Equilibrium Constants- Appropriate Concentration Units for Keq

What Are Equilibrium Constants and Why Units Matter

Equilibrium constants (Keq) describe the ratio of product concentrations to reactant concentrations at equilibrium. Sounds simple. But here's where people get tripped up: the units you use actually matter, and understanding when to include them versus when to treat them as dimensionless will save you from costly calculation errors.

Most textbooks throw Keq at you as a unitless number. That's technically true for the thermodynamic definition, but practically, you'll encounter Kc, Kp, and K with various units in real problems. Know the difference.

Kc vs Kp: Concentration vs Pressure

Kc uses concentration units (typically mol/L or M). Kp uses pressure units (typically atm or bar). The one you use depends on the phase of your reaction components.

• Gases? Use Kp or express them as partial pressures
• Aqueous solutions? Use Kc with molarity
• Mixed phases? You need both, and you'll convert between them

The Kc to Kp Conversion

When you have gaseous reactions, you might need to switch between Kc and Kp. The relationship is:

Kp = Kc(RT)^Δn

Where:

• R = 0.0821 L·atm/(mol·K) or 0.0831 L·bar/(mol·K)
• T = temperature in Kelvin
• Δn = moles of gaseous products minus moles of gaseous reactants

This conversion exists because concentration and pressure are related through the ideal gas law.

Acceptable Concentration Units for Keq

You have options here. The most common units in textbooks are molarity (M), but other units appear depending on context.

Common Units You'll Encounter

Most instructors expect you to use M (mol/L) unless they specify otherwise. When in doubt, check the problem statement or the phase of your reactants.

The Dimensionless Treatment: Standard States

Here's the bitter truth about the "unitless Keq" you see in textbooks: it's not truly unitless. It's normalized to standard state concentrations.

For the thermodynamic equilibrium constant:

K = Π (concentration/standard concentration)^(stoichiometric coefficient)

The standard state is 1 M for solutes and 1 bar for gases. When you divide your actual concentration by the standard state, you get a dimensionless number.

This is why chemists can report Keq as a unitless value. It's not voodoo—it's just math that removes the units by convention.

How to Write Keq Correctly

For the reaction: aA + bB ⇌ cC + dD

The equilibrium constant expression is:

Keq = [C]^c [D]^d / [A]^a [B]^b

Where brackets denote concentration in whatever unit you're using. The exponents come from the balanced equation coefficients—always.

Working Example

For the reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

With Kc: Kc = [NH₃]² / ([N₂][H₂]³)

Units would be (M)² / (M)(M)³ = M⁻², or (mol/L)⁻²

With Kp: Kp = (P_NH₃)² / (P_N₂·P_H₂³)

Units would be (atm)² / (atm)(atm)³ = atm⁻²

The units are inverse concentration or inverse pressure to some power, depending on Δn.

Getting Started: Solving Equilibrium Problems

Follow this process when you encounter equilibrium calculations:

1. Write the balanced equation. Non-negotiable. Everything downstream depends on this.
2. Identify the correct K form. Use Kc for aqueous, Kp for gases (or convert).
3. Express all concentrations in consistent units. Don't mix M and molality unless you know what you're doing.
4. Set up the K expression with your balanced coefficients as exponents.
5. Substitute equilibrium concentrations (often using x for the unknown change).
6. Solve algebraically or use the quadratic formula when necessary.
7. Check your answer. Plug values back into K to verify you get the known constant.

Common Mistakes That Kill Your Answer

• Using partial pressures when the problem asks for Kc (or vice versa) without converting
• Forgetting to raise coefficients to their powers in the equilibrium expression
• Ignoring solids and liquids in the K expression—they don't appear because their concentrations are constant
• Mixing up Kc and Kp when the reaction involves gases
• Not converting temperature to Kelvin when using the ideal gas constant

Which Unit Should You Actually Use?

It depends on the problem context:

• General chemistry course → Stick with M (mol/L) for everything
• Gas-phase problems → Kp with atm or bar, or convert to Kc
• Thermodynamics/physical chemistry → Dimensionless K using standard states
• Industrial applications → Often bar, because 1 bar ≈ 1 atm and it's the standard in engineering

When a problem doesn't specify, M is the safest default. When it specifies "pressure," use atm or bar. When it says "thermodynamic equilibrium constant," treat it as dimensionless.

The Bottom Line

Equilibrium constants aren't mysterious, but the units trip up students constantly. Kc uses concentration, Kp uses pressure, and you can convert between them using the ideal gas law. The "unitless" Keq in textbooks is just normalized to standard states—same information, different presentation.

Know which form your problem expects. Write the expression correctly with coefficients as exponents. Plug in numbers. Solve. Verify.

That's it. No shortcuts, no tricks—just follow the stoichiometry and the math.