Topic 7.4 Notes – Calculating the Equilibrium Constant

1. The Equilibrium Constant K

At equilibrium, a reversible reaction has a constant ratio of products to reactants. That ratio is the equilibrium constant, K.

For a general reaction:

$$\ce{aA + bB <=> cC + dD}$$

The equilibrium constant expression is:

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

$$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$

Here’s what actually matters:

• Use equilibrium values only.
• The exponents come from coefficients in the balanced equation.
• Include only gases (g) and aqueous (aq) species.
• Exclude solids (s) and pure liquids (l).
• On the AP exam, treat K as unitless.
• $K > 1$ means products favored.
• $K < 1$ means reactants favored.
• K is never negative.

Quick example:

$$\ce{2SO2(g) + O2(g) <=> 2SO3(g)}$$

$$K_c = \frac{[SO3]^{2}}{[SO2]^{2}[O2]}$$

Notice the exponents match the coefficients. If you forget that, you lose easy points.

Big picture: K tells you the position of equilibrium, not how fast it was reached.

2. The Two Forms of K

Which version you use depends entirely on what data you’re given.

Kc Concentration-Based

Use Kc when you’re given:

• Molarity (M)
• Moles and volume (convert to molarity)
• Grams (convert grams → moles → molarity)

Square brackets mean mol/L at equilibrium.

If given moles in a container:

$$\text{Molarity} = \frac{\text{moles}}{\text{liters}}$$

Students often forget to convert mL to L. That mistake snowballs through the whole problem.

Kp Pressure-Based

Use Kp when you’re given:

• Partial pressures
• Information to calculate partial pressures

Only gases appear in a Kp expression.

If you’re given total pressure and moles, use mole fraction:

$$P_A = X_A \times P_{\text{total}}$$

where $X_A = \frac{\text{moles of A}}{\text{total moles}}$.

Here’s the side-by-side comparison:

3. Calculating K from Experimental Data

This is usually straightforward if you stay organized.

Step-by-step

1. Write and balance the reaction.
2. Write the correct K expression.
3. Make sure values are at equilibrium.
4. Convert to correct form (M or pressure).
5. Substitute carefully.
6. Raise each term to its coefficient.
7. Calculate.

Example:

$$\ce{H2(g) + I2(g) <=> 2HI(g)}$$

At equilibrium in a 1.50 L container:

• 0.300 mol $\ce{H2}$
• 0.300 mol $\ce{I2}$
• 0.900 mol $\ce{HI}$

Convert to molarity:

$$[H2] = \frac{0.300}{1.50} = 0.200 \text{ M}$$ $$[I2] = 0.200 \text{ M}$$ $$[HI] = 0.600 \text{ M}$$

Write expression:

$$K_c = \frac{[HI]^{2}}{[H2][I2]}$$

Substitute:

$$K_c = \frac{(0.600)^{2}}{(0.200)(0.200)} = \frac{0.360}{0.0400} = 9.0$$

So the reaction is product-favored.

Common trap: using initial values. That gives you Q, not K. On MCQs they love sneaking that in.

Also watch for mixed phases. If a reaction includes $\ce{CaCO3(s)}$, you leave it out of the expression completely.

4. Interpreting the Magnitude of K

K describes the ratio at equilibrium.

• $K > 1$ → more products than reactants.
• $K < 1$ → more reactants than products.
• Very large K (like $10^{6}$) → reaction goes almost to completion.
• Very small K (like $10^{-6}$) → barely forms product.

K does not tell you:

• The speed of the reaction.
• How much you started with.
• The time to reach equilibrium.

It only reflects the system once equilibrium is established.

On FRQs, when they ask you to interpret a K value, they want a statement about relative amounts at equilibrium, not reaction rate.

5. Common AP Mistakes

• Including solids or pure liquids.
• Forgetting coefficients as exponents.
• Using moles instead of molarity for Kc.
• Forgetting mL → L conversion.
• Using total pressure instead of partial pressure.
• Writing reactants over products.
• Using non-equilibrium values.

Most equilibrium constant questions are precision questions. Small setup errors cost big points.