Reaction Quotient Qc

Qc uses the same ratio as Kc but with the concentrations present right now, revealing which way a reaction will shift to reach equilibrium.

Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}

Qc = [C]^c [D]^d / [A]^a [B]^b (using current, non-equilibrium concentrations)

What it means

The reaction quotient is Kc's formula applied to the mixture as it stands right now. If Qc is smaller than Kc, there is relatively too much reactant, so the reaction shifts forward toward products; if Qc is larger than Kc, it shifts backward toward reactants; if Qc equals Kc, the mixture is already at equilibrium and nothing net happens. It is the quantitative heart of predicting equilibrium shifts.

Variables

Symbol	Name	Unit	Meaning
$[C], [D]$	Current concentrations of the products	mol/L (M)	The molar concentrations of each product at the moment being analyzed, whether or not the system is at equilibrium.
$[A], [B]$	Current concentrations of the reactants	mol/L (M)	The molar concentrations of each reactant at the moment being analyzed, whether or not the system is at equilibrium.
$a, b, c, d$	Stoichiometric coefficients	dimensionless	The numbers that balance the chemical equation; each concentration is raised to the power of its own coefficient.
$Qc$	Reaction quotient (concentration basis)	dimensionless	A snapshot of the reaction's progress: comparing Qc to Kc predicts whether the mixture will shift toward products or reactants.

Assumptions

The concentrations are the current ones, which may differ from the equilibrium values.
Qc is compared against the Kc measured at the same temperature.
Concentrations approximate activities, valid for dilute solutions and ideal gases.
Pure solids and pure liquids are omitted, exactly as in the Kc expression.

Worked example

Problem

For A(g) ⇌ 2 B(g), Kc = 0.0500. Right now [A] = 0.500 M and [B] = 0.100 M. Calculate Qc and predict the direction of net change.

Given:

Kc = 0.0500 for A(g) ⇌ 2 B(g)
Current [A] = 0.500 M
Current [B] = 0.100 M
Qc = [B]^2 / [A]

Write the quotient: Qc = [B]^2 / [A].
Substitute the current values: Qc = (0.100)^2 / 0.500.
Square the numerator: (0.100)^2 = 0.0100.
Divide: 0.0100 / 0.500 = 0.0200.
Compare: Qc = 0.0200 is less than Kc = 0.0500.

Qc = 0.0200; net reaction proceeds forward (toward products)

Since Qc < Kc, the mixture is reactant-heavy relative to equilibrium, so A converts into B until the ratio rises back to 0.0500.