Molar Ratio Calculator

A molar ratio is read straight off the coefficients of a balanced chemical equation, and those coefficients exist because atoms and charge are conserved: whatever enters as reactant must appear among the products. In N2 + 3H2 gives 2NH3 the ratio of nitrogen to hydrogen is 1:3 and of nitrogen to ammonia is 1:2, so moles of B = moles of A times coefficient B over coefficient A. Coefficients are only defined up to a common multiplier, so 2:3 and 4:6 describe the same reaction and ratios are normally reduced by their greatest common divisor. The bridge to the bench is the molar mass: n = m/M for a weighed solid, n = c*V for a solution, and n = P*V/(R*T) for a gas. Since 2019 the mole has been defined as exactly 6.02214076e23 elementary entities. The ratio also identifies the limiting reagent. Divide the available moles of each reactant by its coefficient; the smallest quotient is the reagent that runs out first and it alone sets the theoretical yield, while everything else is in excess. Two limitations matter. The ratio describes only the reaction as written, so competing or consecutive side reactions, and equilibria that do not run to completion, mean actual consumption can differ substantially from the stoichiometric prediction. And in synthesis a deliberate excess is often used to push an equilibrium forward or to compensate for a volatile component, so the charged ratio and the reacted ratio are not the same number. Percent yield compares the mass actually isolated with the theoretical value the ratio predicts.

The word stoichiometry was coined by the German chemist Jeremias Benjamin Richter, who published his Anfangsgruende der Stoechyometrie in 1792 and argued that substances combine in fixed and calculable proportions. The empirical foundation was laid over the following decade in the dispute between Joseph Louis Proust, who defended the law of definite proportions from about 1794, and Claude Louis Berthollet, who held that composition could vary continuously. Proust prevailed, and John Dalton drew the consequence between 1803 and 1808 with his law of multiple proportions and an atomic theory that explained why whole-number ratios should appear at all. Coefficients could not be trusted, however, until atomic weights were consistent, and for fifty years they were not. Gay-Lussac's law of combining volumes in 1808 and Amedeo Avogadro's hypothesis of 1811 pointed to the resolution, but Avogadro's work was neglected until Stanislao Cannizzaro circulated his reorganisation of atomic weights at the Karlsruhe Congress of 1860, after which chemists could finally write formulas and balanced equations that agreed with one another. Wilhelm Ostwald introduced the term mol in the 1890s as a practical unit of amount. It became an SI base unit at the 14th General Conference on Weights and Measures in 1971 and was redefined in 2019 by fixing the Avogadro constant.