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Phase Diagrams

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Senior 5 · Chemistry

Phase Diagrams

4 lessons

Lesson 1 of 4

Phase Equilibrium: Homogeneous and Heterogeneous Equilibria

25 min

Why does water boil at about 95 °C in Kigali?

At sea level, pure water boils at 100 °C. In Kigali, about 1,567 m above sea level, a thermometer in boiling water reads close to 95 °C, and on the 4,507 m summit of Mount Karisimbi it would read about 85 °C. Beans and maize cooked at these lower temperatures take longer to soften. Nothing about the water has changed; what has changed is the pressure of the air pressing on it. To understand why, you need the idea of equilibrium between two phases of the same substance, and that idea leads straight to the phase diagrams of the next lessons.

Mount Karisimbi, Rwanda's highest peak (4,507 m), in the Virunga range. At its summit the air pressure is little more than half its sea-level value, so water boils at about 85 °C. Photo: Reneplee, CC BY-SA 4.0, via Wikimedia Commons

Definition

Phase: a part of a system that is uniform in composition and physical state, separated from other parts by a boundary. Ice, liquid water and water vapour are three phases of one substance; a mixture of oil and water has two liquid phases; air is a single gas phase.

Phase equilibrium: a dynamic equilibrium between two or more phases of a substance, in which the rate of change in one direction equals the rate in the other, e.g. $\mathrm{H_2O(l) \rightleftharpoons H_2O(g)}$ in a closed flask.

Vapour pressure: the pressure exerted by a vapour in equilibrium with its liquid (or solid) at a given temperature. Water at 25 °C: 3.17 kPa.

Boiling point: the temperature at which the vapour pressure of a liquid equals the external pressure. The normal boiling point is the boiling point at 101.325 kPa (1 atm).

Homogeneous equilibrium: all species are in the same phase. Heterogeneous equilibrium: the species are in two or more phases.

Equilibrium between liquid and vapour

Put some water in a flask, pump out the air and close it. Fast-moving molecules escape from the surface (evaporation), and the pressure of vapour above the liquid rises. As the vapour builds up, more vapour molecules strike the surface and are recaptured (condensation). Soon the two rates are equal: the amount of liquid stops falling and the pressure stops rising, although molecules keep crossing in both directions. The steady pressure is the vapour pressure.

Vapour pressure depends only on the substance and the temperature, not on how much liquid is present or the size of the flask.
It rises steeply with temperature, because a larger fraction of molecules has enough energy to escape.
Liquids with weaker intermolecular forces have higher vapour pressures. Ethanol's hydrogen bonds are weaker overall than water's, so ethanol is more volatile (Figure 10.1).

Figure 10.1: Vapour pressure curves, drawn to scale from the Antoine equation. A liquid boils where its curve meets the line of the surrounding pressure.

A liquid boils when bubbles of vapour can form inside it, which needs its vapour pressure to reach the pressure of the surroundings. Lower the outside pressure and the curve reaches it at a lower temperature:

Place	Altitude / m	Typical air pressure / kPa	Boiling point of water / °C	Boiling point of ethanol / °C
sea level	0	101.3	100.0	78.3
Kigali	1,567	83.9	94.8	73.6
Karisimbi summit	4,507	57.7	85.0	64.8

Table 10.1: Pressures from the International Standard Atmosphere; boiling points from the Antoine equation. Real air pressure varies a little with the weather.

Homogeneous and heterogeneous equilibria

The equilibria you met in earlier units are classified by the number of phases they involve:

Homogeneous (one phase)	Heterogeneous (two or more phases)
$\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$	$\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$
$\mathrm{CH_3COOH(l) + C_2H_5OH(l) \rightleftharpoons CH_3COOC_2H_5(l) + H_2O(l)}$	$\mathrm{AgCl(s) \rightleftharpoons Ag^{+}(aq) + Cl^{-}(aq)}$
$\mathrm{CH_3COOH(aq) \rightleftharpoons H^{+}(aq) + CH_3COO^{-}(aq)}$	$\mathrm{H_2O(l) \rightleftharpoons H_2O(g)}$ ; $\mathrm{H_2O(s) \rightleftharpoons H_2O(l)}$

In a heterogeneous equilibrium, the concentration of a pure solid or pure liquid is fixed by its density, so it does not change as the reaction proceeds. It is therefore left out of $K_{c}$ and $K_{p}$ . For the decomposition of limestone, $K_p = p_{\mathrm{CO_2}}$ : at a given temperature, the pressure of carbon dioxide over the solids has a single equilibrium value, however much $\mathrm{CaCO_3}$ or CaO is present. In the same way, for $\mathrm{H_2O(l) \rightleftharpoons H_2O(g)}$ , $K_p = p_{\mathrm{H_2O}}$ , which is the vapour pressure.

Worked example

Problem. State whether each equilibrium is homogeneous or heterogeneous, and write its $K_{p}$ or $K_{c}$ expression: (a) $\mathrm{3Fe(s) + 4H_2O(g) \rightleftharpoons Fe_3O_4(s) + 4H_2(g)}$ ; (b) $\mathrm{2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)}$ ; (c) $\mathrm{I_2(s) \rightleftharpoons I_2(g)}$ .

Solution.

(a) Heterogeneous (two solids, one gas phase). Leave out Fe and $\mathrm{Fe_3O_4}$ : $K_p = \frac{p_{\mathrm{H_2}}^{4}}{p_{\mathrm{H_2O}}^{4}}$

(b) Homogeneous, all gases: $K_p = \frac{p_{\mathrm{SO_3}}^{2}}{p_{\mathrm{SO_2}}^{2}\,p_{\mathrm{O_2}}}$

(c) Heterogeneous: $K_p = p_{\mathrm{I_2}}$ , the vapour pressure of solid iodine at that temperature (a sublimation equilibrium).

Worked example

Problem. Use Figure 10.1 to find (a) the vapour pressure of water at 70 °C; (b) the pressure to which a cook must lower the pressure over water for it to boil at 70 °C; (c) why a sealed bottle of ethanol at 25 °C contains ethanol vapour at the same pressure whether it is half full or nearly empty.

Solution. (a) Read up from 70 °C to the water curve and across: about 31 kPa. (b) Water boils when its vapour pressure equals the outside pressure, so the pressure must be lowered to about 31 kPa. (c) Vapour pressure is an equilibrium property: it depends only on temperature, provided some liquid remains. At 25 °C it is 7.8 kPa for ethanol in both bottles.

Warning

"Evaporation" and "boiling" are not the same. Evaporation happens at any temperature, only from the surface. Boiling happens throughout the liquid, at the one temperature where vapour pressure equals the outside pressure. Also, a lower boiling point at altitude does not mean water heats faster: food cooks more slowly because the water is cooler.

Safety: ethanol vapour is flammable. Never heat ethanol over a naked flame; use a water bath or electric heater.

Tip

Leaving out solids and pure liquids from $K$ is easy to remember if you ask: "Can this concentration change?" A lump of chalk is just as concentrated at the end as at the start, so it has no place in the expression.

The Video Textbook of Chemistry (Steven Farmer): Vapor Pressure and Boiling Point. Watch how the dynamic equilibrium in a closed container sets the vapour pressure, and why boiling happens when vapour pressure equals the outside pressure.

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Practice

How many phases are present in: (a) a glass of water with ice cubes; (b) a sealed bottle of soda water with a gas space; (c) a mixture of iron filings and sulfur powder?
Classify as homogeneous or heterogeneous, and write $K_{c}$ or $K_{p}$ : (a) $\mathrm{C(s) + H_2O(g) \rightleftharpoons CO(g) + H_2(g)}$ ; (b) $\mathrm{H_2(g) + I_2(g) \rightleftharpoons 2HI(g)}$ ; (c) $\mathrm{Cu^{2+}(aq) + 4NH_3(aq) \rightleftharpoons [Cu(NH_3)_4]^{2+}(aq)}$ .
Use Figure 10.1 to estimate the boiling point of water when the outside pressure is 60 kPa.
Explain, using the idea of dynamic equilibrium, why the vapour pressure of water at 40 °C (7.4 kPa) is greater than at 20 °C (2.3 kPa).
At a certain temperature $K_{p}$ for $\mathrm{CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)}$ is 0.50 atm. What is the pressure of $\mathrm{CO_2}$ at equilibrium if (a) 10 g, (b) 50 g of $\mathrm{CaCO_3}$ is heated in a sealed container at that temperature, with some solid left in each case?
A student in Musanze measures the boiling point of pure water as 94 °C and concludes the thermometer is faulty. Evaluate this conclusion.

Show answersHide answers

(a) 2 (solid, liquid); (b) 2 (solution, gas); (c) 2 (two different solids).
(a) heterogeneous, $K_p = \frac{p_{\mathrm{CO}}\,p_{\mathrm{H_2}}}{p_{\mathrm{H_2O}}}$ ; (b) homogeneous, $K_p = \frac{p_{\mathrm{HI}}^{2}}{p_{\mathrm{H_2}}\,p_{\mathrm{I_2}}}$ ; (c) homogeneous, $K_c = \frac{[\mathrm{[Cu(NH_3)_4]^{2+}}]}{[\mathrm{Cu^{2+}}][\mathrm{NH_3}]^{4}}$ .
About 86 °C.
At 40 °C a larger fraction of molecules has enough energy to leave the surface, so the evaporation rate is higher; equilibrium is reached only when the vapour is denser, making the condensation rate equally high, i.e. at a higher pressure.
0.50 atm in both cases: $K_p = p_{\mathrm{CO_2}}$ , which does not depend on the amount of solid.
The conclusion is probably wrong. Musanze is about 1,850 m above sea level, where the standard-atmosphere pressure is about 81 kPa; water's vapour pressure reaches 81 kPa at about 94 °C, so 94 °C is the expected reading.

Sources and credits

Vapour pressures: Antoine-equation constants for water and ethanol from Antoine equation, Wikipedia contributors, licensed under CC BY-SA 4.0; pressures with altitude from the International Standard Atmosphere (ISO 2533). Altitudes of Kigali, Musanze and Karisimbi from the Wikipedia articles on each place.
Image: Mount Karisimbi.jpg by Reneplee, via Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Vapor Pressure and Boiling Point, The Video Textbook of Chemistry, embedded from YouTube.
The text, Figure 10.1, the tables, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Why does water boil at about 95 °C in Kigali?

2Equilibrium between liquid and vapour

3Homogeneous and heterogeneous equilibria

Why does water boil at about 95 °C in Kigali?

Equilibrium between liquid and vapour

Homogeneous and heterogeneous equilibria