Chemistry math practice
Every calculation the Chemistry exam asks for, with new numbers every time. Type the answer rather than picking from four options — producing a number is a different skill from eliminating three wrong ones, and only one of them is what the exam scores.
Molarity from mass
Two conversions in one problem, and both are needed. Grams become moles through molar mass; milliliters become liters through a factor of 1000. Skipping the second is the single commonest error in the course.
What is the molarity of a solution made by dissolving 8.4 g of glucose (C₆H₁₂O₆) (molar mass 180.16 g/mol) in enough water to make 470 mL of solution?
Every skill in this set
- Molarity from massAtomic Structure & Properties
- M = mol / L · mol = mass / molar mass
- Two conversions in one problem, and both are needed. Grams become moles through molar mass; milliliters become liters through a factor of 1000. Skipping the second is the single commonest error in the course.
- DilutionAtomic Structure & Properties
- M₁V₁ = M₂V₂
- Works with any volume unit as long as both sides use the same one, so there is no need to convert to liters here. The quantity asked for is usually the stock volume.
- pH, pOH and ion concentrationAcids & Bases
- pH = −log[H⁺] · pH + pOH = 14
- A change of one pH unit is a factor of ten in concentration. Questions often give pOH and want [H⁺], which needs both relationships in sequence.
- Ideal gas lawIntermolecular Forces & Properties
- PV = nRT · R = 0.08206 L·atm/(mol·K)
- Temperature must be in kelvin, always. Using Celsius here is not a small error — at room temperature it is off by a factor of roughly twelve.
- CalorimetryThermodynamics
- q = mcΔT
- The sign of ΔT carries the physics: heat absorbed is positive, heat released is negative. An answer with the wrong sign describes the opposite process.
- Percent yieldAtomic Structure & Properties
- % yield = (actual / theoretical) × 100
- Percent yield above 100% means the product is wet or impure, not that the reaction over-performed. Questions test whether you notice that.
- Gibbs free energy and spontaneityThermodynamics
- ΔG° = ΔH° − TΔS°
- ΔH is in kilojoules and ΔS in joules, so one of them has to be converted before subtracting. Failing to do that is a factor-of-1000 error that produces an obviously wrong sign.
- Beer's lawAtomic Structure & Properties
- A = εbc
- Absorbance is proportional to concentration, so a calibration line through the origin lets you read an unknown straight off. The exam usually gives you one standard and asks you to scale.
- First-order half-lifeKinetics
- t½ = 0.693 / k
- Only first-order half-life is independent of starting concentration. If a question says the half-life does not change as the reaction proceeds, it has told you the order.
- Mass-to-mass stoichiometryAtomic Structure & Properties
- mass → mol → (mole ratio) → mol → mass
- The mole ratio comes from the balanced equation and is the only place the chemistry enters. Every other step is unit conversion, and skipping straight from grams to grams ignores the ratio entirely.
Common questions
What math is on the AP Chemistry exam?
10 distinct calculations: molarity from mass, dilution, ph, poh and ion concentration, ideal gas law, calorimetry, percent yield, gibbs free energy and spontaneity, beer's law, first-order half-life, mass-to-mass stoichiometry. Each one appears on the exam's formula sheet or is assumed by it, so the work is applying the relationship rather than recalling it.
Do the problems repeat?
No. Every problem is generated with fresh numbers, so the same skill can be practiced indefinitely without memorizing an answer. That is the whole point — being able to run a procedure on numbers you have not seen is what the exam actually tests.
How precise does my answer need to be?
Answers are accepted within about 1–3% of the exact value, which allows for rounding at intermediate steps the way a calculator does. Units are optional — type the number and the unit if you like, or just the number.