E. Chemical Systems and Equilibrium · Chemical Equilibrium

Reversible Reactions and Dynamic Equilibrium

E3.1 E2.1 A1.12About 70 minutes

Learning goals

I can explain what a reversible reaction and a closed system are.
I can describe dynamic equilibrium in terms of equal forward and reverse rates and constant concentrations.
I can give examples of physical (phase and solubility) and chemical equilibrium systems.
I can use mole ratios to find equilibrium amounts and the percent reaction from one measured value.

Words to know

reversible reaction
A reaction that can go in both directions: reactants form products, and products re-form reactants. Written with the double arrow ⇌.

closed system
A system that no matter can enter or leave (energy can still be exchanged), such as a sealed flask.

dynamic equilibrium
The state of a reversible process in a closed system where the forward and reverse rates are equal, so concentrations and other observable properties stay constant even though both reactions continue.

phase equilibrium
A dynamic equilibrium between two states of the same substance, such as liquid water and water vapour in a sealed bottle.

solubility equilibrium
A dynamic equilibrium in a saturated solution between the undissolved solid and its dissolved particles.

percent reaction
The equilibrium amount of a product as a percentage of the amount that would form if the reaction went to completion (sometimes called the equilibrium yield).

The bottle that never dries out

Leave an open glass of water on a sunny windowsill and in a few days it is empty. Leave a sealed bottle with a little water in it beside the glass and, weeks later, the water is still there. Tiny droplets bead on the inside of the bottle, the water level stops dropping, and nothing seems to happen.

But a lot is happening. Water molecules are still escaping from the liquid every second. Others are returning to it just as fast. This balance of two opposite processes is called dynamic equilibrium, and it is the big idea of this whole unit.

Remember from Grade 11

In Quantities in Chemical Reactions (SCH3U) you learned that some reactions stop part-way, leaving reactants and products mixed together. In Solutions and Solubility you met saturated solutions, and in Gases and Atmospheric Chemistry you met vapour pressure, the pressure of a vapour in equilibrium with its liquid. This unit explains all three with one idea.

Reversible reactions

In Grade 11 most reactions were treated as if they went to completion: one arrow, →, and the limiting reagent was used up. Many reactions can also run backwards. Hydrogen and iodine gases react to form hydrogen iodide, and hydrogen iodide also breaks down into hydrogen and iodine:

forward: H₂(g) + I₂(g) → 2 HI(g)
reverse: 2 HI(g) → H₂(g) + I₂(g)

We combine the two with a double arrow: H₂(g) + I₂(g) ⇌ 2 HI(g). The substances on the left are still called the reactants and those on the right the products, but both reactions happen at once.

How equilibrium is reached

Put 1.00 mol of H₂ and 1.00 mol of I₂ into a sealed 1.00 L flask at about 450 °C.

At first there is no HI, so only the forward reaction happens, and it is fast because [H₂] and [I₂] are high. (Square brackets mean concentration in mol/L.)
As H₂ and I₂ are used up, the forward reaction slows down. As HI builds up, the reverse reaction speeds up.
Eventually the two rates become equal. From then on, HI forms exactly as fast as it breaks down, so all the concentrations stay constant. The system is at equilibrium.

Concentrations in the H₂ + I₂ ⇌ 2 HI flask. H₂ and I₂ fall from 1.00 mol/L and HI rises from zero until all three level off (shaded): equilibrium. The concentrations are constant, but they are not equal.

The forward rate falls and the reverse rate rises until they are equal. Both reactions keep going; that is why the equilibrium is called dynamic.

The four conditions of dynamic equilibrium

A system is at dynamic equilibrium when:

It is a closed system (nothing can escape or be added) at a constant temperature.
The forward and reverse rates are equal.
The observable (macroscopic) properties are constant: colour, pressure, concentration, mass of solid, and so on.
It can be reached from either direction. Start with pure HI instead of H₂ and I₂, and the same kind of equilibrium mixture forms.

Two common misconceptions:

Equilibrium means equal amounts. No. It means equal rates. In the HI flask, there is about seven times as much HI as H₂ at equilibrium.
At equilibrium the reaction has stopped. No. On the particle level, both reactions continue. Chemists showed this with isotopes: if solid sodium iodide made with radioactive iodide ions is added to a saturated sodium iodide solution, the solution soon becomes radioactive, although the amount of dissolved salt does not change. Labelled ions are dissolving while unlabelled ones crystallize.

In an open glass, water vapour escapes, so the liquid keeps evaporating. In a sealed bottle, vapour builds up until condensation is as fast as evaporation: a phase equilibrium.

Three kinds of equilibrium

Phase equilibrium: a substance in two states, such as H₂O(l) ⇌ H₂O(g) in a sealed bottle, or ice and water at 0 °C in an insulated cooler.
Solubility equilibrium: a saturated solution with extra solid, such as NaCl(s) ⇌ Na⁺(aq) + Cl⁻(aq). (You will calculate these with Ksp in the unit Acid-Base and Solubility Equilibria.)
Chemical equilibrium: a reversible reaction, such as N₂O₄(g) ⇌ 2 NO₂(g). Dinitrogen tetroxide is colourless and nitrogen dioxide is reddish brown, so a sealed tube of the mixture settles to a steady shade of brown.

When all the substances are in the same phase (all gases, or all in one solution), it is a homogeneous equilibrium. When more than one phase is present (a solid and a solution, a liquid and a gas), it is a heterogeneous equilibrium.

Worked example

Example 1: Finding equilibrium amounts from one measurement

1.00 mol of H₂ and 1.00 mol of I₂ are sealed in a 1.00 L flask. At equilibrium, [HI] = 1.56 mol/L. Find the equilibrium [H₂] and [I₂], and the percent reaction.

Use the mole ratio. Making 2 mol of HI uses 1 mol of H₂ and 1 mol of I₂, so the H₂ used = 1.56 ÷ 2 = 0.780 mol/L.
[H₂] at equilibrium = 1.00 − 0.780 = 0.220 mol/L. By the same reasoning, [I₂] = 0.220 mol/L.
If the reaction went to completion, 1.00 mol/L of H₂ would make 2.00 mol/L of HI.
Percent reaction = 1.56 ÷ 2.00 × 100 % = 78.0 %.

[H₂] = [I₂] = 0.220 mol/L; percent reaction = 78.0 %. Organizing this kind of work in a table of Initial, Change and Equilibrium values is called an ICE table; you will use it all unit.

Worked example

Example 2: Same equilibrium from either side

At 25 °C, flask A starts with 0.100 mol/L of N₂O₄ and no NO₂. Flask B starts with 0.200 mol/L of NO₂ and no N₂O₄. At equilibrium, flask A has [NO₂] = 0.0203 mol/L. Predict [NO₂] and [N₂O₄] at equilibrium in flask B, and find [N₂O₄] in flask A.

Flask A: N₂O₄ ⇌ 2 NO₂. Making 0.0203 mol/L of NO₂ uses 0.0203 ÷ 2 = 0.01015 mol/L of N₂O₄.
[N₂O₄] in A = 0.100 − 0.01015 = 0.0898 mol/L (0.08985 before rounding).
Flask B contains the same atoms: 0.200 mol/L of NO₂ is equivalent to 0.100 mol/L of N₂O₄ (2 : 1 ratio), at the same temperature and volume.
So B reaches the same equilibrium mixture from the other direction: [NO₂] = 0.0203 mol/L and [N₂O₄] = 0.0898 mol/L.

Both flasks: [NO₂] = 0.0203 mol/L and [N₂O₄] = 0.0898 mol/L. In flask B the reverse reaction ran first. Notice that only about 10 % of the N₂O₄ broke apart: this equilibrium favours the reactant at 25 °C.

System	Type	Homogeneous or heterogeneous?
H₂O(l) ⇌ H₂O(g) in a sealed bottle	phase	heterogeneous
NaCl(s) ⇌ Na⁺(aq) + Cl⁻(aq), saturated	solubility	heterogeneous
N₂O₄(g) ⇌ 2 NO₂(g)	chemical	homogeneous
CaCO₃(s) ⇌ CaO(s) + CO₂(g) in a sealed kiln	chemical	heterogeneous

Examples of equilibrium systems.

Just for fun

A chemist's idea of a relaxing weekend: sitting perfectly still on the couch while doing exactly as much work as they undo. Very dynamic, very balanced, and the dishes never change.

Hands-on activity

Straw transfer: a model of dynamic equilibrium

You need: two identical tall straight-sided glasses or jars, water (a drop of food colouring makes reading easier), a ruler, two clean drinking straws of different widths (a regular straw and a wide bubble-tea or smoothie straw), a partner, paper.

Fill glass A with water to about 12 cm. Leave glass B empty. Record both heights at round 0.
In each round, you push the wide straw to the bottom of glass A, cover its top with a finger, lift it out and empty it into glass B. At the same time your partner does the same with the narrow straw from B into A (if B is empty, they transfer nothing).
Measure both heights after each round. Do at least 20 rounds.
Graph height against round number for both glasses on the same axes.

What to look for: the heights change quickly at first, then level off, even though water keeps moving both ways. The final heights are not equal: glass B ends up with more because the wide straw carries more per trip. Each straw carries an amount proportional to the water height, just as a reaction rate depends on concentration. At the end, the two transfer rates are equal: a model of dynamic equilibrium. Extension: start with the water in glass B instead. Do you reach the same final heights?

Your turn

What does the double arrow ⇌ tell you about a reaction?

State the four conditions that describe a system at dynamic equilibrium.

A student says, "At equilibrium the reaction has stopped and there are equal amounts of reactants and products." Correct both errors.

Classify each as a phase, solubility or chemical equilibrium: (a) ice and liquid water in an insulated cooler at 0 °C; (b) 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g); (c) undissolved sugar at the bottom of a sealed jar of saturated sugar water.

Which of these are homogeneous? (a) N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g); (b) H₂O(l) ⇌ H₂O(g); (c) CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO⁻(aq) + H₃O⁺(aq)

2.00 mol of PCl₅ is placed in a sealed 1.00 L flask: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g). At equilibrium [Cl₂] = 0.40 mol/L. Find [PCl₅] and [PCl₃] at equilibrium.

More practice: warm-up

What is a closed system?

At equilibrium, which two quantities are equal?

Why can an open glass of water never reach equilibrium with its vapour?

Name the type: CuSO₄(s) ⇌ Cu²⁺(aq) + SO₄²⁻(aq) in a saturated solution.

In N₂O₄(g) ⇌ 2 NO₂(g), which gas is brown?

More practice: on your own

Sketch and describe the concentration-time graph for 2 HI(g) ⇌ H₂(g) + I₂(g) when the flask starts with pure HI.

0.500 mol of N₂ and 1.50 mol of H₂ are sealed in a 1.00 L flask. At equilibrium [NH₃] = 0.200 mol/L. Find [N₂] and [H₂] at equilibrium.

In the question above, what is the percent reaction?

Explain how the radioactive-iodide experiment shows that a saturated solution is a dynamic, not static, system.

A sealed flask of brown NO₂ and N₂O₄ is left at constant temperature. Its colour stops changing after 2 minutes. What does that tell you, and what does it not tell you?

Challenge

4.00 mol of SO₃ is sealed in a 2.00 L flask: 2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g). At equilibrium, 0.60 mol of O₂ is present. Find all three equilibrium concentrations.

In the straw activity, the wide straw carries twice as much water per centimetre of depth as the narrow straw. The total depth of water is 12 cm. Predict the final heights in glasses A (wide straw out) and B (narrow straw out), and explain.

Equilibrium can be reached from either direction. Design a test, using two sealed flasks of HI, H₂ and I₂ at the same temperature, that would show this. Say what you would start with and what result would support the claim.

Check your understanding

Quiz

Which statement about a system at dynamic equilibrium is true?

Which system can reach dynamic equilibrium?

For N₂O₄(g) ⇌ 2 NO₂(g), what do you observe when equilibrium is reached?

CaCO₃(s) ⇌ CaO(s) + CO₂(g) in a sealed container is best described as:

1.00 mol/L of H₂ and of I₂ react until [HI] = 1.20 mol/L at equilibrium. What is [H₂]?

Which evidence best shows that equilibrium is dynamic?

For parents and teachers

Big idea (E3.1, E2.1): at dynamic equilibrium, a reversible process in a closed system runs both ways at equal rates, so concentrations stay constant. It is reached from either direction, and the concentrations are almost never equal.

How to help: ask your teen to explain the sealed-bottle hook in their own words, using the words rate, closed system and constant. The straw activity needs only water and two straws and makes a good graph for a lab notebook.

Common difficulties:

Thinking equilibrium means equal amounts or that everything stops.
Forgetting to use the mole ratio when finding how much of each substance reacted (Example 1).
Mixing up moles and concentration when the volume is not 1.00 L (divide by the volume first).

Looking ahead: the next lesson turns these constant concentrations into a single number, the equilibrium constant K.