Isooctane, C8H18, is the component of gasoline from which the term octane rating derives (b) The standard molar heat of combustion of isooctane (l) is -5461 kJ/mol. Calculate ΔH°f for isooctane(l)

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Identify the chemical reaction for the combustion of isooctane: \[ \text{C}_8\text{H}_{18}(l) + \frac{25}{2} \text{O}_2(g) \rightarrow 8 \text{CO}_2(g) + 9 \text{H}_2\text{O}(l) \]

Use the standard enthalpy of formation equation: \( \Delta H^\circ_{\text{reaction}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants}) \)

Substitute the known values into the equation: \( -5461 \text{ kJ/mol} = [8 \Delta H^\circ_f(\text{CO}_2) + 9 \Delta H^\circ_f(\text{H}_2\text{O})] - [\Delta H^\circ_f(\text{C}_8\text{H}_{18}) + \frac{25}{2} \Delta H^\circ_f(\text{O}_2)] \)

Recall that the standard enthalpy of formation for elements in their standard state, such as \( \text{O}_2(g) \), is zero.

Rearrange the equation to solve for \( \Delta H^\circ_f(\text{C}_8\text{H}_{18}) \) using the known standard enthalpies of formation for \( \text{CO}_2(g) \) and \( \text{H}_2\text{O}(l) \).

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주요 개념

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Standard Molar Heat of Combustion

The standard molar heat of combustion is the amount of energy released when one mole of a substance is completely burned in oxygen under standard conditions. For isooctane, this value is given as -5461 kJ/mol, indicating that combustion is an exothermic reaction, releasing energy to the surroundings.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows us to calculate the standard enthalpy of formation (ΔH°f) of a compound by using the enthalpy changes of related reactions, such as combustion.

Standard Enthalpy of Formation (ΔH°f)

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 in thermodynamics, as it helps in calculating the energy changes in chemical reactions, including combustion, and is typically expressed in kJ/mol.