Equilibrium moles from total pressure calculator

This equilibrium moles from total pressure calculator takes those inputs, builds mole fractions from the reaction stoichiometry, evaluates the ideal-gas total moles n_total equals P V over R T, and returns each species amount n_i equals y_i times n_total together with Dalton partial pressures. It is built for homework ICE-table follow-ups, lab report checks and automated grading where students already know the equilibrium mole ratios from stoichiometry and only need the absolute scale set by measured total pressure. Total pressure zero is rejected as invalid_input so a non-physical free-gas state never becomes a silent answer.

How total pressure and stoichiometry fix equilibrium moles

Start from a balanced gas-phase reaction whose equilibrium composition has already been reduced to a list of positive relative amounts for each species—exactly the numbers you get when you evaluate an ICE table after solving for extent or degree of dissociation. Those stoichiometric coefficients ν_i do not yet have absolute units; they only fix the composition ratios. Keep pressure, volume and the gas constant on one consistent unit system—for classroom problems that usually means atmospheres, litres and R near 0.08205746 litre-atmospheres per mole-kelvin; SI work pairs pascals, cubic metres and R equal to 8.314462618 joules per mole-kelvin. Temperature and volume must likewise be strictly positive so the ideal-gas quotient remains defined and physical. The mole fraction of species i is therefore y_i equals ν_i divided by the sum of all ν_j over the gas-phase list. For an ideal-gas mixture the total amount of substance follows from the measured total equilibrium pressure P, the free volume V and the absolute temperature T through n_total equals P times V divided by R times T. Multiplying each mole fraction by that total amount yields the moles of every species: n_i equals y_i times n_total. Dalton’s law then supplies the matching partial pressures p_i equals y_i times P in the same pressure unit you used for the total pressure. This workflow is the natural second step after a Kp or α calculation: first find the relative composition, then scale it with the barometer and vessel data. Total pressure must be strictly positive: a reported total pressure of zero would imply either an empty vessel or a non-physical free-gas state, so the calculator fails with invalid_input instead of inventing moles.

Input contract, response shape and error behaviour

Wire the free browser form for quick checks, then call the identical contract from scripts when you need bulk answer keys or grading oracles. POST a JSON body with four required fields and one optional constant. total_pressure is the absolute total pressure of the equilibrium mixture and must be a finite number strictly greater than zero—aliases include P, P_total, pressure and P_eq. volume is the mixture volume in a unit consistent with your pressure and gas constant—aliases V and vol—and must be strictly positive. temperature is absolute temperature in kelvin—aliases T, temp, kelvin—and must be strictly positive; Celsius values must be converted before the call. coefficients is a non-empty array of strictly positive finite stoichiometric relative amounts, one entry per gas-phase species in fixed order—aliases stoich, stoichiometry, nu, coeffs, relative_moles and nu_i—with at most fifty species. gas_constant is optional and defaults to 0.08205746 litre-atmospheres per mole-kelvin so that P in atmospheres and V in litres yield moles without extra conversion; supply 8.314462618 or another matching R when you work in SI. Missing fields, non-numeric strings, empty coefficient lists, non-positive coefficients, non-positive volume or temperature, non-positive R, and especially total pressure zero or negative all fail with invalid_input and are not billed. On success the response echoes cleaned total_pressure, volume, temperature, gas_constant and coefficients; reports gas_constant_defaulted; provides coefficient_sum, mole_fractions, total_moles, moles, partial_pressures and a per-species table with index, coefficient, mole_fraction, moles and partial_pressure; and attaches formula, method, message and step strings for homework write-ups. Example: P equals 2 atm, V equals 10 L, T equals 298.15 K, coefficients [1, 2, 1] and default R produce y equals [0.25, 0.5, 0.25], a positive n_total from PV/RT, and species moles in that same 1:2:1 ratio. Successful API calls use the published base price of $0.002 per item.