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Foundations: Chemistry

Equilibrium constant Kc

Ratio of product to reactant concentrations when a reaction is at equilibrium.

Ref: FCH-22
Rev: v1
Field: Foundations: Chemistry
Result: K_c

K_{c} = \frac{{[C]}^{c}}{{[A]}^{a} {[B]}^{b}}

For aA + bB ⇌ cC at equilibrium at a given temperature, concentrations in mol/dm³. The default is H₂ + I₂ ⇌ 2HI. Solids and pure liquids are left out of K_c.

At equilibrium the ratio of products to reactants settles at a fixed number for a given temperature. A large value means the reaction favours products.

Calculator

Solve for

K_cEquilibrium constantComputed

[A]Concentration of A

mol/dm³

1e-65

[B]Concentration of B

mol/dm³

1e-65

[C]Concentration of C

mol/dm³

1e-65

aCoefficient of A

bCoefficient of B

cCoefficient of C

log₁₀ K_c1.69
K_c for the reverse reaction0.02041

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Equilibrium constant () current value 49

aCoefficient of AKey driver

6,130,000

bCoefficient of B

6,130,000

[A]Concentration of A

0.196980,000

[B]Concentration of B

0.196980,000

[C]Concentration of C

2.5e-962,500

cCoefficient of C

0.96350

A K_c above 1 means products are favoured; below 1 means reactants are favoured.
K_c changes with temperature only, not with concentration or a catalyst.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing ()	Local step	Change in result
a Coefficient of A	1 to 4	49	6,125,000	6,125,000	+10%	+47.9 %
b Coefficient of B	1 to 4	49	6,125,000	6,125,000	+10%	+47.9 %
[A] Concentration of A	1e-6 to 5 mol/dm³	0.196	980,000	980,000	+10%	−9.09 %
[B] Concentration of B	1e-6 to 5 mol/dm³	0.196	980,000	980,000	+10%	−9.09 %
[C] Concentration of C	1e-6 to 5 mol/dm³	2.5e-9	62,500	62,500	+10%	+21 %
c Coefficient of C	1 to 4	0.9604	350	349	+10%	−32.5 %

Sweep of Concentration of C

Concentration of C (mol/dm³)	Equilibrium constant
1e-6	2.5e-9
6.877e-6	1.182e-7
4.729e-5	5.59e-6
3.252e-4	2.643e-4
0.002236	0.0125
0.01538	0.5911
0.1057	27.95
0.7271	1,322
5	62,500

Sweep one variable

Vary

Equilibrium constant ()Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

K_c

Equilibrium constant

Result ·

What the equation gives you. Everything else feeds it.

[A]

Concentration of A

mol/dm³ · typical 1e-6 to 5

Equilibrium concentration of A (H₂). Lowers K_c as the A power rises.

[B]

Concentration of B

mol/dm³ · typical 1e-6 to 5

Equilibrium concentration of B (I₂). Lowers K_c as the B power rises.

[C]

Concentration of C

mol/dm³ · typical 1e-6 to 5

Equilibrium concentration of C (HI). Raises K_c as the C power rises.

Coefficient of A

· typical 1 to 4

Coefficient of A. Power on [A].

Coefficient of B

· typical 1 to 4

Coefficient of B. Power on [B].

Coefficient of C

· typical 1 to 4

Coefficient of C. Power on [C].

Worked example with the values above

Numerator: [C]² = 0.0196.
Denominator: [A]¹[B]¹ = 4×10⁻⁴.
K_c = 49.

Assumptions and limits

The system is at equilibrium.
Constant temperature.

Common mistakes

Forgetting to raise concentrations to the powers of the coefficients.
Putting reactants on top.

Statistics and uncertainty

Concentrations measured to 2–3% propagate with powers, so the K_c uncertainty can be 10% or more.

Where it is used

Predicting equilibrium composition.
Optimising reversible industrial processes.

Maths you need

Equilibrium: forward rate = reverse rate
Powers: indices from the balanced equation

Related formulas

Practise this formula