Chemistry toolkit

The formula is parsed into a count of each element (parentheses and hydrate dots multiply the group that follows). Each count is multiplied by that element's standard atomic weight and the products are summed. Mass percent of an element is its subtotal divided by the total. This value is the grams in one mole of the substance — divide a mass by it for moles, multiply moles by it for mass. See molar mass.

Assume a 100 g sample so each percent is a mass in grams. Divide each mass by the element's atomic weight to get moles, then divide every mole value by the smallest of them. If the ratios are not already close to whole numbers, they are scaled by a small factor (×2, ×3 …) and rounded, then reduced by their greatest common divisor. Dividing a measured molar mass by the empirical-formula mass gives the multiplier to the molecular formula.

Everything routes through amount in moles: n = m ÷ M from a mass, or n = N ÷ Nₐ from a particle count. From n the tool computes mass (n × M) and particle count (n × 6.02214076 × 10²³). This is the central conversion behind every stoichiometry problem.

Each species is parsed into an element-count vector. Requiring every element (and total atoms) to be conserved gives a system of linear equations in the unknown coefficients; the tool row-reduces it with exact fraction arithmetic, takes the one free parameter, clears denominators, and divides by the greatest common divisor to get the smallest whole-number coefficients. Only coefficients are ever changed — never a subscript. See coefficient and chemical equation.

Adding solvent does not change the moles of solute, so C₁V₁ (moles in the aliquot taken) equals C₂V₂ (moles in the final solution). The tool rearranges this for whichever variable you left blank. Units only need to be consistent on each side. See dilution and molarity.

PV = nRT treats the gas as an ideal gas — point particles with no attractions. The tool solves for the blank field with R = 0.082057 L·atm·mol⁻¹·K⁻¹, so temperature must be in kelvin (add 273.15 to °C) and pressure in atm. Real gases follow this within about 1% near room conditions.

q = mcΔT relates a heat transfer to a substance's mass, its specific heat capacity, and the resulting temperature change, ΔT = T_final − T_initial. The tool solves for whichever field is left blank. Mass and specific heat are always positive; q and ΔT carry a sign — negative means heat is released or the temperature drops. Water's specific heat, 4.184 J g⁻¹ °C⁻¹, is worth memorising since it appears in almost every calorimetry problem this course sets. See calorimetry and Module 8.

From any one input the tool finds pH, using pH = −log[H⁺], pOH = −log[OH⁻], and the water equilibrium pH + pOH = 14 at 25 °C. Then [H⁺] = 10^(−pH) and [OH⁻] = 10^(−pOH). Each whole pH unit is a tenfold change in [H⁺]. See pH, acid, and base.

Percent yield = actual ÷ theoretical × 100%. The theoretical yield comes from a stoichiometry calculation on the limiting reactant; the actual yield is what you recover and weigh. A value above 100% means impure or incompletely dried product. See percent yield.

Pressure and energy conversions go through an SI base unit (pascals, joules): the input is multiplied by the "from" factor and divided by the "to" factor. Temperature is handled separately through kelvin, because those scales have offsets, not just different sizes.

Non-zero digits always count; zeros between non-zero digits count; leading zeros never count; trailing zeros count only when a decimal point is written. The tool applies these rules to the digits you enter, and can also round to a chosen number of significant figures. See significant figures.

The exponent is the power of ten that puts the decimal point after the first non-zero digit — positive for numbers ≥ 10, negative for numbers < 1. The coefficient is then rounded to the requested number of significant figures.

E°cell = E°cathode − E°anode. The more positive of the two half-reactions is always the cathode; the tool doesn't assume which one you'll enter first. A positive E°cell means the reaction is spontaneous as written — the same fact a negative Gibbs free energy states, related by ΔG° = −nFE°cell (F = 96,485.332 C/mol). Give the number of electrons transferred, n, to see that ΔG° value too. Look up half-reaction potentials on the standard reduction potentials table.

Q and K are the identical ratio of products to reactants — K is that ratio locked in at equilibrium; Q is the same ratio evaluated at whatever concentrations exist right now. Q < K means there aren't yet enough products, so the reaction runs forward; Q > K means there are too many, so it runs in reverse; Q = K means it has already arrived. See reaction quotient and equilibrium constant.

pH = pKa + log([A⁻]/[HA]) rearranges a weak acid's own equilibrium expression so a buffer's pH follows directly from its acid's pKa (−log Ka) and the ratio of conjugate base to weak acid actually present, without re-deriving the full equilibrium each time. Equal amounts of acid and base put pH exactly at pKa, since log(1) = 0. See Henderson–Hasselbalch equation and buffer.

ln([A]0/[A]t) = kt is the integrated form of a first-order rate law — it turns "how fast" into "how much is left after how long," the same exponential-decay shape as radioactive decay below. The tool also reports the half-life implied by whichever k is known or solved for, t½ = ln2/k. Keep time and rate-constant units consistent with each other (e.g. seconds and s⁻¹). See rate law, rate constant, and integrated rate law.

ln(N0/Nt) = λt is the mathematically identical exponential-decay relationship as first-order chemical kinetics above, just relabeled: λ (the decay constant) plays the role k plays there. The crucial difference is physical, not mathematical — λ is a fixed nuclear property of a given isotope, unaffected by temperature, concentration, or catalysis the way a chemical rate constant can be. See decay constant, half-life, and alpha decay.

ΔG = ΔH − TΔS determines whether a process is spontaneous as written at a given temperature: negative ΔG is spontaneous, positive is non-spontaneous, zero is equilibrium. ΔH and ΔG are conventionally in kJ/mol while ΔS is in J mol⁻¹ K⁻¹ — the tool applies the ×1000 conversion for you, but watch that unit mismatch when working by hand. See Gibbs free energy, entropy, and spontaneous process.

DoU = C − H/2 − X/2 + N/2 + 1 compares a formula's actual hydrogen count against the maximum a fully saturated, ring-free hydrocarbon with the same carbon count could have; every ring or pi bond (double or triple bond) the real structure contains costs exactly two hydrogens relative to that maximum, so the shortfall reveals how much unsaturation must be present. Oxygen and sulfur don't affect the count; halogens count the same as hydrogen. See degree of unsaturation and functional group.

The titrant is always a strong base. Before equivalence, a strong-acid analyte is worked out directly from leftover moles of acid; a weak-acid analyte is worked out from the full weak-acid equilibrium for a mixture of the remaining acid and the conjugate base formed so far — not bare Henderson–Hasselbalch alone, which breaks down for the first sliver of titrant added. At the equivalence point, a weak acid's conjugate base hydrolyzes water, which is exactly why that point sits above pH 7 rather than at it — a strong acid's equivalence point has no such conjugate-base effect and lands at pH 7 instead. For a weak acid, half the equivalence volume lands at exactly pH = pKa, marked on the graph. See buffer and Henderson–Hasselbalch equation.