Reaction Quotient Calculator

Background.

A reacting mixture carries a record of where it stands relative to equilibrium at every moment, and the reaction quotient reads it. Take each product's activity — its effective concentration or pressure expressed as a pure number — raise it to the power of its coefficient in the balanced equation, multiply the results together, and divide by the same product for the reactants. For aA + bB ⇌ cC + dD, that gives Q = (a_C)^c (a_D)^d / ((a_A)^a (a_B)^b).

Q has exactly the form of the equilibrium constant K. The difference is that K uses the activities a system settles at, while Q uses whatever is present now, so comparing the two tells you which way the reaction will move. If Q is smaller than K there are too few products for equilibrium and the reaction runs forward; if Q is larger it runs in reverse; if they are equal, nothing changes on balance. Thermodynamics says the same thing through ΔG = ΔG° + RT ln Q, which is negative, meaning the forward reaction is spontaneous, precisely when Q is less than K.

Activities are where most errors creep in. For a gas behaving ideally, activity is partial pressure divided by the standard pressure of 1 bar; for a dilute solute it is concentration divided by 1 mol/L; pure solids and liquids, such as a precipitate or the water in a dilute aqueous solution, have an activity of 1. In concentrated solutions or at high pressure, real activities drift away from those approximations, and the values you enter are used as given.

All four slots are always in the expression. For a reaction with fewer species, set the unused activity to 1 — any power of 1 is 1, so it drops out. Balancing the equation and comparing Q with K remain your steps.

What is reaction quotient calculator?

The reaction quotient Q is a dimensionless number built from the activities of the species in a reaction at a particular moment: the product of the products' activities, each raised to its stoichiometric coefficient, divided by the corresponding product for the reactants. It is defined for any composition, not just equilibrium. When the mixture reaches equilibrium, Q becomes equal to the equilibrium constant K for the same written equation and temperature.

How to use this calculator.

1. 01Write the balanced equation and assign the two reactants to A and B and the two products to C and D, in the direction you want Q for.
2. 02Convert each amount to an activity: partial pressure in bar for an ideal gas, molar concentration in mol/L for a dilute solute, and 1 for a pure solid, pure liquid or solvent.
3. 03Enter each species' coefficient from the balanced equation. Fractions such as 0.5 are accepted, and each coefficient can be at most 100.
4. 04If the reaction has only three species, or two, enter an activity of 1 for each empty slot; its coefficient then makes no difference.
5. 05Compare the resulting Q with the K for the same written equation at the same temperature: smaller means the reaction proceeds forward, larger means it proceeds in reverse.

The formula.

Q = (a_C)^c (a_D)^d / ((a_A)^a (a_B)^b). Each activity is raised to its stoichiometric coefficient, so a species with coefficient 2 counts squared and one with coefficient 3 counts cubed; that is why a high-coefficient species usually dominates how Q responds to a change in conditions. Products sit in the numerator and reactants in the denominator, so adding product raises Q and adding reactant lowers it. Because activities are ratios to a standard state, Q has no units. Writing the equation differently changes Q in a predictable way: reversing it gives 1/Q, and multiplying every coefficient by two squares it. K transforms identically, which is why Q must always be compared with a K tabulated for the same written form. All activities and coefficients must be positive.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC Gold Book, reaction quotient.
2. [2]OpenStax, Chemistry 2e, section 13.3, Shifting Equilibria: Le Châtelier's Principle.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.