# Reaction Quotient Calculator

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD and Rijk de Wet
Last updated: Apr 06, 2022

Chemical reactions tend to a state of equilibrium — use our reaction quotient calculator to know in which direction your reaction is moving.

Here you will learn:

• What the reaction quotient is;
• How to find the reaction quotient using the reaction quotient equation; and
• Similarities with the equilibrium constant equation;

We will end with a short step-by-step tutorial explaining how to calculate the reaction quotient.

## What is the reaction quotient?

The reaction quotient (Q) is a function of the concentrations or pressures of the chemical compounds present in a chemical reaction at a particular point in time. The reaction quotient equation is used to determine the direction of the reaction: from a starting point, every reaction (or almost every: there are too) tends to reach an equilibrium state, where the two rates of transformation (reagents into products and vice versa) are equal.

## How to find the reaction quotient?

Both the reaction quotient and the equilibrium constant can be calculated only for reversible reactions: this means that the reaction proceeds in both directions, constantly. This is in contrast to irreversible reactions, like combustion, where it's impossible to obtain the reagents back.

Let us consider a general chemical equation:

$aA + bB \rightleftharpoons cC + dD$

where:

• the lowercase letters indicate the stoichiometric coefficients; and
• the uppercase letters indicate the activities of the substances.

Notice that you can add as many chemical species as you need, as long as you maintain the same notation.

To find the reaction quotient $Q$, multiply the activities for the species of the products and divide by the activities of the reagents, raising each one of these values to the power of the corresponding stoichiometric coefficient.

Here's the reaction quotient equation for the reaction given by the equation above:

$Q = \frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}$

Activities of the chemical species should be used in the calculations, but are usually discarded in favor of concentrations for diluted liquid compounds or partial pressures for gaseous compounds. In most cases, this substitution is fine and won't cause you any trouble, but remember to check if your problem explicitly asks for activities!

If any solid or pure liquid appears in your reaction, either as reagents and/or as products, remember that their activity is 1.

## Relation between the reaction quotient and the equilibrium constant

The reaction quotient equation can be used at any point in time during a chemical reaction. There's a point, however, where its quantity equals the equilibrium constant of that reaction, most often denoted by $K$. At that point, the reaction as attained chemical equilibrium. Chemical equilibrium is the dynamic state where the composition of the chemical system does not change with time (even if the transformation of species is allowed, this does not affect the overall concentrations).

The equilibrium constant equation is entirely similar to the reaction quotient:

$K = \frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b} \ \Bigg|_{\text{equilibrium}}$

Just remember that all of the quantities used in the equation for $K$ are at their equilibrium value. The equilibrium constant quantifies toward which side of the reaction the equilibrium leans. In particular:

• If $K > 1$, then the equilibrium favors the reagents.
• If $K < 1$, then the equilibrium favors the products.

The thermodynamical equilibrium is a stable state of the reaction and the Le Chatelier principles state that a change in conditions is reflected by a change in the equilibrium constant that counteracts and balances the affecting variations.

The equilibrium constant is constant for a given chemical reaction, with a definite value for each temperature. You can find these values in tables, usually for standardized temperature values — for IUPAC, it is 25°C. Its value equals the reaction quotient at the equilibrium: $Q\big|_{\text{equilibrium}} = K$.

The state of the reaction when the equilibrium is not yet attained is given by the reaction quotient:

• If $Q < K$, the reaction will proceed from reagents to products:

$aA + bB → cC + dD$;

• If $Q > K$, the reaction will proceed from products to reagents:

$cC + dD → aA + bB$.

When working on acid and bases, the concept of the equilibrium constant is usually discarded in favor of the characteristic dissociation and association constants.

The acid dissociation reaction is described by a given chemical equation:

$H_aA + H_2O ⇌ aH_3O^+ + A^{a-}$

The equilibrium constant is given by the dissociation constant $K_a$ :

$K_a= \frac{\left[A^{-}\right]^a\left[H^+\right]^a}{\left[H_aA\right]}$

$H_2O$ doesn't show up in this equation because the activity of pure water is $1$.

For a base, the protonation reaction is described by a generic chemical equation:

$B + H_2O \rightleftharpoons OH^- + BH^+$

In analogy with the previously seen acid dissociation constant, one can define the association constant $K_b$ as:

$K_b = \frac{\left[OH^-\right]\left[BH^+\right]}{\left[B\right]}$

Here the activity of water can be omitted as well.

If you know the concentration of the solution, you can calculate the pH of the solution (both of acid and base) by using our pH calculator.

## An example of how to calculate the reaction quotient

Calculating the reaction quotient is pretty easy — the implications are the interesting part!

• Choose your reaction. Let's assume that it is :
$Cd^{2+}_{(aq)} + 4Cl^-_{(aq)} \rightleftharpoons CdCl_{4(aq)}^{2-}$

At 25°C, this reaction has an equilibrium constant $K = 108$.

• Choose the concentration of the products and reagents. We will use these values:
• $\left[Cd^{2+}\right] = 1\ \text{M}$
• $\left[Cl^-\right] = 0.5\ \text{M}$
• $\left[CdCl_4^{2-}\right] = 0.25\ \text{M}$
• Calculate the reaction quotient by using the equation above:
$Q= \frac{\left[CdCl_4\right]}{\left[Cd^{2+}\right] \left[Cl^-\right]^4} =\frac{0.25}{1\times 0.5^4}=4$

We see that the value of $Q$is smaller than the value of $K$. Hence, the reaction has just set off, and it's highly unbalanced towards the reagents.

## How to use our reaction quotient calculator?

Our reaction quotient calculator can take up to 6 reagents and 6 products. At the beginning, you will only see two of each group — more will appear as you fill the preceding fields.

Remember to write the stoichiometric coefficient and the activities/concentrations in the correct fields!

The concentration of the substances can be computed with our concentration calculator. If you want to calculate the concentration of the diluted solution, why not try our solution dilution calculator?

The concepts of equilibrium and reaction quotient are close to other thermodynamic quantities. You can find more about them at our Gibbs free energy calculator!
We also have a lot of tools to help you with solutions and concentrations, such as:

There's many more on our . You will surely find what you need there!

## FAQ

### What is the reaction quotient definition?

The reaction quotient is a quantity used in chemistry to understand the progress of a chemical reaction with respect to the equilibrium state. In a reversible chemical reaction, the concentrations of the chemical species vary, with reagents transforming into products and vice versa. The reaction quotient measures the relative abundance of a chemical species at any given time.

### How do I calculate the reaction quotient?

Using capital letters to indicate the concentrations of the species and cursive letters to indicate the stoichiometric coefficients, the state of the reaction is defined as Q = ([C]ᶜ·[D]ᵈ) / ([A]ᵃ·[B]ᵇ) (with the products on top and the reagents at the bottom). If Q > 1, then the reaction favors the reagents. If Q < 1, the products are dominant, while Q = 1 implies that the reaction is at the equilibrium.

### What are Q and K in a chemical reaction?

Q is the reaction quotient, while K is the equilibrium constant. They are both defined as ([C]ᶜ·[D]ᵈ) / ([A]ᵃ·[B]ᵇ): the ratio of the product of the concentrations of the reaction's products to the product of the concentrations of the reagents, each of them raised to the power of their relative stoichiometric coefficients. K is defined only at the equilibrium while Q is defined during the whole reaction. They are equal at the equilibrium.

### What is the concentration of water ?

In the calculations for the reaction quotient, the value of the concentration of water is always 1. Water does not participate in a reaction when it's the solvent and its quantity is so big that its variations are negligible, thus it is excluded from the calculations.

Davide Borchia
Reagents
Coefficient of reagent 1
Coefficient of reagent 2
Activity of reagent 1
M
Activity of reagent 2
M
Products
Coefficient of product 1
Coefficient of product 2
Activity of product 1
M
Activity of product 2
M
Reaction quotient
Precision
4
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