Calculate ΔHrxn for the reaction:
5 C(s) + 6 H₂(g) → C₅H₁₂(l)
Use the following reactions and given ΔH's:
C₅H₁₂(l) + 8 O₂(g) → 5 CO₂(g) + 6 H₂O(g) ΔH = –3244.8 kJ
C(s) + O₂(g) → CO₂(g) ΔH = –393.5 kJ
2 H₂(g) + O₂(g) → 2 H₂O(g) ΔH = –483.5 kJ

Verified step by step guidance

1. Identify the target reaction and the given reactions. The target reaction is: 5 C(s) + 6 H2(g) → C5H12(l). The given reactions are: (1) C5H12(l) + 8 O2(g) → 5 CO2(g) + 6 H2O(g), (2) C(s) + O2(g) → CO2(g), and (3) 2 H2(g) + O2(g) → 2 H2O(g).
2. Write the enthalpy changes for the given reactions: ΔH1 = -3244.8 kJ for the first reaction, ΔH2 = -393.5 kJ for the second reaction, and ΔH3 = -483.5 kJ for the third reaction.
3. Reverse the first given reaction to match the products and reactants of the target reaction. The reversed reaction will be: 5 CO2(g) + 6 H2O(g) → C5H12(l) + 8 O2(g) and the enthalpy change for this reaction will be the opposite of ΔH1, i.e., ΔH1' = +3244.8 kJ.
4. Adjust the coefficients of the second and third given reactions to match the coefficients in the target reaction. Multiply the second reaction by 5 and the third reaction by 3. The adjusted reactions are: 5 C(s) + 5 O2(g) → 5 CO2(g) and 6 H2(g) + 3 O2(g) → 6 H2O(g) with enthalpy changes ΔH2' = 5 * (-393.5 kJ) and ΔH3' = 3 * (-483.5 kJ).
5. Add the reversed first reaction and the adjusted second and third reactions to obtain the target reaction. Sum the enthalpy changes of these reactions to find ΔHrxn for the target reaction: ΔHrxn = ΔH1' + ΔH2' + ΔH3'.

Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction, regardless of the pathway taken. This principle allows us to calculate the enthalpy change (ΔHrxn) for a reaction by using known ΔH values from related reactions, making it essential for solving problems involving thermochemical equations.

Standard Enthalpy of Formation

The standard enthalpy of formation (ΔHf°) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This concept is crucial for calculating ΔHrxn, as it provides a reference point for the energy changes associated with the formation of reactants and products in a chemical reaction.

Stoichiometry in Thermochemistry

Stoichiometry in thermochemistry involves using the coefficients from a balanced chemical equation to relate the amounts of reactants and products to their respective enthalpy changes. Understanding stoichiometry is vital for accurately calculating ΔHrxn, as it ensures that the enthalpy changes are applied in proportion to the quantities of substances involved in the reaction.