Easy Hess’s Law Practice Questions

Concept Explanation

Hess’s Law states that the total enthalpy change for a chemical reaction is the same regardless of the path taken, provided the initial and final states are identical. This fundamental principle of thermochemistry is a specific application of the Law of Conservation of Energy, or the first law of thermodynamics, which you can explore further on Wikipedia. Because enthalpy is a state function, we can calculate the enthalpy change of a complex reaction by summing the enthalpy changes of individual steps that lead to the same overall result.

To solve Easy Hess’s Law Practice Questions, you must learn to manipulate intermediate equations so they add up to a target equation. There are two primary rules to follow when adjusting these steps:

• Reversing a Reaction: If you flip a chemical equation (swap reactants and products), you must change the sign of the enthalpy change (ΔH). For example, if a reaction is exothermic (-ΔH), its reverse is endothermic (+ΔH).

• Multiplying by a Coefficient: If you multiply the coefficients in a balanced equation by a factor (like 2 or 0.5), you must multiply the ΔH value by that same factor.

Hess’s Law is incredibly useful because it allows chemists to determine the heat of reaction for processes that are too dangerous, too slow, or otherwise difficult to measure directly in a laboratory setting using standard calorimetry techniques.

Solved Examples

Here are three examples demonstrating how to apply these rules to find the total enthalpy change.

Example 1: Simple Addition

Calculate the ΔH for the reaction: A → C, given the following steps:
1) A → B (ΔH = +50 kJ)
2) B → C (ΔH = -30 kJ)

1. Identify the target: A → C.

2. Notice that if we add reaction 1 and reaction 2, the intermediate "B" appears on both the product and reactant sides.

3. Cancel out B: (A → B) + (B → C) = A → C.

4. Sum the enthalpies: +50 kJ + (-30 kJ) = +20 kJ.

5. The final ΔH for A → C is +20 kJ.

Example 2: Reversing a Reaction

Calculate ΔH for: X + Y → Z, given:
1) Z → X + Y (ΔH = +150 kJ)

1. The target reaction is the exact reverse of the given reaction.

2. Flip the given reaction: X + Y → Z.

3. Change the sign of ΔH: +150 kJ becomes -150 kJ.

4. The final ΔH is -150 kJ.

Example 3: Multiplying Coefficients

Calculate ΔH for: 2S + 3O₂ → 2SO₃, given:
1) S + 1.5O₂ → SO₃ (ΔH = -395 kJ)

1. Compare the target to the given reaction. The target has twice the amount of all substances.

2. Multiply the given reaction by 2: 2(S + 1.5O₂ → SO₃).

3. Multiply the ΔH by 2: 2 × (-395 kJ) = -790 kJ.

4. The final ΔH is -790 kJ.

Practice Questions

Test your understanding with these Easy Hess’s Law Practice Questions. Work through them step-by-step before checking the answers below.

1. Find ΔH for the reaction: C(graphite) → C(diamond), given:
C(graphite) + O₂(g) → CO₂(g) (ΔH = -393.5 kJ)
C(diamond) + O₂(g) → CO₂(g) (ΔH = -395.4 kJ)

2. Calculate the enthalpy change for: 2NO₂(g) → N₂O₄(g), given:
N₂(g) + 2O₂(g) → 2NO₂(g) (ΔH = +67.7 kJ)
N₂(g) + 2O₂(g) → N₂O₄(g) (ΔH = +9.7 kJ)

3. Determine ΔH for the reaction: PCl₃ + Cl₂ → PCl₅, given:
P₄ + 6Cl₂ → 4PCl₃ (ΔH = -1280 kJ)
P₄ + 10Cl₂ → 4PCl₅ (ΔH = -1774 kJ)

4. Given the following data:
2H₂(g) + O₂(g) → 2H₂O(l) (ΔH = -572 kJ)
What is the ΔH for the reaction: H₂O(l) → H₂(g) + 0.5O₂(g)?

5. Calculate ΔH for: 2C + O₂ → 2CO, given:
C + O₂ → CO₂ (ΔH = -394 kJ)
2CO + O₂ → 2CO₂ (ΔH = -566 kJ)

6. Find ΔH for the process: N₂(g) + O₂(g) → 2NO(g), given:
0.5N₂(g) + O₂(g) → NO₂(g) (ΔH = +33.2 kJ)
NO(g) + 0.5O₂(g) → NO₂(g) (ΔH = -57.1 kJ)

7. Compute ΔH for the reaction: 3Fe + 2O₂ → Fe₃O₄, given:
Fe + 0.5O₂ → FeO (ΔH = -272 kJ)
3FeO + 0.5O₂ → Fe₃O₄ (ΔH = -318 kJ)

8. Calculate the enthalpy change for: C₂H₄ + H₂ → C₂H₆, given:
C₂H₄ + 3O₂ → 2CO₂ + 2H₂O (ΔH = -1411 kJ)
C₂H₆ + 3.5O₂ → 2CO₂ + 3H₂O (ΔH = -1560 kJ)
H₂ + 0.5O₂ → H₂O (ΔH = -286 kJ)

Answers & Explanations

1. Answer: +1.9 kJ. Reverse the second equation to get CO₂ → C(diamond) + O₂ (ΔH = +395.4 kJ). Add it to the first equation. The CO₂ and O₂ cancel, leaving C(graphite) → C(diamond). ΔH = -393.5 + 395.4 = +1.9 kJ.

2. Answer: -58.0 kJ. Reverse the first equation: 2NO₂ → N₂ + 2O₂ (ΔH = -67.7 kJ). Add it to the second equation. The N₂ and 2O₂ cancel. ΔH = -67.7 + 9.7 = -58.0 kJ.

3. Answer: -123.5 kJ. Reverse and divide the first equation by 4: PCl₃ → 0.25P₄ + 1.5Cl₂ (ΔH = +320 kJ). Divide the second equation by 4: 0.25P₄ + 2.5Cl₂ → PCl₅ (ΔH = -443.5 kJ). Adding these gives the target. ΔH = 320 - 443.5 = -123.5 kJ.

4. Answer: +286 kJ. Reverse the original reaction (sign changes to +572) and multiply by 0.5 (divide by 2). 572 / 2 = 286 kJ.

5. Answer: -222 kJ. Multiply the first equation by 2: 2C + 2O₂ → 2CO₂ (ΔH = -788 kJ). Reverse the second: 2CO₂ → 2CO + O₂ (ΔH = +566 kJ). Add them: -788 + 566 = -222 kJ.

6. Answer: +180.6 kJ. Multiply the first equation by 2: N₂ + 2O₂ → 2NO₂ (ΔH = +66.4 kJ). Reverse and multiply the second by 2: 2NO₂ → 2NO + O₂ (ΔH = +114.2 kJ). Add them: 66.4 + 114.2 = 180.6 kJ.

7. Answer: -1134 kJ. Multiply the first equation by 3: 3Fe + 1.5O₂ → 3FeO (ΔH = -816 kJ). Add the second equation as is. ΔH = -816 + (-318) = -1134 kJ.

8. Answer: -137 kJ. Keep eq 1 as is (-1411). Reverse eq 2 (+1560). Keep eq 3 as is (-286). Sum: -1411 + 1560 - 286 = -137 kJ.

Quick Quiz

Frequently Asked Questions

What is the primary requirement for Hess’s Law to be valid?

The primary requirement is that the initial reactants and final products must be the same for all compared pathways. Since enthalpy is a state function, the numerical value depends only on these states, not the steps in between.

Can Hess’s Law be used for physical changes?

Yes, Hess’s Law applies to physical changes like phase transitions (melting or boiling) just as it applies to chemical reactions. You can sum the enthalpies of fusion and vaporization to find the total enthalpy of sublimation.

Do I need to include the states of matter in Hess’s Law calculations?

Yes, states of matter (solid, liquid, gas) are crucial because the enthalpy of a substance changes with its state. For example, the ΔH for forming liquid water is different from forming water vapor.

Is Hess’s Law related to the First Law of Thermodynamics?

Hess’s Law is a direct consequence of the First Law of Thermodynamics, which states that energy cannot be created or destroyed. It confirms that the energy change in a system is constant regardless of how the change occurs.

What should I do if my equations don't add up to the target?

Double-check your coefficients and the direction of your reactions. You may need to multiply an equation by a fraction or a whole number, or flip it to ensure that all intermediate species cancel out properly.

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