Why begin with physical equilibria
When a liquid evaporates inside a closed container, molecules with relatively higher kinetic energy escape from the liquid surface into the vapour phase, while molecules already in the vapour strike the liquid surface and are retained. A constant vapour pressure arises because the number of molecules leaving the liquid eventually equals the number returning to it. At this stage we say the system has reached an equilibrium state. The defining insight of NCERT §6.1 is that this is not a static equilibrium: there is intense, continuous activity at the boundary between the two phases even though no net change is visible.
Equilibrium can be established for both physical processes and chemical reactions. Physical equilibria are introduced first because they involve no change in chemical identity — only the distribution of a substance between phases changes. The familiar examples are the phase transformations represented as $\ce{solid <=> liquid}$, $\ce{liquid <=> gas}$ and $\ce{solid <=> gas}$. The double half-arrows ($\ce{<=>}$) signal that the processes in both directions proceed simultaneously, and the coexisting mixture is called an equilibrium mixture.
| Physical process | Representation | Forward / reverse |
|---|---|---|
| Melting / freezing | $\ce{H2O(s) <=> H2O(l)}$ | melting / freezing |
| Evaporation / condensation | $\ce{H2O(l) <=> H2O(g)}$ | evaporation / condensation |
| Sublimation / deposition | $\ce{I2(s) <=> I2(g)}$ | sublimation / deposition |
| Dissolution / crystallisation | $\ce{Sugar(s) <=> Sugar(aq)}$ | dissolution / crystallisation |
Solid–liquid equilibrium
Consider ice and water kept together in a perfectly insulated thermos flask — one that allows no exchange of heat with the surroundings — at 273 K and atmospheric pressure. The system is at equilibrium, and we observe that the mass of ice and the mass of water do not change with time while the temperature remains constant. Yet the equilibrium is not static. Intense activity can be noticed at the boundary between ice and water: molecules from the liquid collide against the ice and adhere to it, while some molecules of ice escape into the liquid phase. The masses stay constant only because the rate of transfer of molecules from ice into water exactly equals the rate of the reverse transfer.
This balance can be written as $\ce{H2O(s) <=> H2O(l)}$. Ice and water are in equilibrium only at one particular temperature and pressure. For any pure substance at atmospheric pressure, the temperature at which the solid and liquid phases are in equilibrium is called the normal melting point (equivalently, the normal freezing point) of that substance.
Figure 1 — At the ice–water boundary, melting and freezing occur simultaneously and at equal rates. The masses of the two phases stay constant, but molecular exchange across the boundary never stops.
Two conclusions follow for this dynamic equilibrium: both opposing processes occur simultaneously, and both occur at the same rate, so that the amount of ice and the amount of water remain constant. The condition of an insulated flask matters — if no heat is exchanged with the surroundings, the mass of the two phases stays fixed.
Liquid–vapour equilibrium
This equilibrium is best understood through a closed-vessel experiment. A transparent box fitted with a mercury manometer is first dried thoroughly with a drying agent such as anhydrous calcium chloride. A watch glass containing water is then placed inside and the box is sealed. As water evaporates, the pressure inside the box rises and the mercury level in the manometer climbs, while the volume of water in the watch glass falls. The rate of evaporation stays constant, but the rate at which pressure increases slows down as condensation of vapour back into water sets in. Finally a state is reached where there is no net evaporation.
Figure 2 — In a closed vessel the rate of evaporation stays constant while the rate of condensation rises until the two become equal. At that point the vapour pressure reaches its constant equilibrium value.
At equilibrium, $\ce{H2O(l) <=> H2O(g)}$ with the rate of evaporation equal to the rate of condensation. The pressure exerted by the water molecules at a given temperature then stays constant and is called the equilibrium vapour pressure of water (or simply its vapour pressure). Vapour pressure increases with temperature. Different liquids have different equilibrium vapour pressures at the same temperature: the liquid with the higher vapour pressure is more volatile and has a lower boiling point.
Water and water vapour are in equilibrium at atmospheric pressure (1.013 bar) and 100 °C in a closed vessel; the boiling point of water is therefore 100 °C at 1.013 bar. For any pure liquid at one atmospheric pressure, the temperature at which the liquid and its vapour are at equilibrium is the normal boiling point. Because boiling point depends on atmospheric pressure, it falls with altitude — at high altitude, where pressure is lower, water boils below 100 °C.
Open systems never reach equilibrium
If acetone, ethyl alcohol or water is left on an open watch glass, the liquid eventually disappears entirely. In an open system the vapour molecules disperse into the large volume of the room, so the rate of condensation stays far below the rate of evaporation. The two rates can never become equal.
A constant equilibrium vapour pressure can be measured only in a closed container. "Equilibrium in an open system" is a contradiction the examiner will exploit.
Solid–vapour equilibrium
Some solids pass directly into the vapour phase without melting — a process called sublimation. If solid iodine is placed in a closed vessel, the vessel gradually fills with violet vapour whose colour intensifies with time; once the intensity becomes constant, equilibrium is attained. Solid iodine sublimes to give iodine vapour, and the vapour deposits back to solid iodine, so the equilibrium is $\ce{I2(s) <=> I2(g)}$.
| System | Equilibrium | Observation at equilibrium |
|---|---|---|
| Iodine | $\ce{I2(s) <=> I2(g)}$ | Intensity of violet vapour becomes constant |
| Camphor | $\ce{Camphor(s) <=> Camphor(g)}$ | Vapour concentration becomes constant |
| Ammonium chloride | $\ce{NH4Cl(s) <=> NH4Cl(g)}$ | Vapour concentration becomes constant |
The situation is closely analogous to the liquid–vapour case: in a closed container at constant temperature the rate of sublimation and the rate of the reverse deposition become equal, and the concentration of vapour above the solid attains a fixed value. Sublimation is also the basis of an important purification technique, as a recent NEET question on the purification of solids that pass directly from solid to vapour confirms.
The same dynamic balance of opposing rates underlies chemical reactions. See Equilibrium in Chemical Processes — Dynamic Equilibrium.
Dissolution of solids and gases in liquids
Solids in liquids
Only a limited amount of salt or sugar dissolves in a given quantity of water at a fixed temperature. If a thick syrup is made by dissolving sugar at a higher temperature and then cooled, sugar crystals separate out. A solution in which no more solute can dissolve at a given temperature is called a saturated solution, and the concentration of solute in it depends only on temperature. In a saturated solution a dynamic equilibrium exists between solute in the solid state and solute in solution: $\ce{Sugar(s) <=> Sugar(aq)}$, with the rate of dissolution equal to the rate of crystallisation.
The dynamic nature of this equilibrium has been confirmed using radioactive sugar. When radioactive sugar is dropped into a saturated solution of ordinary, non-radioactive sugar, radioactivity later appears in both the solution and the solid. Although the masses do not change, molecules are continuously exchanged between the two phases until the ratio of radioactive to non-radioactive molecules in solution reaches a constant value.
Gases in liquids
When a soda-water bottle is opened, dissolved carbon dioxide fizzes out rapidly because gas solubility depends on pressure. In the sealed bottle an equilibrium exists between gaseous and dissolved carbon dioxide, $\ce{CO2(g) <=> CO2(aq)}$, established under high pressure. This equilibrium is governed by Henry's law: the mass of a gas dissolved in a given mass of solvent at any temperature is proportional to the pressure of the gas above the solvent, and the dissolved amount decreases as temperature rises.
On opening the bottle, the pressure above the liquid drops to the low partial pressure of CO2 in the atmosphere, so dissolved gas escapes until a new equilibrium is reached for the lower pressure. This is exactly why an open soda-water bottle goes "flat" over time.
| Process | Equilibrium | Conclusion (Table 6.1, NCERT) |
|---|---|---|
| Liquid ⇌ Vapour | $\ce{H2O(l) <=> H2O(g)}$ | $p_{\ce{H2O}}$ constant at a given temperature |
| Solid ⇌ Liquid | $\ce{H2O(s) <=> H2O(l)}$ | Melting point fixed at constant pressure |
| Solute(s) ⇌ Solute (solution) | $\ce{Sugar(s) <=> Sugar(aq)}$ | Solubility constant at a given temperature |
| Gas(g) ⇌ Gas(aq) | $\ce{CO2(g) <=> CO2(aq)}$ | $[\text{gas(aq)}]/[\text{gas(g)}]$ constant at a given temperature |
The four general statements that summarise these systems are worth memorising: for solid ⇌ liquid there is a single temperature (the melting point) at 1.013 bar at which the two phases coexist; for liquid ⇌ vapour the vapour pressure is constant at a given temperature; for dissolution of a solid the solubility is constant at a given temperature; and for dissolution of a gas the concentration in the liquid is proportional to the pressure of the gas above it.
General characteristics of physical equilibria
Across all the physical processes above, NCERT §6.1.5 identifies five features common to every system at equilibrium. These are the statements most often quoted verbatim in objective questions, so they reward precise recall.
| # | Characteristic | What it means |
|---|---|---|
| 1 | Closed system, fixed temperature | Equilibrium is possible only in a closed system at a given temperature. |
| 2 | Dynamic but stable | Both opposing processes occur at the same rate; the condition is dynamic yet stable. |
| 3 | Constant macroscopic properties | All measurable properties of the system remain constant. |
| 4 | Characteristic parameter | Equilibrium is marked by a constant value of one parameter at a given temperature (see the conclusions table). |
| 5 | Indicator of extent | The magnitude of that parameter shows how far the physical process has proceeded before reaching equilibrium. |
"Reaction stopped" is the wrong picture
Constancy of mass, vapour pressure, colour or concentration does not mean the forward and reverse processes have ceased. They proceed at full speed but at equal rates, leaving no net change. Mistaking "no net change" for "no activity" is the classic conceptual error punished in both physical and chemical equilibrium questions.
Equilibrium = equal opposing rates, not zero rates. The radioactive-sugar experiment is the standard proof.
Q. A drop of radioactive sugar is added to a saturated solution of non-radioactive sugar already in equilibrium with solid sugar. After some time, where is radioactivity detected, and why?
A. Radioactivity is detected in both the solution and the solid sugar. At equilibrium $\ce{Sugar(s) <=> Sugar(aq)}$ the rate of dissolution equals the rate of crystallisation, but molecular exchange between phases continues. Radioactive molecules therefore distribute themselves across both phases until the ratio of radioactive to non-radioactive molecules in solution becomes constant — direct evidence that the equilibrium is dynamic, not static.
Equilibrium in Physical Processes
- Phase equilibria — $\ce{H2O(s) <=> H2O(l)}$, $\ce{H2O(l) <=> H2O(g)}$, $\ce{I2(s) <=> I2(g)}$ — are all dynamic: opposing processes run at equal rates.
- Solid–liquid: the normal melting point is the single temperature at 1.013 bar where solid and liquid coexist.
- Liquid–vapour: equilibrium vapour pressure is constant at a given temperature and rises with temperature; the normal boiling point of water is 100 °C at 1.013 bar.
- Solid–vapour: sublimation ⇌ deposition reaches constant vapour concentration; it is the basis of purification by sublimation.
- Dissolution: solubility of a solid is constant at fixed temperature; for a gas, dissolved amount ∝ pressure (Henry's law) and falls as temperature rises.
- Five characteristics: closed system, dynamic-but-stable, constant macroscopic properties, a characteristic constant parameter, and that parameter indicating the extent of the process.