Forward and reverse at the same time
Many processes can run both ways: a liquid evaporates and its vapor condenses; a solid dissolves and its ions crystallize again; N₂O₄ breaks apart into NO₂ and NO₂ joins back into N₂O₄. In a closed system both directions happen at once. At first the forward process is faster; as reactants are used up and products build up, the forward process slows and the reverse speeds up, until the two rates are equal. The system is then at chemical equilibrium化学平衡 (or physical equilibrium, for a physical process).
At equilibrium:
- the forward and reverse rates are equal;
- the concentrations (or partial pressures) stay constant, but are generally not equal to each other;
- neither process has stopped, so the equilibrium is dynamic;
- the system must be closed and at constant temperature.
Physical equilibrium: evaporation in a closed container
When a liquid evaporates in a closed container, more and more gas molecules build up, and more of them hit the surface and are captured again. Once condensation catches up with evaporation, the number of gas molecules stops changing; the pressure of the gas is then the vapor pressure of the liquid at that temperature (U3.3). Compare closed and open containers, two temperatures, and two amounts of liquid:
The rates and numbers are schematic: the evaporation rate at 45 °C is taken as 3 times that at 25 °C.
Chemical equilibrium: reachable from either side
N₂O₄(g) ⇌ 2NO₂(g) can start from N₂O₄ alone or from NO₂ alone. Watch how the concentrations and rates change with time:
Whichever side it starts from, at the same temperature and with equivalent amounts of atoms, it reaches the same equilibrium composition.
Example 1: Reading experimental data
At a certain temperature, 0.500 mol of A(g) is placed in a closed 1.00 L container, where A(g) ⇌ 2B(g). The concentration of A is measured:
| Time (s) | 0 | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|---|
| [A] (M) | 0.500 | 0.380 | 0.320 | 0.300 | 0.300 | 0.300 |
When is equilibrium reached, and what is [B] at equilibrium?
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Find the plateau. [A] is 0.300 M at 30 s, 40 s and 50 s and no longer changes, so equilibrium has been reached by 30 s.
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Organize the concentrations in a table. At the start [A] = 0.500 mol ÷ 1.00 L = 0.500 M, with no B. If A decreases by x, B increases by 2x, following the coefficients (concentrations in M):
A 2B Start 0.500 0 Change −x +2x Equilibrium 0.300 2x -
Find x from A.
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Find [B]. Each mole of A that reacts forms 2 mol of B:
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Note. At equilibrium [A] = 0.300 M and [B] = 0.400 M, which are not equal. The sign of equilibrium is that the concentrations stop changing, not that they become equal.
Example 2: How can you show equilibrium is dynamic?
A saturated NaCl solution at 25 °C has NaCl crystals at the bottom. A little solid NaCl containing radioactive ²⁴Na is added, stirred in, and left to stand. Later, radioactivity is detected in the solution, while the total [Na⁺] in the solution has not changed. What does this show?
- Solution concentration. The solution stays saturated, so the total [Na⁺] is unchanged; nothing seems to happen.
- Where the radioactivity went. The ²⁴Na started only in the solid but ended up in the solution, so solid is still dissolving.
- Why the concentration is constant. At the same time an equal amount of Na⁺ and Cl⁻ crystallizes back onto the solid; dissolving and crystallizing happen at the same rate.
- Conclusion. The solubility equilibrium is dynamic: both processes continue at equal rates.
- The forward rate equals the reverse rate
That is what equilibrium means.
- The reactant concentrations equal the product concentrations
They are constant, but generally not equal.
- No concentration changes with time any more
The rates are equal, so the net change is zero.
- Both the forward and reverse reactions have stopped
Both continue; equilibrium is dynamic.
- The color of a colored substance no longer changes
Its concentration is constant, so its color is too.
- All of the reactants have turned into products
At equilibrium reactants and products are both present.
- At the same temperature, starting from the products leads to the same equilibrium
A reversible reaction can reach equilibrium from either side (with equivalent amounts of atoms, the composition is the same).
- The ratio of the amounts of reactants and products equals the ratio of coefficients
The coefficients give the ratio of the changes, not of the amounts at equilibrium.
Common mistakes
Mistake 1: “At equilibrium, the reactant and product concentrations are equal.” At equilibrium the concentrations stop changing, but they are generally not equal. Constant ≠ equal.
Mistake 2: “Once equilibrium is reached, the reaction stops.” Both the forward and reverse reactions continue at equal rates, so there is no visible change.
Mistake 3: “A liquid in an open container reaches evaporation equilibrium too.” In an open container, gas molecules keep escaping and condensation never catches up with evaporation. Equilibrium can only be established in a closed system.
Quick check
In a closed container, a reversible reaction starts with only reactants. Before equilibrium is reached, which statement is correct?
As reactants are used up the forward reaction slows; as products build up the reverse reaction speeds up, until the two are equal.
A sealed flask contains a little liquid ethanol at a constant 20 °C, and the pressure of ethanol vapor in the flask is no longer changing. Which statement is correct?
A constant pressure means evaporation and condensation occur at equal rates; both continue. Liquid remains, so C is wrong.
Which observation shows that a reversible reaction in solution has reached equilibrium?
An unchanging color means the colored substance’s concentration is constant. B isn’t a condition for equilibrium; C means the reaction went to completion; D has nothing to do with equilibrium.
Two identical closed containers are at the same temperature. Container 1 starts with 0.20 mol of N₂O₄ and container 2 with 0.40 mol of NO₂. After a long time, the gases in the two containers:
0.40 mol of NO₂ and 0.20 mol of N₂O₄ contain the same atoms; at the same temperature, starting from either side gives the same equilibrium.
For X ⇌ Y in a closed container, a concentration–time graph is drawn. What marks the point at which equilibrium is reached?
Flat curves mean the concentrations no longer change. A only means the two concentrations are equal at that moment; they may keep changing afterward.
Which of these systems cannot reach equilibrium?
In an open beaker water vapor keeps escaping, so condensation never catches up with evaporation. Physical processes (evaporation, dissolving) and chemical reactions can all reach equilibrium in a closed system.
AP-style free response
With an acid catalyst, acetic acid and ethanol react to form ethyl acetate and water: CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O. A student mixes 1.00 mol of acetic acid with 1.00 mol of ethanol at constant temperature and measures the amount of ethyl acetate (schematic data):
| Time (h) | 0 | 1 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|---|
| n(ethyl acetate) (mol) | 0 | 0.30 | 0.50 | 0.62 | 0.67 | 0.67 |
(a) By what time has the system reached equilibrium? Justify your answer.
(b) How many moles of acetic acid, ethanol, ethyl acetate, and water are present at equilibrium?
(c) Compare the forward and reverse rates at 6 h.
(d) After 6 h the amount of ethyl acetate stops increasing, yet the reaction has not stopped. Explain this statement.
(e) Another student starts from 1.00 mol of ethyl acetate and 1.00 mol of water under the same conditions. Predict the amount of ethyl acetate at equilibrium, and justify your prediction.
Model answer and scoring
(a) By 6 h. The amounts at 6 h and 8 h are the same, so it is no longer changing.
(b) Ethyl acetate 0.67 mol and water 0.67 mol; acetic acid and ethanol 1.00 − 0.67 = 0.33 mol each.
(c) Equal. The system is at equilibrium, so the forward and reverse rates are equal.
(d) Acetic acid and ethanol are still forming ethyl acetate, while ethyl acetate is hydrolyzed at the same rate, so the net change is zero.
(e) About 0.67 mol. Both starting mixtures contain the same atoms, and at the same temperature both directions reach the same equilibrium composition.
Scoring: (a) amount no longer changing; (b) amounts from the coefficients; (c) equal rates; (d) dynamic equilibrium; (e) the same equilibrium from either side.
Summary
- When a reversible process reaches equilibrium in a closed system, the forward and reverse rates are equal and the concentrations (partial pressures) stop changing.
- At equilibrium concentrations are constant but generally not equal; the equilibrium is dynamic, with both processes still occurring.
- Physical processes (evaporation, dissolving) and chemical reactions can both reach equilibrium, and the same equilibrium can be reached from the reactant side or the product side.
- Signs of equilibrium: concentration, pressure, color, and so on no longer change.
AP tip: When explaining equilibrium, state both points: “the forward and reverse rates are equal” and “the concentrations remain constant (but are not necessarily equal).” On a graph, look for where the curves level off; don’t mistake the point where curves cross for equilibrium.