AP Chemistry: Thermochemistry Concepts and Calculations

Worked Example: Finding $\Delta H_{comb}$ for Propane If you are given:

1. $3 \mathrm{C}(\mathrm{s}) + 4 \mathrm{H}{2}(\mathrm{g}) \rightarrow \mathrm{C}{3} \mathrm{H}_{8}(\mathrm{g}) \quad \Delta H = x$
2. $\mathrm{C}(\mathrm{s}) + \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}) \quad \Delta H = y$
3. $\mathrm{H}_{2}(\mathrm{g}) + \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell) \quad \Delta H = z$

To find the combustion of propane ($\mathrm{C}_{3} \mathrm{H}_{8} + 5 \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O}$), you would manipulate the equations so that propane is a reactant and the products match. By reversing the first equation and multiplying the others, you find the expression:

$$\Delta H_{comb} = (3y + 4z) - x$$

(Note: Depending on the sign convention of the target reaction, this may be expressed as $x - (3y + 4z)$ if the target is the reverse).

Standard Enthalpy of Formation

The standard enthalpy of formation ($\Delta H_{f}^{\circ}$) is the change in enthalpy when exactly one mole of a substance is formed from its constituent elements in their standard states.

A common AP Chemistry task is to calculate the standard enthalpy change ($\Delta H_{rxn}^{\circ}$) of a reaction using a table of $\Delta H_{f}^{\circ}$ values. The formula is:

$$\Delta H_{rxn}^{\circ} = \sum n \Delta H_{f}^{\circ}(\text{products}) - \sum m \Delta H_{f}^{\circ}(\text{reactants})$$

where $n$ and $m$ are the stoichiometric coefficients.

Example Calculation: For the reaction $3 \mathrm{C}_{3} \mathrm{H}_{3(g)} \rightarrow \mathrm{C}_{6} \mathrm{H}_{6(g)}$, given:

• $\Delta H_{f}^{\circ} \text{ of } \mathrm{C}_{3} \mathrm{H}_{3(g)} = 230 \mathrm{~kJ/mol}$
• $\Delta H_{f}^{\circ} \text{ of } \mathrm{C}_{6} \mathrm{H}_{6(g)} = 83 \mathrm{~kJ/mol}$

The calculation is:

$$\Delta H_{rxn}^{\circ} = [1(83)] - [3(230)] = 83 - 690 = -607 \mathrm{~kJ}$$

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Calorimetry and Heat Transfer

Beyond theoretical equations, we often measure heat in a laboratory setting using calorimetry. The fundamental equation for heat transfer is:

$$q = m c \Delta T$$

Where:

• $q$ is the heat (in Joules or kiloJoules).
• $m$ is the mass (in grams).
• $c$ is the specific heat capacity ($\mathrm{J/g \cdot K}$ or $\mathrm{J/g \cdot ^{\circ}C}$).
• $\Delta T$ is the change in temperature ($T_{final} - T_{initial}$).

Critical Concept: Calorimeter Errors If a student performs a neutralization reaction in an open cup and loses heat to the surrounding air, the measured $\Delta T$ will be smaller than it should be. Consequently, the calculated $q$ and the resulting molar enthalpy of neutralization ($\Delta H_{neut}$) will be lower than the true value.

By mastering these relationships—scaling thermochemical equations, applying Hess's Law, using formation enthalpies, and applying the calorimetry equation—you will be well-prepared for any Chapter 5 problems on the AP exam.