Pentane (C₅H₁₂) is a component of gasoline that burns according to the following balanced equation: C₅H₁₂(l) + 8 O₂(g) → 5 CO₂(g) + 6 H₂O(g) Calculate ΔH°_rxn for this reaction using standard enthalpies of formation. (The standard enthalpy of formation of liquid pentane is –146.8 kJ/mol.)

Verified step by step guidance

1. Identify the balanced chemical equation for the combustion of pentane: \( \text{C}_5\text{H}_{12}(l) + 8 \text{O}_2(g) \rightarrow 5 \text{CO}_2(g) + 6 \text{H}_2\text{O}(g) \).
2. Recall that the standard enthalpy change of reaction (\( \Delta H^\circ_{\text{rxn}} \)) can be calculated using the formula: \( \Delta H^\circ_{\text{rxn}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \).
3. Look up the standard enthalpies of formation (\( \Delta H^\circ_f \)) for each substance involved in the reaction: \( \text{CO}_2(g) \), \( \text{H}_2\text{O}(g) \), and \( \text{O}_2(g) \). Note that the \( \Delta H^\circ_f \) for \( \text{O}_2(g) \) is zero because it is in its standard state.
4. Calculate the total \( \Delta H^\circ_f \) for the products: \( 5 \times \Delta H^\circ_f(\text{CO}_2(g)) + 6 \times \Delta H^\circ_f(\text{H}_2\text{O}(g)) \).
5. Calculate \( \Delta H^\circ_{\text{rxn}} \) by substituting the values into the formula: \( \Delta H^\circ_{\text{rxn}} = [5 \times \Delta H^\circ_f(\text{CO}_2(g)) + 6 \times \Delta H^\circ_f(\text{H}_2\text{O}(g))] - [\Delta H^\circ_f(\text{C}_5\text{H}_{12}(l)) + 8 \times \Delta H^\circ_f(\text{O}_2(g))] \).

Key Concepts

Standard Enthalpy of Formation

The standard enthalpy of formation (ΔH°f) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial value used in thermodynamics to calculate the overall enthalpy change of a reaction. For example, the ΔH°f of liquid pentane is given as -146.8 kJ/mol, indicating that energy is released when pentane is formed from its elemental components.

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 of a reaction by using the standard enthalpies of formation of the reactants and products. It is particularly useful when direct measurement of ΔH°rxn is difficult.

Enthalpy Change of a Reaction (ΔH°rxn)

The enthalpy change of a reaction (ΔH°rxn) is the difference between the total enthalpy of the products and the total enthalpy of the reactants, calculated under standard conditions. It indicates whether a reaction is exothermic (releases heat, ΔH°rxn < 0) or endothermic (absorbs heat, ΔH°rxn > 0). In the combustion of pentane, this value can be determined using the standard enthalpies of formation of the products and reactants.