Introductory General Chemistry · Unit 14

Chemical Equilibrium

Start here: equilibrium is not a stopped reaction. It is a reversible system that settles into balance. In this unit, you will learn how to compare Q and K, predict shifts, and use ICE tables without guessing. This is the bridge from solutions and concentration into acids, bases, and pH.

What you'll learn

Write equilibrium expressions (K) for homogeneous and heterogeneous reactions. Use the reaction quotient Q to predict which direction a reaction will shift. Apply Le Châtelier's Principle to changes in concentration, pressure, and temperature. Set up and solve ICE tables to find equilibrium concentrations.

14.1 Start Here: What Chemical Equilibrium Actually Means

Some reactions do not just run forward once and stop. Many are reversible, which means the products can react to form reactants again. We show that with a double arrow (⇌).

As reactants are used up, the forward reaction slows down. At the same time, the reverse reaction speeds up because more product is available.

When those two rates become equal, the system reaches equilibrium.

Do not miss this: at equilibrium, concentrations stop changing, but particles are still reacting in both directions. This is a dynamic equilibrium, not a frozen one.

General Reversible Reaction

aA + bB ⇌ cC + dD

▸

Equal rates ≠ equal concentrations.
Equal rates means equal rates — not equal concentrations, not a 50/50 split.

14.2 Q vs K: How to Tell Which Way a Reaction Will Shift

Start here: Q tells you where the system is right now, and K tells you where equilibrium wants that ratio to end up. If you can compare those two values, you can predict the direction of shift before doing any ICE table work.

For the general reversible reaction aA + bB ⇌ cC + dD, use this ratio of product concentrations to reactant concentrations, each raised to its stoichiometric coefficient:

Reaction Quotient and Equilibrium Constant

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

When that ratio is calculated using equilibrium concentrations, it becomes the equilibrium constant K. For one reaction at one temperature, K has one fixed value.

Concrete read: if K = 4.0 × 10³, products are strongly favored at equilibrium. If K = 2.0 × 10⁻⁵, reactants are strongly favored. If this feels shaky, read K as a snapshot of which side wins out at equilibrium.

Comparison	Meaning	Direction of Shift
Q < K	Too many reactants relative to equilibrium	Forward (→) to make more products
Q = K	System is at equilibrium	No net shift
Q > K	Too many products relative to equilibrium	Reverse (←) to make more reactants

▸

A large K (≫1) means products are favored at equilibrium.
A small K (≪1) means reactants are favored.
Notice the mistake to avoid: Q tells you the current direction of shift. K tells you the equilibrium target for that reaction at that temperature.

14.3 Which Substances Go Into K and Which Ones Stay Out

In a homogeneous equilibrium, all species are in the same phase, such as all gases or all aqueous ions. In a heterogeneous equilibrium, more than one phase is present.

The most commonly skipped rule: pure solids and pure liquids are omitted from the K expression. Their concentrations do not meaningfully change, so they are built into the constant itself.

Concrete check: for CaCO₃(s) ⇌ CaO(s) + CO₂(g), both solids stay out, so CO₂ is the only term that appears in K.

Example Reaction	K Expression	Why?
CaCO₃(s) ⇌ CaO(s) + CO₂(g)	K = [CO₂]	Both solids omitted
C(s) + O₂(g) ⇌ CO₂(g)	K = [CO₂] [O₂]	Solid C omitted
N₂(g) + 3H₂(g) ⇌ 2NH₃(g)	K = [NH₃]² [N₂][H₂]³	All gases included

14.4 Le Châtelier's Principle: Predicting How Equilibrium Responds

Le Châtelier's Principle: when a system at equilibrium is stressed, it shifts in the direction that partly reduces that stress.

Start with the stress. Then ask what change would counter it. That thinking will carry you through concentration changes, pressure changes, and temperature changes without memorizing random arrows.

Concentration changes

Change	System response	Effect on K
Add a reactant	Shift right to use some of the added reactant	K unchanged
Remove a reactant	Shift left to replace some of the reactant	K unchanged
Add a product	Shift left to use some of the added product	K unchanged
Remove a product	Shift right to replace some of the product	K unchanged

Pressure or volume changes (gases only)

Change	System response	Effect on K
Increase pressure by decreasing volume	Shift toward the side with fewer moles of gas	K unchanged
Decrease pressure by increasing volume	Shift toward the side with more moles of gas	K unchanged
Same total moles of gas on both sides	No shift	K unchanged

Temperature changes

Change	System response	Effect on K
Increase temperature	Shift in the endothermic direction	K changes
Decrease temperature	Shift in the exothermic direction	K changes

Treat heat as part of the reaction. If the forward reaction is exothermic, heat acts like a product. If the forward reaction is endothermic, heat acts like a reactant. This connects directly to the energy ideas from thermochemistry.

▸

Temperature is the only disturbance that changes K.
Concentration changes, pressure changes, and catalysts do not change K.
Keep these two ideas separate: shifting the equilibrium position is not the same as changing K.

14.5 ICE Tables: Setting Up Equilibrium Problems Step by Step

If this feels shaky, slow down and make the setup do the thinking for you. Use an ICE table only after you know which way the reaction must move. ICE stands for Initial concentrations, Change in concentrations, and Equilibrium concentrations.

Step 1 — Write the balanced equation and the K expression

Use the balanced equation to place the correct species and exponents into K. If your equation is wrong here, the rest of the math will be wrong too.

Step 2 — Decide the direction of shift

If Q < K, the reaction shifts right. If Q > K, the reaction shifts left. If the system starts with no products, then Q = 0, so it shifts right.

Step 3 — Fill in the I row

Write the initial concentration of each species.

Step 4 — Fill in the C row with x

If the reaction shifts right, reactants decrease and products increase. If the reaction shifts left, products decrease and reactants increase. Use the coefficients to scale each change. This is where sign mistakes usually happen.

Step 5 — Write the E row

For each species, equilibrium concentration = initial + change.

Step 6 — Substitute into K and solve

Substitute the equilibrium expressions into K and solve for x.

What a real ICE table looks like: here is a simple setup for the water-gas shift reaction starting with only reactants present.

Worked ICE Setup

CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)

K = [CO₂][H₂][CO][H₂O]

Row	CO(g)	H₂O(g)	CO₂(g)	H₂(g)
Initial	0.100 M	0.100 M	0 M	0 M
Change	−x	−x	+x	+x
Equilibrium	0.100 − x	0.100 − x	x	x

Because the reaction starts with no products, Q = 0, so the system must shift right. That is why the reactants get −x and both products get +x. Notice that the signs come from the direction of shift, not from a guess.

Then substitute the equilibrium row into K

Every concentration in the equilibrium expression must come from the E row of the ICE table.

K = [CO₂][H₂][CO][H₂O]

K = (x)(x)(0.100 − x)(0.100 − x)

K = x²(0.100 − x)²

This is the equation you would solve once the problem gives you a value for K.

Quick sign check

Shift right: reactants get −x, products get +x

Shift left: reactants get +x, products get −x

▸

Before you simplify

If K is very small (<10⁻⁴) and initial concentrations are not tiny, you can often assume x is negligible compared to the initial concentration.
Always verify: x must be <5% of initial concentration.
Do not use the small-x shortcut unless the numbers justify it.

14.6 Catalysts: What Changes Faster and What Does Not Change at All

A catalyst lowers the activation energy of both the forward and reverse reactions equally. That means equilibrium is reached faster, but the equilibrium position, the value of K, and the final concentrations are not changed.

Keep this straight: rate is about how fast the system gets there. Equilibrium position is about where it ends up.

Catalyst Effect Summary

Catalyst → faster rate, same K, same equilibrium concentrations

Use these tools the way you would work through equilibrium in class: identify the rule first, make the prediction second, then check the reasoning. If you want a full mixed set after this, move into the Unit 14 Practice page before you head to acids and bases.

Explore 1 — Dynamic Equilibrium: Rates or Amounts?

Read This First

At equilibrium, what must be true?

Focus on what must stay true at equilibrium, not on what only happens sometimes.

Scenario: You are looking at a reversible reaction that has settled into dynamic equilibrium. Choose the statement that must be true before you check.

Choose one statement, then click Check.

Explore 2 — Q vs K: Which Way Will It Shift?

Read This First

Compare Q with K, then choose the net shift.

Ask one question first: does the system need more products or more reactants to match K?

Problem: Use the values below to decide whether the reaction shifts right, left, or not at all.

Q = 0.20

K = 5.0

Choose a shift, then click Check.

Explore 3 — Pressure Change: Which Side Is Favored?

Read This First

Choose the net shift.

Count gas moles on each side before deciding how a pressure change affects the system.

Scenario: Use the reaction and the pressure stress below to predict the net shift.

Reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Stress: Pressure increases because volume decreases

Choose a shift, then click Check.

Explore 4 — Temperature and K

Read This First

What happens to K?

Treat heat like a reactant or a product before you decide how K changes.

Problem: Use the reaction type and temperature change below to predict what happens to the equilibrium constant.

Reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

Forward reaction: Exothermic

Change: Temperature increases

Choose what happens to K, then click Check.

Example 1 · Writing the K Expression

Problem: Write the equilibrium-constant expression.

Given: 2NO(g) + O₂(g) ⇌ 2NO₂(g)

Find: K expression

Step 1 — Identify products and reactants with coefficients

Products: NO₂ with coefficient 2. Reactants: NO with coefficient 2, O₂ with coefficient 1.

Step 2 — Write K as a fraction with products on top and reactants on the bottom, each raised to its coefficient

K = [NO₂]²[NO]²[O₂]

Step 3 — Check: all species are gaseous → homogeneous equilibrium → all included

There are no pure solids or liquids to omit.

Final answer:

K = [NO₂]²[NO]²[O₂]

Example 2 · Comparing Q to K to Predict Shift Direction

Problem: Compare Q to K to predict the shift direction.

Given: N₂(g) + 3H₂(g) ⇌ 2NH₃(g), K = 6.0 × 10⁻², [N₂] = 1.0 M, [H₂] = 2.0 M, [NH₃] = 3.0 M

Find: direction of shift

Step 1 — Write the Q expression (same form as K)

Q = [NH₃]²[N₂][H₂]³

Step 2 — Substitute current concentrations

Q = (3.0)²(1.0)(2.0)³ = 9.08.0 = 1.125

Step 3 — Compare Q to K

Q = 1.125 and K = 0.060, so Q > K.

That means the mixture has too many products compared with equilibrium, so the reaction shifts in the reverse direction (←) until the ratio drops back to K.

Example 3 · ICE Table — Finding Equilibrium Concentrations

Problem: Use an ICE table to find equilibrium concentrations.

Given: H₂(g) + I₂(g) ⇌ 2HI(g), K = 49.0, [H₂]₀ = 0.500 M, [I₂]₀ = 0.500 M, [HI]₀ = 0 M

Find: equilibrium concentrations of all species

Step 1 — Write the K expression that matches the balanced equation

K = [HI]²[H₂][I₂]

This tells you exactly which equilibrium-row expressions must be substituted later.

Step 2 — Decide the direction first

At the start, [HI] = 0, so Q = 0.

Since Q < K, the reaction shifts right to make more HI.

Step 3 — Set up the ICE table

	H₂	I₂	HI
I	0.500	0.500	0
C	−x	−x	+2x
E	0.500−x	0.500−x	2x

Step 4 — Substitute E expressions into K

K = [HI]²[H₂][I₂]

The column heading stays HI. The coefficient 2 appears in the change row as +2x and in the equilibrium expression as the exponent on [HI].

K = (2x)²(0.500−x)² = 49.0

Take the square root of both sides (both sides are perfect squares):

2x0.500 − x = 7.00

Step 5 — Solve for x

2x = 7.00(0.500 − x) → 2x = 3.50 − 7.00x

9.00x = 3.50 → x = 0.389 M

Step 6 — Calculate equilibrium concentrations

[H₂] = 0.500 − 0.389 = 0.111 M

[I₂] = 0.111 M

[HI] = 2(0.389) = 0.778 M

Check:

K = (0.778)²(0.111)² = 0.60530.01232 ≈ 49.1 ✓

Example 4 · Le Châtelier's Principle — Pressure Change

Problem: Predict the effect of a pressure increase using Le Châtelier's principle.

Given: N₂(g) + 3H₂(g) ⇌ 2NH₃(g); total pressure increases because volume decreases

Find: direction of shift

Step 1 — Count moles of gas on each side

Reactants: 1 mol N₂ + 3 mol H₂ = 4 mol gas. Products: 2 mol NH₃ = 2 mol gas.

Step 2 — Apply Le Châtelier's Principle

Increasing pressure (by decreasing volume) stresses the system. To reduce this stress, the system shifts toward the side with fewer moles of gas.

Step 3 — State the result

The reaction shifts forward (→), producing more NH₃ and reducing the total number of gas molecules.

This is why the Haber process is run at high pressure: it improves NH₃ yield.

Important check: pressure only changes the equilibrium position if the two sides have different total moles of gas. If the gas moles are equal on both sides, there is no shift, and K still stays the same.

▸

Next step after Unit 14

Once equilibrium makes sense, acids and bases become much easier to follow. You will use the same ideas about reversible reactions, favored sides, and equilibrium constants again in Unit 15: Acids & Bases.

Introductory General Chemistry · Unit 14 · Chemical Equilibrium