Where does quotient collide?

First set out by Cato Guldberg and Peter Waage in their 1864 Studier over affiniteten (studies concerning affinity) and expanded in their 1879 Ueber die chemische Affinität, the reaction quotient is the ratio of product amounts to reactant amounts, each raised to its stoichiometric power, evaluated for a reaction at its current state. Comparing this number, written Q, against the equilibrium constant K tells which way a reaction will shift: when Q is below K the reaction runs forward, and when above K it runs in reverse. The referent is a number computed from concentrations that says where a chemical mixture sits relative to equilibrium, and it has nothing to do with a number produced by division in arithmetic or a score from an intelligence test.[1][2]

Unit

A number formed from current concentrations, read against the equilibrium constant K

Recovery means

Not applicable

Measured by

Computed from measured concentrations or partial pressures of the reactants and products

The quotient is, at its most basic, the result of dividing one quantity by another, the number an arithmetic division returns. Mathematics also gives the word a structural meaning whose abstract form Otto Hölder set out in his 1889 paper Zurückführung einer beliebigen algebraischen Gleichung auf eine Kette von Gleichungen: the quotient group, formed by collapsing a subgroup so that its cosets become single elements. Emmy Noether's 1927 axiomatic work carried the same construction into ring and ideal theory, and topology reuses it as the quotient space. Either way the referent is a mathematical object, a computed answer or a collapsed structure, and not a chemical ratio at equilibrium or a score from an intelligence test.[3][4]

Unit

A number returned by a division, or an equivalence-class structure such as G/N

Recovery means

Not applicable

Measured by

Obtained by carrying out the division, or by forming cosets or equivalence classes

William Stern coined the intelligence quotient in his 1912 Die psychologischen Methoden der Intelligenzprüfung, defining it as a child's mental age divided by chronological age, a ratio that expresses how a child's measured ability compares with the typical ability for that age. Lewis Terman's 1916 The measurement of intelligence multiplied the ratio by 100 and built it into the Stanford-Binet scale, giving the familiar IQ score. The referent is a standardized measure of tested cognitive performance, and although it too is called a quotient, it belongs to psychometrics rather than to a ratio of chemical concentrations or an object of algebra.[5][6]

Unit

A score, historically mental age divided by chronological age, scaled to a mean of 100

Recovery means

Not applicable

Measured by

Derived from performance on standardized intelligence test items