Stoichiometry Engine
Balance equations, calculate moles · mass · volume · concentration for every species, detect limiting reagents, and analyse % by mass — powered by a backend chemistry engine.
Step 1 — Equation
% by Mass Calculator
Enter any chemical formula to see the percentage by mass of each element. Uses the active atomic mass system (HKDSE / IB).
Empirical & Molecular Formula
Enter the percentage or mass of each element to find the empirical formula. Provide the molar mass to also get the molecular formula.
Converter A
Convert between moles and number of particles (atoms, molecules, formula units) using Avogadro's constant L = 6.022 × 10²³ mol⁻¹.
Converter B
Enter any two of the three values — the third is calculated instantly.
c = n ÷ V | n = c × V | V = n ÷ c
Converter C
Leave one field blank — it is calculated from the other three.
c₁ × V₁ = c₂ × V₂
Converter D
Leave one field blank — it is calculated from the other three.
P V = n R T | R = 8.314 J K⁻¹ mol⁻¹
Titration A
Leave one of the four c/V fields blank — it is calculated from the others.
c(A)·V(A) / n(A) = c(B)·V(B) / n(B)
Titration B
Add a measured excess of reagent R to the analyte, then titrate the unreacted R with standard titrant T. The difference gives moles of analyte.
n(analyte) = [c(R)·V(R)/1000 − nRT·c(T)·V(T)/1000] ÷ nAR
nRT = moles of reagent per mole of titrant; nAR = moles of analyte per mole of reagent
Purity Calculation
Titration C
Enter burette readings for each run. Only accurate trials agreeing within 0.10 cm³ are averaged; the rough trial and outliers are excluded automatically.
Titration D
Balances moles of electrons transferred. Pick standard half-reactions or enter electrons manually.
c(ox)·V(ox)·e(ox) = c(red)·V(red)·e(red)
Oxidant
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O (purple → colourless; self-indicating).
Reductant
Fe²⁺ → Fe³⁺ + e⁻.
Titration · Indicator recommender
Enter the equivalence-point pH (or pull it from the calculator above) to see which indicators straddle it. The best choice changes colour over a range containing the equivalence pH.
Equilibrium A
Presets
Equilibrium A2
Sequentially solves each dissociation. pH is dominated by Ka₁; stepwise species concentrations are also shown.
Presets
Equilibrium A3
For MₐXᵦ(s) ⇌ a·cation + b·anion. Convert Ksp ↔ molar solubility and include the common-ion effect.
Presets
Equilibrium B
Enter species with stoichiometric coefficients and initial concentrations. Leave exactly one [eq] blank to solve for it.
Reaction presets
Equilibrium C
Enter the moles of gas on each side and the thermicity of the forward reaction, choose a stress, and see the predicted shift and effect on K.
Presets
Equilibrium D
Kp = Kc(RT)^Δn, where Δn = (moles gas products − moles gas reactants), R = 0.08206 L·atm·mol⁻¹·K⁻¹. Kp = Kc when Δn = 0.
pH A
Enter any one value — all others are computed instantly.
pH B
pH C
pH C2
pH of a salt solution. Salt of weak acid + strong base → basic (Kb = Kw/Ka). Salt of weak base + strong acid → acidic (Ka = Kw/Kb). Salt of weak acid + weak base → compare Ka and Kb.
Presets
pH D
pH = pKa + log([A⁻]/[HA])
Enter any 3 of the 4 values; leave one blank to solve for it.
Thermo A
ΔH = Σ(bonds broken) − Σ(bonds formed)
Thermo B
ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants)
Thermo C
ΔG = ΔH − TΔS
Leave exactly one of ΔG, ΔH, ΔS or T blank to solve for it.
Thermo D
ΔG° = −RT·ln(K)
Enter ΔG° and T to find K, or enter K and T to find ΔG°. Leave exactly one of ΔG°/K blank.
Thermo E
ΔH_f = ΔH_sub + ½D + IE + EA + ΔH_lattice
Enter the known steps (kJ/mol) and leave exactly one blank to solve via Hess's law around the cycle.
Preset
Thermo F
ΔS°rxn = ΣS°(products) − ΣS°(reactants)
Add species rows; pick a preset S° (J·mol⁻¹·K⁻¹) or enter your own.
Kinetics A
r = k[A]ᵐ[B]ⁿ — leave exactly one blank to solve
Presets
Determine Orders from Experiments
Enter 3–4 experiments. Orders for [A] and [B] are found from pairs where only one reactant changes. Leave [B] blank to study a single reactant.
Kinetics B
Presets
Kinetics C
Kinetics C2
N = N₀·e^(−λt), λ = ln2 / t½
First-order decay of N₀, N (or activity). Provide t½ or λ, then leave exactly one of {N₀, N, t} blank to solve.
Presets
Kinetics D
k = A·e^(−Ea/RT) — leave one blank to solve
Presets
Two-Temperature Form
ln(k₂/k₁) = −Ea/R × (1/T₂ − 1/T₁)
Electrochem A
E°cell = E°cathode − E°anode
Electrochem B
E = E° − (RT/nF)·ln(Q)
Electrochem C
ΔG° = −nFE° · Kc = e^(nFE°/RT) · E° = (RT/nF)·ln(Kc)
Enter n plus either E°cell or Kc — the other is found, along with ΔG°. This bridges Electrochem with the Thermo ΔG° ↔ K tool.
Electrochem D
n(e⁻) = It/F · n = n(e⁻)/z · m = n·Mr
Find the mass deposited or gas evolved, or solve for the time/current needed for a target mass. F = 96485 C/mol.
Presets
Electrochem E
E = (RT/nF)·ln([conc]/[dilute])
Same electrode on both sides; EMF is driven by the concentration difference. The dilute half-cell is the anode.
Gas Laws A
P₁V₁ / T₁ = P₂V₂ / T₂
Leave exactly one field blank to solve for it. Temperatures must be in kelvin (K = °C + 273.15).
Gas Laws B
Pᵢ = xᵢ · P_total · xᵢ = nᵢ / n_total
Choose a mode, add a row per gas, then enter the known quantities. Partial pressures, the total, and mole fractions are all computed.
Gas Laws C
rate₁ / rate₂ = √(M₂ / M₁)
Presets
Gas Laws D
(P + a·n²/V²)(V − n·b) = nRT
Units: V in L, T in K, P in atm. R = 0.08206 L·atm·mol⁻¹·K⁻¹, a in L²·atm·mol⁻², b in L·mol⁻¹. Solves real P and compares to the ideal-gas P.
Colligative A
ΔTb = i·Kb·m · ΔTf = i·Kf·m
Colligative B
Π = i·M·R·T
R = 0.08206 L·atm·mol⁻¹·K⁻¹, T in K, M in mol/L, Π in atm. Leave exactly one of Π, M, T blank to solve it. Optionally find molar mass from mass & volume.
Colligative C
Enter solute & solvent details to compute molality, molarity, mole fraction, and mass %.
Colligative D
Ideal i = number of dissolved particles per formula unit. Real values are slightly lower due to ion pairing, especially at higher concentration.
| Solute | Type | Ideal i |
|---|---|---|
| Glucose, sucrose, urea | Non-electrolyte | 1 |
| NaCl, KCl, KNO₃ | 1:1 salt | 2 |
| CaCl₂, MgCl₂, Na₂SO₄ | 1:2 / 2:1 salt | 3 |
| FeCl₃, Na₃PO₄, AlCl₃ | 1:3 salt | 4 |
Note: real i < ideal i because of ion pairing (e.g. NaCl measures ≈1.9 in dilute solution). Weak electrolytes give 1 < i < 2 depending on degree of dissociation.
Nuclear A
Enter the known nuclides on each side with mass number A and atomic number Z. Set one row's symbol to ? to solve for the missing particle. Conservation of A and Z is enforced.
Decay presets
Reactants (left side)
Products (right side)
Nuclear B
E = Δm·c² · 1 u = 931.5 MeV
Nuclear C
Effect of each decay mode on mass number A and atomic number Z.
| Mode | Particle emitted | ΔA | ΔZ |
|---|---|---|---|
| Alpha (α) | ⁴₂He | −4 | −2 |
| Beta-minus (β⁻) | ⁰₋₁e | 0 | +1 |
| Beta-plus (β⁺) | ⁰₊₁e (positron) | 0 | −1 |
| Electron capture | captures ⁰₋₁e | 0 | −1 |
| Gamma (γ) | ⁰₀γ | 0 | 0 |
| Neutron emission | ¹₀n | −1 | 0 |
| Proton emission | ¹₁p | −1 | −1 |
Atomic A
Enter an element symbol or atomic number (1–103). Builds the configuration in Aufbau filling order, with noble-gas shorthand and valence count.
Atomic B
Rules: l = 0…n−1 · mₗ = −l…+l · mₛ = ±½ · l: 0=s, 1=p, 2=d, 3=f.
Validate a full set, or enter only n to list its allowed subshells.
Atomic C
E = hν = hc / λ
h = 6.626×10⁻³⁴ J·s, c = 2.998×10⁸ m/s, 1 eV = 1.602×10⁻¹⁹ J. Enter exactly one of E, ν, λ.
Atomic D
1/λ = R_H(1/n₁² − 1/n₂²) · R_H = 1.097×10⁷ m⁻¹
Presets
Sig Figs A
Enter any number — decimals, leading/trailing zeros, or scientific notation (e.g. 6.022e23). Reports the significant-figure count with the reasoning per digit.
Round
Round a number to a chosen number of significant figures, shown in both plain and scientific notation.
Sig Figs B
× / ÷ → result keeps the fewest sig figs of any operand. + / − → result keeps the fewest decimal places.
Enter operands separated by commas (e.g. 4.56, 1.4, 0.250).
Sig Figs C
+ / − → absolute uncertainties add (δz = δa + δb). × / ÷ → relative uncertainties add (δz/z = δa/a + δb/b). Power → relative uncertainty ×|n|.
Enter each measurement as its value and its ± absolute uncertainty.