Scientific Constants — Which to Memorise and Why
Most exams supply a data sheet, so memorising forty constants is wasted effort. But a handful appear so often that looking them up costs you time you do not have, and two of them come in more than one version — pick the wrong version and the answer is out by a factor you will never spot. This guide lists what is genuinely worth knowing by heart, gives the current values, and shows three calculations where the choice of constant decides the answer.
Memorise these six
| Constant | Symbol | Value to remember | Where it earns its keep |
|---|---|---|---|
| Avogadro constant | NA | 6.022 × 10²³ mol⁻¹ | Every mole calculation, from Class 11 onwards |
| Gas constant | R | 8.314 J K⁻¹ mol⁻¹ or 0.08206 L atm K⁻¹ mol⁻¹ | PV = nRT, ΔG° = −RT ln K, Nernst, Arrhenius |
| Faraday constant | F | 96 485 C mol⁻¹ | Electrolysis, Nernst equation, electrochemical cells |
| Planck constant | h | 6.626 × 10⁻³⁴ J s | E = hν, de Broglie, photoelectric effect |
| Speed of light | c | 3.00 × 10⁸ m s⁻¹ | c = νλ, photon energy, mass–energy conversion |
| Elementary charge | e | 1.602 × 10⁻¹⁹ C | Converting joules to electronvolts and back |
Everything else — Boltzmann's constant, the Rydberg constant, permittivity of free space, the Bohr radius — is on the data sheet when you need it, and is not worth the memory space.
The SI 2019 redefinition, in one paragraph
Since the 2019 revision of the SI, several of these constants are exact by definition: they no longer carry an experimental uncertainty, because the units are now defined from them rather than the other way round.
| Constant | Exact defined value |
|---|---|
| c | 299 792 458 m s⁻¹ |
| h | 6.626 070 15 × 10⁻³⁴ J s |
| e | 1.602 176 634 × 10⁻¹⁹ C |
| kB | 1.380 649 × 10⁻²³ J K⁻¹ |
| NA | 6.022 140 76 × 10²³ mol⁻¹ |
Two familiar constants are now exact products of those definitions:
F = NA × e = 96 485.332 12… C mol⁻¹
Constants still measured, and therefore still carrying uncertainty, include the gravitational constant G = 6.674 30 × 10⁻¹¹ N m² kg⁻² and the electron mass me = 9.109 383 7 × 10⁻³¹ kg. Standard gravity g = 9.806 65 m s⁻² is a defined conventional value, not a measured one — the actual value varies with latitude and altitude.
The trap: R has two everyday versions
R is the same physical quantity, but its numerical value depends on the units of pressure and volume you feed it.
| Value of R | Use when | Answer comes out in |
|---|---|---|
| 8.314 J K⁻¹ mol⁻¹ | Pressure in Pa, volume in m³ (also all energy work: ΔG, Arrhenius, Nernst) | joules |
| 0.08206 L atm K⁻¹ mol⁻¹ | Pressure in atm, volume in litres | L atm |
| 0.08314 L bar K⁻¹ mol⁻¹ | Pressure in bar, volume in litres | L bar |
| 62.36 L Torr K⁻¹ mol⁻¹ | Pressure in Torr or mmHg, volume in litres | L Torr |
Check the derivation yourself: 8.314462 J K⁻¹ mol⁻¹ ÷ 101.325 J L⁻¹ atm⁻¹ = 0.082057 L atm K⁻¹ mol⁻¹. The rule to carry into the exam: if the answer must be an energy, use 8.314. In ΔG° = −RT ln K and Ea in the Arrhenius equation, the answer is always an energy, so 8.314 is always correct there — the litre-atmosphere value has no business in those formulas.
The second trap: two molar volumes at STP
Textbook editions genuinely differ here, and both numbers are correct for their own definition of standard conditions. State which one you are using.
| Standard condition | Molar volume of an ideal gas | Used by |
|---|---|---|
| 273.15 K and 1 atm (101.325 kPa) | 22.414 L mol⁻¹ | Older textbooks, many school syllabi |
| 273.15 K and 100 kPa (1 bar) | 22.711 L mol⁻¹ | Current IUPAC definition of STP |
Both come from V = RT/P. Confirm the first: (8.314462 × 273.15) ÷ 101 325 = 0.0224140 m³ = 22.414 L. And the second: (8.314462 × 273.15) ÷ 100 000 = 0.0227110 m³ = 22.711 L. Note also that 22.4 L mol⁻¹ applies at 0 °C, never at room temperature — at 25 °C and 1 atm the molar volume is about 24.5 L mol⁻¹.
Worked example 1 — the hc = 1240 eV nm shortcut
This one shortcut saves more exam time than any other constant on the page.
Derive it.
hc = (6.626 070 15 × 10⁻³⁴) × (2.997 924 58 × 10⁸) = 1.986 446 × 10⁻²⁵ J m
Convert to eV: ÷ (1.602 176 634 × 10⁻¹⁹) = 1.239 842 × 10⁻⁶ eV m
Convert metres to nanometres: × 10⁹ = 1239.84 eV nm ≈ 1240 eV nm
Use it. Energy of a 500 nm photon:
E = 1240 ÷ 500 = 2.48 eV
Cross-check the long way.
E = hc/λ = (1.986 446 × 10⁻²⁵) ÷ (500 × 10⁻⁹) = 3.9729 × 10⁻¹⁹ J
÷ (1.602 177 × 10⁻¹⁹) = 2.48 eV ✓
Worked example 2 — Faraday's constant in electrolysis
A current of 2.00 A passes through molten NaCl for 30.0 minutes. What mass of sodium is deposited? M(Na) = 22.990 g/mol, n = 1 electron per Na⁺.
Q = 2.00 × (30.0 × 60) = 2.00 × 1800 = 3600 C
moles of electrons = 3600 ÷ 96 485 = 0.037311 mol
moles of Na = 0.037311 mol (1 : 1)
mass = 0.037311 × 22.990 = 0.858 g
Using 96 500 instead of 96 485 gives 0.8578 g — the same to three significant figures. The rounded value is safe here; it is not safe in a five-figure calculation.
Worked example 3 — which R to use
Question A. Volume of 2.00 mol of an ideal gas at 300 K and 1.50 atm.
Pressure is in atm, so use R = 0.08206:
V = nRT/P = (2.00 × 0.08206 × 300) ÷ 1.50 = 49.236 ÷ 1.50 = 32.8 L
Question B. ΔG° at 298 K for a reaction with K = 1.00 × 10³.
The answer must be an energy, so use R = 8.314:
ΔG° = −RT ln K = −(8.314 × 298 × ln 1000) = −(8.314 × 298 × 6.9078)
= −17 113 J mol⁻¹ = −17.1 kJ mol⁻¹
Feed 0.08206 into question B and you get −0.169, in litre-atmospheres per mole, which is not what anyone asked for.
Common mistakes that cost marks
- Using R = 8.314 with pressure in atm. Match the constant to the units in the question, every time.
- Using 22.4 L mol⁻¹ at 25 °C. It belongs to 0 °C. And say which STP you mean — 22.414 L at 1 atm, 22.711 L at 100 kPa.
- Mixing joules and electronvolts without the 1.602 × 10⁻¹⁹ conversion.
- Using g = 10 m s⁻² in an answer that will be marked against 9.8. Fine for a rough estimate, not for a final answer.
- Forgetting per-mole. R, F and NA all carry mol⁻¹; h and c do not. Writing ΔG in J instead of J mol⁻¹ is a real deduction.
- Quoting more digits than the data supports. The constant may be exact; your measurements are not.
Where these appear in exams
| Exam | Constants that come up most |
|---|---|
| CBSE/ICSE Class 11–12 | NA, R, F, h, c — data sheet usually supplied but time is short |
| JEE/NEET | h, c, e for atomic structure; R for gas and thermodynamics questions |
| IIT-JAM / CUET-PG | R in both forms, F for electrochemistry, kB for statistical questions |
| GATE / CSIR-NET | Full set, including kB, the Rydberg constant and the Bohr radius |
Look a constant up without leaving the page you are working on. The suite carries a built-in constants reference with the SI values, so you can check R, F, h and the rest mid-calculation.
Open the Scientific Constants Reference →Knowing which constant to use is a taught skill, not a memory exercise. ABC Chemistry runs Class 11–12 chemistry coaching at its Gurugram centre and online classes across India — details at abcchemistry.in.