Topic 7.7 Notes – Calculating Equilibrium Concentrations

1. Dynamic Equilibrium and the Role of K

At dynamic equilibrium, the forward and reverse reactions are happening at the same rate. Concentrations stop changing, but particles are still reacting.

The equilibrium constant $K$ tells you the ratio of products to reactants at equilibrium.

For a general reaction:

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

The equilibrium expression is:

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

Key details you must remember:

• Use $K_c$ for concentrations (M), $K_p$ for partial pressures (atm).
• Only gases and aqueous species go into the expression.
  • Skip solids and pure liquids.
• Coefficients become exponents.

Interpreting K

• $K \gg 1$ → mostly products at equilibrium.
• $K \ll 1$ → mostly reactants.
• $K$ only changes if temperature changes.

When you calculate equilibrium concentrations, you’re finding the values that satisfy this ratio.

2. Using Q to Predict the Direction of Change

Before doing any algebra, check which way the reaction will shift.

The reaction quotient $Q$ uses the same expression as $K$, but with current (usually initial) values.

Compare $Q$ to $K$:

• $Q < K$ → shifts right (makes products)
• $Q > K$ → shifts left (makes reactants)
• $Q = K$ → already at equilibrium

This determines the signs in your ICE table.

A common trap on tests: products are already present initially. If you skip calculating $Q$, you might assume the reaction shifts right when it actually shifts left.

3. The ICE Table Setup

ICE stands for Initial, Change, Equilibrium.

Here’s the general structure, shown for the reaction $\ce{I2 + I^{-} <=> I3^{-}}$:

Example ICE table for $\ce{I2 + I^{-} <=> I3^{-}}$

Initial row

• Write given concentrations or pressures.
• If a species isn’t present initially, write 0.

Change row

• Use $x$ to represent change.
• Reactants decrease.
• Products increase.
• Multiply $x$ by coefficients.

Equilibrium row

Add Initial + Change.
These expressions go into the $K$ equation.

4. Solving for Equilibrium Concentrations

Let’s walk through the structure using:

$$\ce{SO2Cl2(g) <=> SO2(g) + Cl2(g)} \quad K_c = 4.0 \times 10^{-3}$$

Suppose initial $[\ce{SO2Cl2}] = 0.80\,\text{M}$, others are 0.

Step-by-step

1. Write K expression

   $$K_c = \frac{[\ce{SO2}][\ce{Cl2}]}{[\ce{SO2Cl2}]}$$

2. Set up ICE

   • Initial: 0.80, 0, 0
   • Change: −x, +x, +x
   • Equilibrium: 0.80 − x, x, x

3. Substitute into K

   $$4.0 \times 10^{-3} = \frac{x^{2}}{0.80 - x}$$

When K Is Small

Here, $K$ is small. That means very little product forms.

So $0.80 - x \approx 0.80$

$$4.0 \times 10^{-3} = \frac{x^{2}}{0.80}$$

$$x^{2} = (0.80)(4.0 \times 10^{-3})$$

$$x = 0.056$$

Now check the 5% rule:

$$\frac{0.056}{0.80} \times 100\% = 7\%$$

That’s greater than 5%, so technically you’d need the quadratic. On the AP exam, they often choose numbers that pass the 5% rule cleanly.

The 5% Rule

You may approximate $a - x \approx a$ only if:

$$\frac{x}{a} \times 100\% < 5\%$$

Important:

• You can only eliminate $x$ when it’s added to or subtracted from a large number.
• Never drop terms like $4x$. That destroys the equation.

5. Special Situations to Watch For

Non-zero Initial Products

If products are present initially:

• Calculate $Q$.
• Reaction might shift left.
• That means reactants increase and products decrease in the Change row.

Sign mistakes here are one of the most common quiz errors.

Using Partial Pressures

For gases:

• Use $K_p$
• ICE table uses atm
• Math is identical.

Checking Your Answer

At equilibrium:

• All concentrations must be positive.
• Values must match the size of $K$.
  • Small $K$ → mostly reactants.
  • Large $K$ → mostly products.

If your answer contradicts what $K$ suggests, something went wrong in setup.