Vapor pressure lowering calculator

Mole fractions outside the closed interval from zero to one are rejected with a clear invalid_input error because a true mole fraction cannot be negative or greater than one; pure solvent vapor pressure must be strictly positive so the product never invents a non-physical zero or negative magnitude from bad inputs.

What vapor pressure lowering and Raoult’s colligative form mean

In introductory physical chemistry the ideal dilute limit follows from Raoult’s law: the solvent’s partial pressure above the solution equals the solvent mole fraction times the pure solvent vapor pressure at the same temperature, so P equals x_solvent times P°. The lowering is therefore defined as ΔP equals P° minus P, which simplifies at once to ΔP equals x_solute times P° when x_solvent equals one minus x_solute. That single product is what this calculator evaluates. Teachers and automated graders care about the out-of-range mole-fraction rejection as much as the success path: a learner who confuses mass fraction with mole fraction or who pastes a percentage greater than one should see an explicit invalid_input message instead of a nonsense result larger than P°.

How to call the API and what comes back

The solute mole fraction x must lie in the closed interval from zero to one; pure solvent vapor pressure p0 must be strictly positive. Send a JSON body with two required finite numbers: x (aliases mole_fraction, solute_mole_fraction, x_solute, chi, and fraction) and p0 (aliases pure_vapor_pressure, P0, p_pure, pure_solvent_vapor_pressure, solvent_vapor_pressure, and P_pure). Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded x and p0, mirrors them as mole_fraction, solute_mole_fraction, x_solute, pure_vapor_pressure, and pure_solvent_vapor_pressure, sets x_solvent and solvent_mole_fraction to one minus x, sets delta_p, vapor_pressure_lowering, and lowering to the same rounded ΔP, sets p_solution and solution_vapor_pressure to P° minus ΔP, formula to the string ΔP equals x times P°, equation to a filled substitution string, message to a short English summary, and steps to an ordered array of calculation lines including the residual solution vapor pressure. Failed validation—missing fields, non-finite numbers, values outside absolute limits, mole fraction outside zero to one, or non-positive pure vapor pressure—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related chemistry searches

When teaching chemistry, pair examples: water at about twenty-three point eight torr with x equals zero point one recovers ΔP equals two point three eight torr and solution pressure about twenty-one point four two torr; a more dilute x equals zero point zero one with the same P° yields a tenfold smaller lowering; x equals zero recovers pure solvent pressure with zero lowering; and deliberately send x equals one point five or x equals negative zero point one to demonstrate the hard invalid_input path that guards against non-physical mole fractions. This landing targets people searching for a vapor pressure lowering calculator, Raoult’s law mole fraction colligative tool, or ΔP equals x P° homework help online; it is not a full multi-component Raoult’s-law total-pressure solver for volatile solutes, not an Antoine vapor-pressure table, and not a boiling-point elevation or freezing-point depression calculator. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send out-of-range mole fractions. Round-trip checks are easy: recompute x times P° by hand and confirm it equals the published vapor_pressure_lowering within the same twelve-decimal rounding, and confirm that P° minus ΔP equals solution_vapor_pressure.