Equilibrium Constant- Chemical Reaction Calculations
What the Equilibrium Constant Actually Is
The equilibrium constant (K) is a number that tells you the ratio of product concentrations to reactant concentrations at equilibrium. That's it. No philosophy, no metaphors.
When a reaction reaches equilibrium, the forward and reverse reactions happen at the same rate. The constant captures where that balance sits. A big K means the reaction favors products. A small K means reactants win out.
You calculate it from the balanced chemical equation. Change the equation, and you change the constant.
The Basic Formula You Need to Memorize
For a general reaction:
aA + bB ⇌ cC + dD
The equilibrium constant expression is:
Keq = [C]c[D]d / [A]a[B]b
Products go on top. Reactants go on bottom. Each concentration gets raised to the power of its coefficient in the balanced equation.
Concentrations are in molarity (mol/L) for reactions in solution. For gases, you use partial pressures.
Kc vs Kp — Which One Do You Use?
Kc uses concentrations in mol/L. You see this with reactions happening in solution.
Kp uses partial pressures. You see this with gas-phase reactions.
For gas reactions, you can convert between them:
Kp = Kc(RT)Δn
Where:
- R = 0.0821 L·atm/(mol·K)
- T = temperature in Kelvin
- Δn = (moles of gaseous products) − (moles of gaseous reactants)
When Δn = 0
Kp equals Kc. This happens when the number of gas molecules on both sides is the same.
What the Value of K Actually Means
K > 1: Products are favored at equilibrium. The reaction "goes" in the forward direction.
K < 1: Reactants are favored. The equilibrium lies toward the left.
K ≈ 1: Neither products nor reactants are strongly favored. The equilibrium sits roughly in the middle.
K ≈ 0: The reaction essentially doesn't proceed in the forward direction. You get almost no products.
K very large (1030+): The reaction goes essentially to completion. You get essentially 100% products.
Homogeneous vs Heterogeneous Equilibrium
Homogeneous Equilibrium
All reactants and products are in the same phase (usually all gases or all in solution).
Example: 2SO2(g) + O2(g) ⇌ 2SO3(g)
You include everything in the K expression.
Heterogeneous Equilibrium
Reactants and products are in different phases.
Example: CaCO3(s) ⇌ CaO(s) + CO2(g)
Solids and pure liquids don't appear in the equilibrium expression. Their concentrations are constant and built into the K value.
So for the CaCO3 decomposition:
Kp = PCO2
Only the gas matters. The solids are ignored.
Solubility Product Constant (Ksp)
For salts dissolving in water:
AgCl(s) ⇌ Ag+(aq) + Cl−(aq)
Ksp = [Ag+][Cl−]
Solids don't appear. You only include the dissolved ions.
Using Ksp to Find Solubility
If Ksp for AgCl = 1.8 × 10−10
Let s = molar solubility (mol/L)
[Ag+] = s and [Cl−] = s
Ksp = s²
s = √(1.8 × 10−10) = 1.3 × 10−5 M
Writing Equilibrium Expressions — Common Mistakes
- Forgetting to balance the equation. Coefficients become exponents. If you don't balance first, your K will be wrong.
- Including solids or liquids. Only gases and aqueous species go in the expression.
- Reversing the numerator and denominator. Products top, reactants bottom. Always.
- Using initial concentrations instead of equilibrium concentrations. K uses equilibrium values, not what you started with.
How to Calculate Equilibrium Constants
Step 1: Write the balanced equation
Everything depends on getting this right. Balance first.
Step 2: Write the K expression
Products over reactants. Coefficients become exponents.
Step 3: Plug in equilibrium concentrations
Use the equilibrium concentrations (or partial pressures), not the initial values.
Step 4: Solve
Work through the math. Watch your significant figures.
Example Problem
For the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g)
At equilibrium, concentrations are:
- [N2] = 0.40 M
- [H2] = 0.60 M
- [NH3] = 0.20 M
Find Kc.
Kc = [NH3]2 / ([N2][H2]3)
Kc = (0.20)2 / (0.40 × 0.603)
Kc = 0.04 / (0.40 × 0.216)
Kc = 0.04 / 0.0864
Kc = 0.463
Using ICE Tables to Find Equilibrium Concentrations
ICE stands for Initial, Change, Equilibrium. You use these when you're given initial concentrations and asked to find equilibrium values.
Example
2.0 mol PCl5 is placed in a 1.0 L container. It decomposes:
PCl5(g) ⇌ PCl3(g) + Cl2(g)
Kc = 0.040
Find equilibrium concentrations.
Step 1: Set up the ICE table
| PCl5 | PCl3 | Cl2 | |
|---|---|---|---|
| I | 2.0 | 0 | 0 |
| C | −x | +x | +x |
| E | 2.0−x | x | x |
Step 2: Write K expression and solve
Kc = [PCl3][Cl2] / [PCl5]
0.040 = (x)(x) / (2.0 − x)
0.040(2.0 − x) = x²
0.080 − 0.040x = x²
x² + 0.040x − 0.080 = 0
Using the quadratic formula:
x = 0.24 M
Step 3: Find equilibrium concentrations
- [PCl5] = 2.0 − 0.24 = 1.76 M
- [PCl3] = 0.24 M
- [Cl2] = 0.24 M
When to Use the Quadratic vs Approximation
If K is very small (< 10−4) and initial concentration is reasonable, x will be tiny. You can ignore it in the denominator and avoid the quadratic.
If K is larger, solve the quadratic. The approximation fails.
Reaction Quotient (Q) — Predicting Direction
Q uses the same formula as K, but you plug in concentrations at any point in the reaction—not just at equilibrium.
If Q < K: Reaction shifts right (toward products) to reach equilibrium.
If Q > K: Reaction shifts left (toward reactants) to reach equilibrium.
If Q = K: The system is already at equilibrium. Nothing shifts.
This is useful for predicting what happens when you disturb a system.
Le Chatelier's Principle and K
When you change conditions (concentration, pressure, temperature), the system shifts to counteract the change. That's Le Chatelier's principle.
Concentration changes: K doesn't change. The system just uses up or produces more reactants/products until Q = K again.
Pressure changes: K doesn't change (unless the change affects temperature). Only the equilibrium position shifts.
Temperature changes: K changes. This is the only thing that actually changes the equilibrium constant.
Quick Reference: K Types
| Type | What It Measures | Units |
|---|---|---|
| Kc | Concentration ratio | Varies |
| Kp | Pressure ratio | Varies |
| Ksp | Solubility product | Varies |
| Ka | Acid dissociation | Dimensionless |
| Kb | Base dissociation | Dimensionless |
| Kw | Water ion product | 1 × 10−14 |
Getting Started: Your Calculation Checklist
Before you start any equilibrium problem:
- ✅ Is the equation balanced? If not, balance it first.
- ✅ Are you using Kc or Kp? Use concentrations for solutions, partial pressures for gases.
- ✅ Did you exclude solids and pure liquids from the expression?
- ✅ Are you using equilibrium concentrations, not initial ones?
- ✅ Did you check your units? K often has no units, but sometimes it does.
The Bottom Line
The equilibrium constant is a ratio. Products over reactants, with coefficients as exponents. That's the entire concept.
What trips people up is the algebra—the ICE tables, the quadratic equations, the unit conversions. Master those mechanics and equilibrium problems become routine. The chemistry itself is straightforward.