What K actually tells you

The equilibrium constant is a single number that captures how far a reversible reaction proceeds before the forward and reverse rates balance. A K of 10⁶ tells you the products dominate so completely that you can treat the reaction as essentially complete. A K of 10⁻⁶ tells you almost nothing reacted. A K near 1 means you’ll have meaningful amounts of everything in the flask, and you’ll need an ICE table to figure out exactly how much of each.

For a generic reaction:

aA + bB ⇌ cC + dD

Kc = [C]^c · [D]^d / ([A]^a · [B]^b)

The brackets mean equilibrium molar concentrations — not initial, not arbitrary. That distinction is where most errors enter.

The straightforward case: equilibrium concentrations given

When the problem hands you the equilibrium concentrations directly, the calculation is plug-and-chug.

Example: N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g)

Equilibrium values: [N₂] = 0.50 M, [H₂] = 0.30 M, [NH₃] = 0.20 M

Kc = [NH₃]² / ([N₂]·[H₂]³) = (0.20)² / [(0.50)(0.30)³] Kc = 0.040 / (0.50 × 0.027) = 0.040 / 0.0135 = 2.96

Two things that should already be reflexive: each concentration is raised to its stoichiometric coefficient, and pure solids and liquids never appear in the expression. Their activities are taken as 1. So for CaCO₃(s) ⇌ CaO(s) + CO₂(g), the entire expression collapses to Kc = [CO₂].

When you need an ICE table

Most real problems give you initial conditions plus one equilibrium value, and ask you to back out the rest. The ICE table (Initial, Change, Equilibrium) is the bookkeeping tool.

Example: H₂(g) + I₂(g) ⇌ 2 HI(g). Start with 1.00 mol H₂ and 1.00 mol I₂ in a 1.00 L flask. At equilibrium, [HI] = 1.56 M. Find Kc.

	H₂	I₂	2 HI
I	1.00	1.00	0
C	−x	−x	+2x
E	1.00−x	1.00−x	2x

The known: 2x = 1.56, so x = 0.78.

[H₂] = 0.22 M, [I₂] = 0.22 M

Kc = (1.56)² / [(0.22)(0.22)] = 2.434 / 0.0484 = 50.3

The stoichiometry sets the change row. For every mole of H₂ consumed, you also consume one mole of I₂ and produce two moles of HI. If you forget the 2 on HI’s change line, your x comes out wrong by a factor of two and the whole table is off.

Kp from Kc

Gas-phase equilibria can be expressed in partial pressures instead of concentrations:

Kp = Kc · (RT)^Δn

where Δn = (moles of gaseous products) − (moles of gaseous reactants).

Example: N₂O₄(g) ⇌ 2 NO₂(g), Kc = 4.63 × 10⁻³ at 25 °C.

Δn = 2 − 1 = 1 RT = (0.08206 L·atm/mol·K)(298.15 K) = 24.47 Kp = 4.63 × 10⁻³ × 24.47 = 0.113

Use 0.08206 for R when you want pressures in atm. If Δn = 0 (same number of gas moles on both sides), Kp = Kc and the conversion is trivial.

Q vs. K — predicting direction

Q has the exact same algebraic form as K, but you plug in current (not necessarily equilibrium) concentrations. Comparing Q to K tells you which way the system will shift to reach equilibrium:

Q < K → too few products, reaction shifts right
Q > K → too many products, reaction shifts left
Q = K → already at equilibrium, no net change

This is how you handle “is the system at equilibrium?” questions without solving the full ICE table. Compute Q, compare, done.

Traps that bite students

Including solids and liquids in the expression. If a species is a pure solid or pure liquid in the balanced equation, it does not appear in K. Its activity is 1.

Skipping the stoichiometric exponents. Every concentration gets raised to its coefficient. The exponent on [HI] in the H₂/I₂/HI example is 2, not 1. Forgetting this gives an answer that’s off by a factor of [HI].

Mixing K and Q. K is computed from equilibrium concentrations. Q is computed from whatever concentrations you have right now and is used to predict shift direction. They look identical algebraically — keep them straight by tracking what you plugged in.

Ignoring temperature. K depends on temperature. A K value at 25 °C does not apply at 500 °C, and you cannot fix that with a unit conversion. You need a different K (typically obtained from ΔH° via the van’t Hoff equation).

Practice

Use the Equilibrium Calculator to check:

Write Kc for 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g) and compute it from [SO₂] = 0.40 M, [O₂] = 0.20 M, [SO₃] = 0.80 M.
PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), Kc = 0.042 at 250 °C. Find equilibrium concentrations starting from 1.00 mol PCl₅ in a 2.00 L flask.
Convert Kc = 1.7 × 10⁻² for 2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g) to Kp at 1000 K.
CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g), Kc = 5.10 at 700 K. With [CO] = [H₂O] = 0.300 M and [CO₂] = [H₂] = 0.500 M, which way does the system shift?
H₂(g) + Br₂(g) ⇌ 2 HBr(g), Kc = 2.2 × 10⁶. What does this tell you about the position of equilibrium?

How to Calculate the Equilibrium Constant