Using the Official Equation Sheet and Periodic Table官方公式表与周期表的使用

~30 min

Learning goals

  • Know the sections of the official equations and constants sheet, what each contains, and what the periodic table shows
  • Pick the right constants and units, including the two values of R, kelvin temperatures, ln vs log, and bold M
  • Remember the relationships and rules the exam uses that are not on the sheet

Before you start

  • Exam format and scoring (4.1.1)

The reference material you get

The AP Chemistry exam provides two pieces of reference information参考资料, available at any time in Bluebook and on paper:

  • The equations and constants sheet. It starts with unit symbols, unit conversions (1 atm = 760 mm Hg = 760 torr, K = °C + 273.15, 1 V = 1 J/C, 1 A = 1 C/s) and metric prefixes (G, M, k, c, m, μ, n, p). Then come the equations, in five sections: atomic structure; gases, liquids, and solutions; kinetics; equilibrium; and thermodynamics/electrochemistry. Beside each section is a list of what each symbol means, plus the constants used: Planck’s constant h, the speed of light c, Avogadro’s number, two values of R, the definition of STP, the molar volume of an ideal gas at STP, and Faraday’s constant F.
  • The periodic table. Each box has the atomic number, the element symbol and the atomic mass. Electronegativity, ion charges and electron configurations aren’t there; you work them out from periodic trends.

Five rules for using the sheet well

  1. Know the symbols first. The same letter means different things in different equations: c is the speed of light in c = λν, specific heat in q = mcΔT, and concentration in A = εbc. The sheet uses a bold M for molar mass and a plain M for molarity.
  2. Choose the right constant. There are two values of R. In PV = nRT with pressure in atm and volume in L, use R = 0.08206 L atm mol⁻¹ K⁻¹; in equations involving energy (ΔG° = −RT ln K, the Nernst equation), use R = 8.314 J mol⁻¹ K⁻¹.
  3. Temperatures are always in K. K = °C + 273.15.
  4. Tell ln from log. pH, pKa and the Henderson–Hasselbalch equation use log base 10; the integrated first-order rate law, ΔG° = −RT ln K and the Nernst equation use ln.
  5. Check when an equation applies. t½ = 0.693/k is for first-order reactions only; Kw = 1.0 × 10⁻¹⁴ and pH + pOH = 14 hold only at 25 °C; the Henderson–Hasselbalch equation is for buffers only.

Not on the sheet, but you need it

Things missing from the sheet are still tested; you either memorize them or the question supplies them:

  • Memorize: E°cell = E°(cathode) − E°(anode); dilution, M₁V₁ = M₂V₂; estimating ΔH from bond enthalpies (bonds broken minus bonds formed); Hess’s law; the common strong acids and bases; the solubility rules (all sodium, potassium and ammonium salts and all nitrates are soluble); the names and charges of common polyatomic ions.
  • Supplied by the question: standard reduction potentials, values of Ka and Ksp, the specific heat of water, bond enthalpies, enthalpies of formation and similar data.

Pick a section and click an equation to see what it’s for and where it trips people up:

Tour of the official equation sheet: pick a section, then click an equation

What it’s for:Energy of one photon from its frequency (U3.11, U3.12).

Watch out:h = 6.626 × 10⁻³⁴ J·s is on the sheet. If you’re given a wavelength, convert it to frequency with c = λν first, with the wavelength in meters.

Example 1: choosing R

0.500 mol of an ideal gas is in a 2.00 L container at 25 °C. Find the pressure in atm.

Step-by-step solution

  1. Find the equation. In “Gases, liquids, and solutions,” PV = nRT rearranges to:

    P=nRTVP = \frac{nRT}{V}

  2. Choose R. The pressure is wanted in atm and the volume is in L, so use:

    R=0.08206 L atm mol−1 K−1R = 0.08206\ \text{L atm mol}^{-1}\text{ K}^{-1}

  3. Convert the temperature to K. Using K = °C + 273.15 from the sheet:

    T=25+273.15=298.15 KT = 25 + 273.15 = 298.15\ \text{K}

  4. Substitute.

    P=0.500×0.08206×298.152.00=6.12 atm\begin{aligned} P &= \frac{0.500 \times 0.08206 \times 298.15}{2.00} \\ &= \boxed{6.12\ \text{atm}} \end{aligned}

  5. Compare with the wrong choice. Using R = 8.314 instead gives P = 620, whose units aren’t atm at all, and the number is absurd. Checking that the units cancel before substituting catches this mistake.

Example 2: linking two lines of the sheet

A cell reaction transfers 2 electrons and has E° = +0.46 V at 25 °C. Find its equilibrium constant K.

Step-by-step solution

  1. The sheet doesn’t relate K and E° directly, but two lines both contain ΔG°. In “Thermodynamics/electrochemistry”:

    ΔG∘=−nFE∘ΔG∘=−RTln⁡K\begin{gathered} \Delta G^\circ = -nFE^\circ \\ \Delta G^\circ = -RT\ln K \end{gathered}

  2. Find ΔG° first. F = 96,485 C/mol is on the sheet, and C × V = J:

    ΔG∘=−2×96 485×0.46=−8.88×104 J/mol\begin{aligned} \Delta G^\circ &= -2 \times 96\,485 \times 0.46 \\ &= -8.88 \times 10^{4}\ \text{J/mol} \end{aligned}

  3. Then find ln K. ΔG° is in J, so use R = 8.314 J mol⁻¹ K⁻¹:

    ln⁡K=−ΔG∘RT=8.88×1048.314×298.15=35.8\begin{aligned} \ln K &= -\frac{\Delta G^\circ}{RT} = \frac{8.88 \times 10^{4}}{8.314 \times 298.15} \\ &= 35.8 \end{aligned}

  4. Find K.

    K=e35.8=3.6×1015K = e^{35.8} = \boxed{3.6 \times 10^{15}}

  5. Check. E° > 0 means ΔG° < 0, so K should be greater than 1. It is.

Practice: is this equation or value on the official sheet?
  1. PV = nRT
  2. E°cell = E°(cathode) − E°(anode)
  3. pH = pKa + log([A⁻]/[HA])
  4. Specific heat of water, 4.18 J/(g·°C)
  5. t½ = 0.693/k
  6. The list of common strong acids
  7. Nernst equation, E = E° − (RT/nF) ln Q
  8. M₁V₁ = M₂V₂

Common mistakes

Mistake 1: “If it’s on the sheet, I don’t need to know it.” The sheet shows what an equation looks like, not when it applies or which units go with it. Looking up every equation during the exam also costs time, so know the common ones well enough not to look.

Mistake 2: “Either value of R works.” The two values of R differ in both number and units. For PV = nRT in atm and L, use 0.08206; for anything in joules, use 8.314. Using the wrong one makes the answer off by a factor of about 100.

Mistake 3: “If an equation isn’t on the sheet, it won’t be tested.” Calculating E°cell, the solubility rules and the strong acids and bases are all missing from the sheet and all commonly tested. Missing from the sheet just means you memorize it.

Quick check

Using PV = nRT for a pressure in atm with volume in L, which value of R do you use?

Which of these is NOT on the official equation sheet?

What does the bold M on the equation sheet stand for?

Given k for a second-order reaction, can you find its half-life with t½ = 0.693/k?

What can you read from the exam’s periodic table?

The letter c appears in several equations. What does it mean in A = εbc?

AP-style practice

AP-style free response

A colored solution absorbs most strongly at 520 nm. In a 1.00 cm cuvette, its absorbance at 520 nm is 0.448; the solute’s molar absorptivity at 520 nm is ε = 1.12 × 10⁴ L mol⁻¹ cm⁻¹.

(a) Calculate the frequency of 520 nm light.

(b) Calculate the energy of one photon of 520 nm light.

(c) Calculate the molarity of the solution.

(d) For each of (a)–(c), name the equation you used and the section of the sheet it’s in.

(e) Which value in the question is not on the equation sheet and has to be supplied? Explain why.

Model answer and scoring

(a) ν = c/λ = (2.998 × 10⁸ m/s) ÷ (520 × 10⁻⁹ m) = 5.77 × 10¹⁴ s⁻¹.

(b) E = hν = (6.626 × 10⁻³⁴ J s)(5.77 × 10¹⁴ s⁻¹) = 3.82 × 10⁻¹⁹ J.

(c) c = A/(εb) = 0.448 ÷ (1.12 × 10⁴ × 1.00) = 4.00 × 10⁻⁵ M.

(d) (a) c = λν and (b) E = hν are in “Atomic structure,” along with h and the speed of light; (c) A = εbc is in “Gases, liquids, and solutions.”

(e) The molar absorptivity ε. It depends on the substance and the wavelength, so it isn’t a universal constant and can’t be listed on the sheet; the question has to give it. (The path length and absorbance are measurements from this experiment, so they’re given too.)

Scoring: (a) frequency, with the wavelength in m; (b) photon energy; (c) molarity; (d) the three equations and their sections; (e) names ε and explains why.

Summary

  • The reference material is the equations and constants sheet (units, conversions, prefixes, and five sections of equations and constants) and a periodic table showing only atomic number, symbol and atomic mass.
  • When using the sheet, read the symbols first, choose the right constant (two values of R), use kelvin, tell ln from log, and check when an equation applies.
  • Calculating E°cell, dilution, bond enthalpies, strong acids and bases and the solubility rules aren’t on the sheet, so memorize them; data values are supplied by the question.

AP tip: Before substituting, write the equation, then put units after every number. If the units cancel, you’ve almost certainly picked the right constant, and readers give credit for a written equation and setup too.

Sources: the contents of the equation sheet follow College Board’s AP Chemistry Exam Reference Information (2025 edition); the layout and notes in this lesson and its tool are this site’s own.

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