AP Chemistry: Thermochemistry

Thermochemistry is the part of chemistry that connects reactions to energy. In AP Chemistry, you are expected to interpret heat flow, calculate reaction enthalpies, apply Hess’s law, analyze calorimetry data, estimate energies using bond enthalpies, and connect enthalpy and entropy to spontaneity through Gibbs free energy. Done well, thermochemistry makes reactions feel less like memorized equations and more like predictable physical processes.

Core ideas: system, surroundings, and energy flow

Every thermochemistry problem starts with a clear boundary:

• System: the chemicals (or solution) you are focusing on
• Surroundings: everything else that can exchange energy with the system

Energy transfer in AP Chem thermochemistry is usually discussed as heat at constant pressure and is tracked with signs:

• Exothermic: system releases heat to surroundings, $\Delta H<0$
• Endothermic: system absorbs heat from surroundings, $\Delta H>0$

A quick reality check: if a reaction makes the container warmer, the reaction is exothermic.

Enthalpy ($\Delta H$): what it means and how to use it

Enthalpy change, $\Delta H$, is the heat absorbed or released by a process at constant pressure. For reactions, it is reported as a reaction enthalpy, often written $\Delta H_{\text{rxn}}^{\circ }$ under standard conditions.

Key properties AP Chemistry leans on:

Enthalpy is state-function based

Enthalpy depends on the initial and final states, not the path. This is why Hess’s law works and why you can combine reactions algebraically.

Enthalpy scales with the reaction amount

If you double the balanced equation, you double $\Delta H$. If you reverse the reaction, you flip the sign.

Students commonly lose points by forgetting that $\Delta H$ is tied to the stoichiometric amounts in the balanced equation, not “per mole of anything you want.” Always anchor your calculation to the balanced reaction.

Hess’s law: building reaction enthalpy from known steps

Hess’s law states that if a reaction can be expressed as the sum of multiple steps, then:

$$\Delta H_{\text{overall}}=\sum \Delta H_{\text{steps}}$$

This is especially useful when you have enthalpy data for related reactions (formation reactions, combustion reactions, or intermediate transformations).

Practical workflow for Hess’s law

1. Write the target reaction.
2. Choose given reactions that can be manipulated to match it.
3. Reverse reactions if needed (change sign of $\Delta H$).
4. Multiply reactions to match coefficients (multiply $\Delta H$ accordingly).
5. Add them up and cancel species that appear on both sides.

A strong habit is to do the algebra on the chemical equations first and only combine the enthalpy values at the end.

Standard enthalpy of formation shortcut

If you are given standard enthalpies of formation, the most direct route is:

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

Remember: elements in their standard states have $\Delta H_f^{\circ }=0$.

Calorimetry: connecting temperature change to heat

Calorimetry measures heat by tracking temperature change. The core equation is:

$$q=mc\Delta T$$

Where:

• $q$ is heat (J)
• $m$ is mass (g)
• $c$ is specific heat capacity (J g${}^{-1}$ °C${}^{-1}$)
• $\Delta T$ is temperature change (°C)

Solution calorimetry: the AP Chemistry standard setup

Most AP problems assume the solution behaves like water unless told otherwise:

• density $\approx 1.00$ g/mL (so volume in mL becomes mass in g)
• $c\approx 4.184$ J g${}^{-1}$ °C${}^{-1}$

Once you find $q_{\text{solution}}$, connect it to the reaction with the conservation of energy:

$$q_{\text{rxn}}=-q_{\text{solution}}$$

If the solution warms ($\Delta T>0$), then $q_{\text{solution}}>0$ and the reaction is exothermic ($q_{\text{rxn}}<0$).

From heat to molar enthalpy

Calorimetry gives you heat for the amount that reacted. To report $\Delta H$ per mole of limiting reactant:

1. Determine moles reacted (usually limiting reagent).
2. Compute $\Delta H$ as:

$$\Delta H=\frac{q_{\text{rxn}}}{\text{mol reacted}}$$

Common pitfall: using total moles present instead of moles actually consumed.

Bond energies: estimating reaction enthalpy from bonds

Bond enthalpies provide an approximate method:

$$\Delta H_{\text{rxn}}\approx \sum E(\text{bonds broken})-\sum E(\text{bonds formed})$$

Breaking bonds requires energy (endothermic contribution). Forming bonds releases energy (exothermic contribution). Since bond enthalpies are averaged over many compounds, this method is an estimate, not an exact value.

When bond energies are most useful

• Comparing which of two reactions is likely more exothermic
• Estimating $\Delta H$ when formation enthalpies are unavailable
• Explaining why forming strong bonds (like C=O) often drives reactions energetically

A frequent error is reversing the subtraction. If you compute “formed minus broken,” your sign will be flipped.

Gibbs free energy ($\Delta G$): predicting spontaneity

Thermochemistry in AP Chemistry does not stop at heat. Gibbs free energy combines enthalpy and entropy to predict whether a process is spontaneous at a given temperature:

$$\Delta G=\Delta H-T\Delta S$$

Interpretation:

• $\Delta G<0$: spontaneous (thermodynamically favorable)
• $\Delta G>0$: nonspontaneous (requires continuous input)
• $\Delta G=0$: equilibrium

Spontaneous does not mean fast. A reaction can be spontaneous but slow if it has a high activation energy.

Temperature matters

Because $T\Delta S$ scales with temperature, some reactions change spontaneity depending on $T$. This is why you cannot decide spontaneity from $\Delta H$ alone.

Standard free energy and equilibrium link

Under standard conditions:

$$\Delta G^{\circ }=-RT\ln K$$

This is a powerful connection: large $K$ implies negative $\Delta G^{\circ }$, while $K<1$ implies positive $\Delta G^{\circ }$.

The most common ΔG calculation errors (and how to avoid them)

Unit and conversion mistakes are the main reason students miss points on Gibbs free energy problems.

1) Mixing J and kJ

Often $\Delta H$ is in kJ/mol, while $\Delta S$ is in J/(mol·K). Convert one so units match before computing $\Delta G$.

A safe habit: convert $\Delta S$ to kJ/(mol·K) by dividing by 1000.

2) Using Celsius instead of Kelvin

Temperature must be in Kelvin: $$T(\text{K})=T{(}^{\circ }\text{C})+273.15$$

Using °C will throw off the magnitude and can flip the sign of $\Delta G$.

3) Losing the sign on entropy

Entropy changes can be positive or negative. If $\Delta S$ is negative, then $-T\Delta S$ becomes positive, which can make spontaneity less likely at higher temperatures. Track signs deliberately.

4) Treating “spontaneous” as “exothermic”

Plenty of spontaneous processes are endothermic if entropy increases enough (especially at higher temperatures). Spontaneity is a $\Delta G$ question, not a $\Delta H$ question.

A practical approach to AP thermochemistry problems

When you face a thermochemistry question, take ten seconds to decide what the problem is really asking:

• Heat measured from temperature change? Use calorimetry and then connect to $\Delta H$ per mole.
• Overall enthalpy from reaction manipulations? Use Hess’s law or formation enthalpies.
• Approximate enthalpy from structure? Use bond energies.
• Spontaneous at a given temperature? Use $\Delta G=\Delta H-T\Delta S$ with strict unit discipline.

Thermochemistry becomes manageable when you treat it as consistent bookkeeping: energy flows have signs, state functions add cleanly, and units are nonnegotiable. Once those habits are in place, the calculations stop feeling like tricks and start functioning like tools.