chemical production and environmental science. For more foundational practice, you might also explore Enthalpy Change Practice Questions with Answers for a broader range of difficulties.

Key Formulas and Units

The standard unit for enthalpy is the Joule (J) or kiloJoule (kJ), often expressed per mole (kJ/mol). Common calculation methods include:

• Calorimetry: q = m × c × ΔT, where q is heat, m is mass, c is specific heat capacity, and ΔT is the change in temperature.

• Hess's Law: ΔH_total = ΣΔH_products - ΣΔH_reactants.

• Bond Enthalpy: ΔH = Σ(Bonds Broken) - Σ(Bonds Formed).

Solved Examples

Example 1: Calculating Enthalpy from Calorimetry
A 50.0 g sample of water at 25.0°C is heated by a chemical reaction. The temperature of the water rises to 32.5°C. Calculate the heat energy absorbed by the water (c = 4.18 J/g°C).

1. Identify the known values: m = 50.0 g, c = 4.18 J/g°C, ΔT = 32.5°C - 25.0°C = 7.5°C.

2. Apply the formula: q = m × c × ΔT.

3. Calculate: q = 50.0 × 4.18 × 7.5 = 1567.5 J.

4. Convert to kJ: 1.57 kJ (rounded to three significant figures).

Example 2: Enthalpy of Formation
Calculate the standard enthalpy change for the reaction: 2CO(g) + O₂(g) → 2CO₂(g). Given ΔH_f[CO(g)] = -110.5 kJ/mol and ΔH_f[CO₂(g)] = -393.5 kJ/mol.

1. Recall that the ΔH_f for pure elements like O₂(g) is 0 kJ/mol.

2. Use the formula: ΔH_rxn = ΣΔH_f(products) - ΣΔH_f(reactants).

3. Substitute values: ΔH_rxn = [2 × (-393.5)] - [2 × (-110.5) + 0].

4. Solve: ΔH_rxn = -787.0 - (-221.0) = -566.0 kJ.

Example 3: Bond Enthalpy Estimation
Estimate the ΔH for the reaction H₂(g) + Cl₂(g) → 2HCl(g) using bond energies: H-H (436 kJ/mol), Cl-Cl (242 kJ/mol), and H-Cl (431 kJ/mol).

1. List bonds broken (reactants): 1 mol H-H and 1 mol Cl-Cl. Energy = 436 + 242 = 678 kJ.

2. List bonds formed (products): 2 mol H-Cl. Energy = 2 × 431 = 862 kJ.

3. Calculate ΔH: Σ(Broken) - Σ(Formed) = 678 - 862 = -184 kJ.

Practice Questions

1. A 2.00 g sample of octane (C₈H₁₈) is burned in a bomb calorimeter, raising the temperature of 1200 g of water from 22.0°C to 41.5°C. Calculate the heat released in kJ.

2. Calculate the ΔH for the reaction C(s) + 2H₂(g) → CH₄(g) using the following data: C(s) + O₂(g) → CO₂(g) ΔH = -393.5 kJ; H₂(g) + ½O₂(g) → H₂O(l) ΔH = -285.8 kJ; CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ΔH = -890.3 kJ.

3. When 50.0 mL of 1.0 M HCl is mixed with 50.0 mL of 1.0 M NaOH in a coffee-cup calorimeter, the temperature increases from 21.0°C to 27.5°C. Determine the enthalpy of neutralization in kJ/mol, assuming the density of the solution is 1.00 g/mL and c = 4.18 J/g°C.

4. Using standard enthalpies of formation (ΔH_f), calculate ΔH for the combustion of propane: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l). (ΔH_f: propane = -103.8 kJ/mol, CO₂ = -393.5 kJ/mol, H₂O(l) = -285.8 kJ/mol).

5. How much heat (in kJ) is required to decompose 25.0 g of CaCO₃(s) given the reaction: CaCO₃(s) → CaO(s) + CO₂(g) ΔH = +178.3 kJ/mol?

6. Calculate the molar enthalpy of solution for NH₄NO₃ if dissolving 5.00 g of the salt in 100.0 g of water causes the temperature to drop from 23.0°C to 19.1°C.

7. Given the bond energies C-H (413 kJ/mol), Br-Br (193 kJ/mol), C-Br (285 kJ/mol), and H-Br (366 kJ/mol), calculate the enthalpy change for: CH₄(g) + Br₂(g) → CH₃Br(g) + HBr(g).

8. A reaction releases 45.0 kJ of heat. If this heat is used to warm 500.0 g of copper (c = 0.385 J/g°C) initially at 20.0°C, what will be the final temperature of the copper?

9. Determine the ΔH for the reaction 2Al(s) + Fe₂O₃(s) → 2Fe(s) + Al₂O₃(s) using ΔH_f: Fe₂O₃ = -824.2 kJ/mol and Al₂O₃ = -1675.7 kJ/mol.

10. If the enthalpy of combustion of ethanol (C₂H₅OH) is -1367 kJ/mol, how many grams of ethanol must be burned to provide 5000 kJ of energy?

Answers & Explanations

1. Answer: 97.8 kJ. Calculation: q = m × c × ΔT = 1200 g × 4.18 J/g°C × (41.5 - 22.0)°C = 97,812 J = 97.8 kJ.

2. Answer: -74.8 kJ. Using Hess's Law: ΔH = (-393.5) + 2(-285.8) - (-890.3) = -74.8 kJ/mol.

3. Answer: -54.3 kJ/mol. Total mass = 100 g. q = 100 × 4.18 × 6.5 = 2717 J = 2.717 kJ. Moles of HCl = 0.050 L × 1.0 M = 0.050 mol. ΔH = -2.717 / 0.050 = -54.3 kJ/mol.

4. Answer: -2220.1 kJ/mol. ΔH = [3(-393.5) + 4(-285.8)] - [-103.8 + 0] = [-1180.5 - 1143.2] + 103.8 = -2220.1 kJ/mol.

5. Answer: 44.5 kJ. Molar mass CaCO₃ = 100.09 g/mol. Moles = 25.0 / 100.09 = 0.2498 mol. Heat = 0.2498 mol × 178.3 kJ/mol = 44.5 kJ.

6. Answer: +26.1 kJ/mol. q_water = 100 g × 4.18 × (19.1 - 23.0) = -1630.2 J. Heat absorbed by salt = +1.63 kJ. Moles NH₄NO₃ = 5.00 / 80.04 = 0.06247 mol. ΔH = 1.63 / 0.06247 = +26.1 kJ/mol.

7. Answer: -45 kJ/mol. Bonds broken: 1(C-H) + 1(Br-Br) = 413 + 193 = 606 kJ. Bonds formed: 1(C-Br) + 1(H-Br) = 285 + 366 = 651 kJ. ΔH = 606 - 651 = -45 kJ/mol. Refer to Bond Energy Practice Questions for similar problems.

8. Answer: 253.8°C. q = 45000 J. ΔT = q / (m × c) = 45000 / (500.0 × 0.385) = 233.8°C. Final T = 20.0 + 233.8 = 253.8°C.

9. Answer: -851.5 kJ. ΔH = [-1675.7 + 0] - [0 + (-824.2)] = -1675.7 + 824.2 = -851.5 kJ.

10. Answer: 168.6 g. Moles needed = 5000 kJ / 1367 kJ/mol = 3.658 mol. Molar mass ethanol = 46.07 g/mol. Mass = 3.658 × 46.07 = 168.6 g.

Quick Quiz

Frequently Asked Questions

What is the difference between ΔH and q?

While both represent heat, q is the heat exchanged under any conditions, whereas ΔH specifically refers to the heat exchanged at constant pressure. In most laboratory chemistry experiments conducted in open containers, q is equal to ΔH.

Why is the enthalpy of formation for elements zero?

By convention, the standard enthalpy of formation is defined as the change in enthalpy when one mole of a substance is formed from its elements in their standard states. Since an element in its standard state is already formed, no energy change occurs, making the value zero.

Does a negative enthalpy change mean a reaction is spontaneous?

Not necessarily. While exothermic reactions (negative ΔH) are often spontaneous, spontaneity is actually determined by the Gibbs Free Energy (ΔG), which accounts for both enthalpy and entropy.

How do you convert Joules to kiloJoules?

To convert Joules to kiloJoules, you divide the value by 1,000. For example, 5,000 Joules is equal to 5 kiloJoules, a common step in standard enthalpy calculations.

What is a coffee-cup calorimeter used for?

A coffee-cup calorimeter is a simple device used to measure the heat of reaction at constant pressure for aqueous solutions. It is highly effective for determining the enthalpy of neutralization or solution for educational purposes.

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