Hess's Law: Standard Enthalpy Calculation Examples

📚 Quick Study Guide

🌡️ Hess's Law states that the enthalpy change of a reaction is independent of the pathway taken. This means you can calculate the enthalpy change by adding up the enthalpy changes of individual steps. ⚛️ The standard enthalpy of formation, denoted as $\Delta H_f^\circ$, is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. ➕ Hess's Law Formula: $\Delta H_{reaction}^\circ = \sum n \Delta H_f^\circ(products) - \sum n \Delta H_f^\circ(reactants)$, where $n$ is the stoichiometric coefficient. 📐 Remember to pay attention to the stoichiometric coefficients in the balanced chemical equation. ♨️ If a reaction is reversed, the sign of $\Delta H$ is also reversed. 💯 Standard conditions are typically 298 K (25 °C) and 1 atm pressure.

🧪 Practice Quiz

1. Question 1: Calculate the standard enthalpy change for the reaction: $C(s) + O_2(g) \rightarrow CO_2(g)$, given that $\Delta H_f^\circ[CO_2(g)] = -393.5 kJ/mol$.
1. A) -196.75 kJ/mol
2. B) -393.5 kJ/mol
3. C) 393.5 kJ/mol
4. D) 0 kJ/mol
2. Question 2: Given the following reactions:
   • $N_2(g) + O_2(g) \rightarrow 2NO(g)$, $\Delta H_1 = 180.6 kJ$
   • $2NO(g) + O_2(g) \rightarrow 2NO_2(g)$, $\Delta H_2 = -114.1 kJ$
   Calculate the enthalpy change for the reaction: $N_2(g) + 2O_2(g) \rightarrow 2NO_2(g)$.
1. A) 66.5 kJ
2. B) 294.7 kJ
3. C) -66.5 kJ
4. D) -294.7 kJ
3. Question 3: Determine the enthalpy change for the reaction: $2H_2O(l) \rightarrow 2H_2(g) + O_2(g)$, given that $\Delta H_f^\circ[H_2O(l)] = -285.8 kJ/mol$.
1. A) -285.8 kJ/mol
2. B) -571.6 kJ/mol
3. C) 285.8 kJ/mol
4. D) 571.6 kJ/mol
4. Question 4: Use Hess's Law to find the enthalpy change for the reaction $A \rightarrow C$ given:
   • $A \rightarrow B$, $\Delta H = -50 kJ$
   • $B \rightarrow C$, $\Delta H = 20 kJ$
1. A) -70 kJ
2. B) -30 kJ
3. C) 30 kJ
4. D) 70 kJ
5. Question 5: What is the standard enthalpy of formation of an element in its standard state?
1. A) Always positive
2. B) Always negative
3. C) Zero
4. D) Depends on the element
6. Question 6: Calculate the standard enthalpy change for the reaction: $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$, given:
   • $\Delta H_f^\circ[CH_4(g)] = -74.8 kJ/mol$
   • $\Delta H_f^\circ[CO_2(g)] = -393.5 kJ/mol$
   • $\Delta H_f^\circ[H_2O(g)] = -241.8 kJ/mol$
1. A) -890.3 kJ/mol
2. B) -604.5 kJ/mol
3. C) 604.5 kJ/mol
4. D) 890.3 kJ/mol
7. Question 7: If the enthalpy change for the reaction $X \rightarrow Y$ is $-100 kJ$, what is the enthalpy change for the reaction $Y \rightarrow X$?
1. A) -100 kJ
2. B) 100 kJ
3. C) 0 kJ
4. D) -200 kJ