Mass fraction to mole fraction calculator

Zero molar mass is rejected with a clear invalid_input error so a bad denominator never becomes Infinity or NaN.

How mass fraction converts to mole fraction

Start from a fixed basis of one unit mass of mixture. Molar masses must use consistent units, typically grams per mole when mass fractions are weight fractions of the same mixture; only the ratio of masses to molar masses matters, so any mass-per-mole unit works if both species use it. Mass fractions should be non-negative; for pure weight-percent work convert wt percent to a fraction first by dividing by one hundred. The mass of solute on that basis is the solute mass fraction w_s, and the mass of solvent is w_v. Divide each mass by the corresponding molar mass to obtain moles per unit mass: n_s equals w_s over M_s and n_v equals w_v over M_v. The solute mole fraction is then x_s equals n_s divided by the sum n_s plus n_v, which expands to the closed form x_s equals open parenthesis w_s over M_s close parenthesis over open parenthesis w_s over M_s plus w_v over M_v close parenthesis. The same construction with n_v in the numerator gives the solvent mole fraction, and for a true binary the two mole fractions sum to one. If either molar mass is zero the division is undefined, and this capability fails with invalid_input rather than inventing Infinity. The arithmetic is deterministic floating-point with no random seeds, wall-clock timestamps, or network calls, so identical inputs always produce identical JSON. This landing intentionally stays on the binary mass-to-mole conversion; multi-component tables, formula-based molar-mass lookup, molality, and molarity remain separate search intents.

What you send and what you get back

Classic textbook checks include twenty weight percent sodium chloride in water with M_s of fifty-eight point forty-four and M_v of eighteen point zero one five, equal mass ethanol–water mixtures with M near forty-six and eighteen, and a pure solvent limit where solute mass fraction is zero giving mole fraction zero. Wire the free browser form for homework and quick sanity checks, then call the identical contract from scripts when you need bulk answer keys or grading oracles. Send four required fields: solute_mass_fraction and solvent_mass_fraction as finite non-negative numbers (use 0.2 for twenty weight percent solute, and typically one minus that value for a binary solvent), plus solute_molar_mass and solvent_molar_mass as finite positive numbers in grams per mole or any consistent mass-per-mole unit. Missing fields, non-numeric strings, NaN, Infinity, negative mass fractions, negative molar masses, and zero molar mass fail with invalid_input and are not charged. If both mass fractions are zero there are no moles to normalize and the request fails the same way. On success the response echoes the cleaned four inputs, provides moles_solute_per_unit_mass, moles_solvent_per_unit_mass, and total_moles_per_unit_mass for intermediate checks, returns mole_fraction_solute as the primary dimensionless result, includes mole_fraction_solvent for convenience, attaches a units hint object, sets method to mass_fraction_to_mole_fraction, and formula to x_s equals open parenthesis w_s over M_s close parenthesis over open parenthesis w_s over M_s plus w_v over M_v close parenthesis so lab notebooks can cite the same expression. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.

Where mass-to-mole conversion shows up in real work

Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.