Equilibrium Constant (K) Calculator

What Is an Equilibrium Constant?

A reaction that can run forward and backward is a reversible reaction. It reaches equilibrium when the forward and reverse reactions happen at the same rate, so the amounts of each substance stop changing. The equilibrium constant (K) is a number that compares the amount of product to the amount of reactant at that point. This calculator finds K from the concentrations and coefficients you enter.

Equilibrium Constant Formula

For a balanced reaction:

$aA + bB \rightleftharpoons cC + dD$

the equilibrium constant expression is:

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

Products go on top, reactants go on the bottom. The square brackets mean "concentration in moles per liter (mol/L)." Each concentration is raised to the power of its coefficient from the balanced equation.

How to Calculate the Equilibrium Constant

1. Write the balanced equation and note each coefficient.
2. Find each concentration at equilibrium, not at the start of the reaction.
3. Raise each concentration to the power of its coefficient.
4. Multiply the product terms together, multiply the reactant terms together, then divide the first result by the second.

Example: Hydrogen Iodide Formation

The reaction H₂ + I₂ ⇌ 2HI reaches equilibrium in a sealed container. Measured concentrations are:

• [H₂] = 0.2 mol/L
• [I₂] = 0.1 mol/L
• [HI] = 0.4 mol/L

$K = \frac{[HI]^2}{[H_2][I_2]} = \frac{(0.4)^2}{0.2 \times 0.1} = \frac{0.16}{0.02} = 8.0$

K is close to 1, so both reactants and products are present in measurable amounts at equilibrium.

Example: Ammonia Synthesis (Haber Process)

The reaction N₂ + 3H₂ ⇌ 2NH₃ makes ammonia for fertilizer. Suppose these equilibrium concentrations are measured:

• [N₂] = 0.10 mol/L
• [H₂] = 0.20 mol/L
• [NH₃] = 0.30 mol/L

$K = \frac{[NH_3]^2}{[N_2][H_2]^3} = \frac{(0.30)^2}{0.10 \times (0.20)^3} = \frac{0.09}{0.0008} = 112.5$

The coefficient of 3 on H₂ becomes an exponent of 3 in the formula. A K value above 100 means the reaction favors products under these conditions.

What Counts in the Equilibrium Expression

Only gases and dissolved substances appear in K. Pure solids and pure liquids are left out, because their concentration stays the same no matter how much is present. For the reaction CaCO₃(s) ⇌ CaO(s) + CO₂(g), the expression is just K = [CO₂]. The two solids are dropped.

A K value only applies at the temperature it was measured at. Changing the temperature changes K itself. Pressure and catalysts change how fast a reaction reaches equilibrium, but neither one changes the value of K.

Types of Equilibrium Constants

Chemists use different labels depending on what is measured.

• Kc: based on concentrations in mol/L. This is what the calculator above computes.
• Kp: based on the partial pressures of gases, related to Kc by Kp = Kc(RT)^Δn.
• Ka and Kb: describe how far a weak acid or weak base breaks apart in water.
• Ksp: describes how much of a solid dissolves in water; called the solubility product.

Each one follows the same rule: products over reactants, each raised to its coefficient.

Using the Calculator

Choose how many reactants and products the reaction has, up to five of each. For every substance, enter its concentration in mol/L and its coefficient from the balanced equation. The calculator multiplies out both sides and divides automatically. Results above 1000 or below 0.001 display in scientific notation, for example 1.2340e+4 instead of 12340.

A common mistake is entering starting concentrations instead of equilibrium concentrations. That gives the reaction quotient, Q, instead of K. Q uses the same formula as K but can be calculated at any point in the reaction, not only at equilibrium. Comparing Q with K shows which way a reaction still needs to shift: if Q is less than K, the reaction moves toward products; if Q is greater than K, it moves toward reactants.

Frequently Asked Questions

What does a large or small K value mean?

A K much greater than 1 means the reaction favors products at equilibrium. A K much less than 1 means it favors reactants. A K near 1 means both sides are present in similar amounts.

Why are solids and liquids left out of the K expression?

Because their concentration does not change. A block of solid has the same density whether it is large or small, so including it would only multiply K by a constant, which never changes.

Does temperature change K?

Yes. Raising the temperature increases K for reactions that absorb heat and decreases K for reactions that release heat. A K value is only valid at the temperature it was found for.

Does pressure or a catalyst change K?

No. A catalyst speeds up how fast a reaction reaches equilibrium but does not move the equilibrium itself. Pressure can change the concentrations of gases at equilibrium, but K calculated from those new concentrations stays the same.

Can K be negative?

No. K comes from concentrations, which are always positive, raised to positive whole-number powers. A negative or zero result means reactants and products were mixed up in the formula.

What is the difference between K and Q?

K describes a reaction once it reaches equilibrium. Q uses the same formula but works with concentrations at any other moment. Comparing Q to K predicts which direction a reaction will shift next.

History

Norwegian chemists Cato Guldberg and Peter Waage proposed the law of mass action in 1864. It led to the equilibrium constant expression used today. Dutch chemist Jacobus van 't Hoff later worked out how K depends on temperature, part of the research that earned him the first Nobel Prize in Chemistry in 1901.