AP Chemistry · Exam guide
AP Chemistry Thermochemistry and Thermodynamics: Calorimetry and Gibbs Free Energy
Energy questions come in two families. Calorimetry turns a temperature change into a heat and then into an enthalpy change. Thermodynamics uses \(\Delta G = \Delta H - T\Delta S\) to decide when a reaction goes. Signs and units are where points are lost, so this guide writes them out.
Calorimetry
In a coffee-cup calorimeter, 0.0250 mol of a reactant dissolves in 50.0 g of water. The temperature rises 6.5 \(^\circ\mathrm{C}\). Find the molar enthalpy change. Use \(c = 4.18\) J/(g \(^\circ\mathrm{C}\)).
The heat absorbed by the water is \(q = mc\Delta T = (50.0)(4.18)(6.5) = 1358.5\) J, or 1.36 kJ. The reaction released that heat, so \(q_{\text{rxn}} = -1.36\) kJ. Per mole, \[\Delta H = \dfrac{-1.3585\ \mathrm{kJ}}{0.0250\ \mathrm{mol}} = -54.3\ \mathrm{kJ/mol}\] The reaction is exothermic.
It leaves out the negative sign. The temperature rose, so the reaction released heat and the enthalpy change is negative.
It shows the sign logic, the units, and the division by moles.
Spontaneity
For \(\mathrm{N_2} + 3\,\mathrm{H_2} \rightarrow 2\,\mathrm{NH_3}\), \(\Delta H^\circ = -92.2\) kJ and \(\Delta S^\circ = -198.7\) J/K. (a) Find \(\Delta G^\circ\) at 298 K. (b) Above what temperature does the reaction stop being spontaneous?
(a) Convert \(\Delta S\) to kJ/K first: \(-0.1987\) kJ/K. \[\Delta G^\circ = -92.2 - (298)(-0.1987) = -92.2 + 59.2 = -33.0\ \mathrm{kJ}\] It is spontaneous at 298 K.
(b) \(\Delta G = 0\) at \[T = \dfrac{\Delta H}{\Delta S} = \dfrac{-92.2}{-0.1987} \approx 464\ \mathrm{K}\] Above this temperature the \(-T\Delta S\) term is larger than \(\Delta H\), and \(\Delta G\) becomes positive.
The sign table
| \(\Delta H\) | \(\Delta S\) | Spontaneous when |
|---|---|---|
| Negative | Positive | Always |
| Positive | Negative | Never |
| Negative | Negative | At low temperature |
| Positive | Positive | At high temperature |
Common mistakes
- Mixing kilojoules and joules in \(\Delta G = \Delta H - T\Delta S\).
- Using Celsius instead of kelvin.
- Giving the heat gained by the water as the enthalpy of the reaction, without changing the sign.
- Forgetting to divide by moles when asked for a molar enthalpy.
Frequently asked questions
Why does the temperature rise mean a negative enthalpy change?
The solution gained heat, so the reaction released it. The system lost energy.
Do I need to convert entropy to kilojoules?
Yes, whenever enthalpy is in kilojoules. A mismatch of units is a common loss of points.
What does delta G equal at equilibrium?
Zero, at the equilibrium temperature for a phase change or a reaction at standard conditions.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Chemistry course ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a review with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Chemistry course Free lessons and lesson list
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Multiple choice
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