ΔH°f and Hess's Law: Worked Examples and Step-by-Step Solutions

🧪 Quick Study Guide

• 🔥 Enthalpy of Formation ($\Delta H°_f$): The change in enthalpy when one mole of a compound is formed from its elements in their standard states (298 K and 1 atm). Units are typically kJ/mol.
• 🌡️ Standard State: The most stable form of a substance at 298 K and 1 atm. For example, the standard state of oxygen is $O_2(g)$, not $O(g)$ or $O_3(g)$.
• 📜 Hess's Law: States that the enthalpy change for a reaction is independent of the pathway taken. This means that if a reaction can be carried out in a series of steps, the sum of the enthalpy changes for each step will equal the enthalpy change for the overall reaction. $$\Delta H_{reaction} = \sum \Delta H_f(products) - \sum \Delta H_f(reactants)$$
• ➕ Using Hess's Law: To calculate $\Delta H$ for a reaction using Hess's Law:
  1. Write the balanced chemical equation.
  2. Find or be given the $\Delta H°_f$ values for each reactant and product.
  3. Apply the formula: $\Delta H_{reaction} = \sum n\Delta H_f(products) - \sum n\Delta H_f(reactants)$, where $n$ is the stoichiometric coefficient.
• 💡 Important Notes:
  • The $\Delta H°_f$ of an element in its standard state is zero.
  • Pay attention to stoichiometric coefficients when applying Hess's Law.
  • Ensure all units are consistent (usually kJ/mol).

✍️ Practice Quiz

1. Question 1: What is the standard enthalpy of formation of an element in its standard state?
   1. $\Delta H°_f > 0$
   2. $\Delta H°_f < 0$
   3. $\Delta H°_f = 0$
   4. $\Delta H°_f = 1$
2. Question 2: Given the following reactions: $A \rightarrow B, \Delta H_1 = -50 kJ$ $B \rightarrow C, \Delta H_2 = +20 kJ$ What is the enthalpy change for the reaction $A \rightarrow C$?
   1. -70 kJ
   2. -30 kJ
   3. +70 kJ
   4. +30 kJ
3. Question 3: Which of the following is NOT a standard condition for enthalpy of formation?
   1. 298 K
   2. 1 atm
   3. Standard state of elements
   4. 0°C
4. Question 4: For the reaction: $2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$, given that $\Delta H°_f[H_2O(g)] = -242 kJ/mol$, what is the enthalpy change for the reaction?
   1. -242 kJ
   2. -484 kJ
   3. +242 kJ
   4. +484 kJ
5. Question 5: Hess's Law states that the enthalpy change of a reaction:
   1. Depends on the rate of the reaction.
   2. Is independent of the pathway taken.
   3. Increases with temperature.
   4. Decreases with pressure.
6. Question 6: Given the following standard enthalpies of formation: $\Delta H°_f[CO_2(g)] = -393.5 kJ/mol$ $\Delta H°_f[H_2O(l)] = -285.8 kJ/mol$ $\Delta H°_f[C_2H_5OH(l)] = -277.7 kJ/mol$ Calculate the enthalpy change for the combustion of ethanol: $C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$
   1. -1366.7 kJ
   2. -962.4 kJ
   3. +1366.7 kJ
   4. +962.4 kJ
7. Question 7: What is the enthalpy of formation of $O_2(g)$?
   1. 200 kJ/mol
   2. -200 kJ/mol
   3. 0 kJ/mol
   4. 100 kJ/mol