Premed · Premed · General Chemistry 1

Lecture 17: Liquids and Phase Changes

General Chemistry I

Learning Objectives

By the end of this lecture, students will be able to:

1. Describe the properties of liquids in terms of intermolecular forces
2. Define vapor pressure and explain how it depends on temperature and IMF strength
3. Use the Clausius-Clapeyron equation to relate vapor pressure to temperature
4. Describe and distinguish the types of phase changes and their associated energy terms
5. Interpret heating curves and calculate energy changes during phase transitions
6. Read and interpret phase diagrams, identifying the triple point and critical point

Lecture Content

I. Properties of Liquids (Review and Extension)

Liquids occupy a middle ground between solids and gases. They have a definite volume but take the shape of their container. At the molecular level, liquid molecules are close together but not locked into fixed positions -- they exhibit short-range order without long-range order. Intermolecular forces are strong enough to keep the molecules in close proximity yet not strong enough to prevent them from moving past one another. Surface tension, the energy required to increase a liquid's surface area, arises from the unbalanced inward pull that surface molecules experience from their neighbors below. Viscosity, the resistance to flow, depends on IMF strength, molecular shape (long chains tend to entangle), and temperature. Capillary action results from the interplay between adhesive forces (liquid-surface attraction) and cohesive forces (liquid-liquid attraction).

II. Vaporization and Vapor Pressure

Vaporization (evaporation) occurs when molecules at the liquid surface possess enough kinetic energy to escape into the gas phase. It is an endothermic process (delta_H_vap > 0) and produces a cooling effect on the remaining liquid because the highest-energy molecules preferentially depart. The reverse process, condensation, is exothermic (delta_H_cond = -delta_H_vap).

In a closed container, evaporation and condensation eventually reach dynamic equilibrium, where the rate of evaporation equals the rate of condensation. The gas pressure at this equilibrium is called the vapor pressure. Vapor pressure depends on temperature -- higher temperatures give more molecules sufficient energy to escape, raising the vapor pressure. It also depends on IMF strength -- weaker intermolecular forces allow molecules to escape more easily, resulting in higher vapor pressure. Notably, vapor pressure does not depend on the amount of liquid present, as long as some liquid remains. Substances with high vapor pressures at a given temperature are described as volatile; diethyl ether (boiling point 34.6 C) is far more volatile than water (boiling point 100 C).

III. Boiling Point

The boiling point is the temperature at which a liquid's vapor pressure equals the external pressure acting on it. The normal boiling point is specifically defined as the boiling point at 1 atm. At higher altitudes, atmospheric pressure is lower, so water boils below 100 C and food cooks more slowly. A pressure cooker works in reverse: by raising the pressure above 1 atm, it increases the boiling point, allowing water to reach temperatures above 100 C and cook food faster.

IV. The Clausius-Clapeyron Equation

The Clausius-Clapeyron equation provides a quantitative relationship between vapor pressure and temperature. In its one-point form, ln(P) = -delta_H_vap / (RT) + C. The more practical two-point form is ln(P2/P1) = (-delta_H_vap / R) (1/T2 - 1/T1), where P1 and P2 are vapor pressures at temperatures T1 and T2 (in Kelvin), delta_H_vap is the enthalpy of vaporization in J/mol, and R = 8.314 J/(molK). Plotting ln(P) versus 1/T yields a straight line with a slope of -delta_H_vap / R. This equation can be used to calculate the enthalpy of vaporization from vapor pressure data, predict the vapor pressure at a new temperature, or determine the boiling point at a non-standard pressure.

<image>A two-panel figure illustrating the Clausius-Clapeyron relationship. Left panel: a graph of vapor pressure (P, in torr) vs. temperature (T, in degrees C) for three liquids -- diethyl ether, ethanol, and water. Each curve is exponential, rising steeply. A horizontal dashed line at 760 torr intersects each curve at the normal boiling point (labeled for each substance). The curve for diethyl ether is leftmost (lowest boiling point, highest vapor pressure at any given T), water is rightmost. Right panel: the same data plotted as ln(P) vs. 1/T (in K^-1), showing straight lines for each substance. The slope of each line is labeled as -delta_H_vap / R. Water has the steepest slope (largest delta_H_vap), diethyl ether has the shallowest.</image>

V. Types of Phase Changes

By Hess's law, the enthalpy of sublimation equals the sum of the enthalpies of fusion and vaporization: delta_H_sub = delta_H_fus + delta_H_vap. For any given substance, delta_H_vap is always greater than delta_H_fus because vaporization requires completely overcoming all intermolecular forces, while melting merely loosens the ordered arrangement. For water, the values are delta_H_fus = 6.01 kJ/mol, delta_H_vap = 40.7 kJ/mol, and delta_H_sub = 46.7 kJ/mol.

VI. Heating Curves

A heating curve plots temperature versus heat added as a substance is heated from solid through liquid to gas. It contains five distinct regions. In the first region, the solid is heated and temperature rises according to q = m c_solid delta_T. In the second region, the substance melts at its melting point, and temperature remains constant while heat is absorbed to overcome the lattice forces: q = n delta_H_fus. In the third region, the liquid is heated and temperature rises again: q = m c_liquid delta_T. In the fourth region, the substance boils at its boiling point, and temperature again holds constant as heat goes toward overcoming intermolecular forces: q = n delta_H_vap. This plateau is the longest because delta_H_vap is much larger than delta_H_fus. In the fifth region, the gas is heated: q = m c_gas delta_T. The flat plateaus represent phase changes where added energy overcomes intermolecular forces rather than increasing molecular kinetic energy. The total energy required to traverse the entire curve is the sum of the energies for all five segments.

<image>A labeled heating curve for water showing temperature (y-axis, -20 C to 120 C) vs. heat added (x-axis, in kJ). Five distinct segments are shown: Segment 1: diagonal line from -20 C to 0 C (heating ice, labeled with q = mc_icedelta_T, c_ice = 2.09 J/gC). Segment 2: flat horizontal line at 0 C (melting, labeled q = ndelta_H_fus = 6.01 kJ/mol). Segment 3: diagonal line from 0 C to 100 C (heating liquid water, labeled q = mc_waterdelta_T, c_water = 4.184 J/gC). Segment 4: flat horizontal line at 100 C (boiling, labeled q = ndelta_H_vap = 40.7 kJ/mol, this is the longest plateau). Segment 5: diagonal line above 100 C (heating steam, labeled q = mc_steamdelta_T, c_steam = 2.01 J/g*C). Each segment has a different color, and the slopes of the diagonal regions reflect the different specific heat capacities.</image>

VII. Phase Diagrams

A phase diagram is a graph of pressure versus temperature that shows the regions where each phase (solid, liquid, gas) is stable. Key features include the phase boundaries (coexistence curves), which are lines separating the phase regions. Along these lines, two phases coexist in equilibrium. The solid-liquid boundary usually slopes to the right (positive slope), but water is an important exception -- its negative slope reflects the fact that ice is less dense than liquid water. The liquid-gas boundary traces the vapor pressure curve and terminates at the critical point. The solid-gas boundary represents the sublimation curve.

Two special points are particularly significant. The triple point is the unique temperature and pressure at which all three phases coexist simultaneously in equilibrium. For water, the triple point occurs at 0.01 C and 0.006 atm (611 Pa). The critical point marks the temperature and pressure above which the distinction between liquid and gas disappears, and the substance becomes a supercritical fluid. For water, the critical point is at 374 C and 218 atm. Above the critical temperature, no amount of pressure can liquify the gas.

VIII. Reading Phase Diagrams

Drawing a horizontal line at a given pressure and moving from left to right (increasing temperature) reveals the phase changes that occur at that pressure. At P = 1 atm, the intersections with phase boundaries give the normal melting point and normal boiling point. If the pressure is below the triple point pressure, heating causes sublimation -- the substance passes directly from solid to gas without ever becoming a liquid. This explains why dry ice (solid CO2) sublimes at 1 atm, since CO2's triple point is at 5.11 atm. Supercritical fluids exhibit properties intermediate between liquids and gases and are used in industrial processes such as the supercritical CO2 extraction used in coffee decaffeination.

IX. Critical Temperature and Pressure

The critical temperature (T_c) is the temperature above which a substance cannot exist as a liquid regardless of how much pressure is applied. The critical pressure (P_c) is the minimum pressure needed to liquefy a gas at its critical temperature. Substances with strong intermolecular forces have high critical temperatures (water: T_c = 374 C; CO2: T_c = 31 C). The practical implication is that a gas can only be liquefied by compression if the temperature is below its critical temperature.

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