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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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