Liquids and solutions

Liquids and solutions

The kinetic theory of liquids and solids • A gas : its molecules move freely and it takes up the volume of its container • low density and high compressibility • A liquid: its molecules slide freely against one another and there is a definite volume, but it takes up the form of its container • high density and very small compressibility • A solid: its molecules vibrate in a fixed position and it has a definite shape • High density and practically no compressibility

The Hydrogen Bond • The hydrogen bond is a type of dipole-dipole interaction between an H atom that is already involved in a polar bond (N-H, O-H or F-H) and another electronegative O, N or F atom • A—H……B or A—H……A • The hydrogen bond’s energy can reach up to 40 kJ/mol (≈ 10% of a covalent bond)

The Hydrogen Bond • Hydrogen bonds are a key player in the structure and properties of various compounds • The importance of hydrogen bonds can be noted in the boiling points of group 5A, 6A and 7A hydrides • In each group, the lightest compound has the highest boiling point because the hydrogen bonds must be broken before the molecules can enter the gaseous phase (without hydrogen bonding, the boiling point simply tends to increase with mass)

The Hydrogen Bond • The hydrogen bond gets stronger when the electronegativity of the atom attached to H increases, therefore HF has the strongest individual hydrogen bonds • However, H2O has the highest boiling point because it is the most stabilized by its hydrogen bonds. • H2O is unique because there are two free electron pairs on the O and also has two H atoms. As such, each molecule can participate in four hydrogen bonds: twice as a donor, twice as an acceptor. • NH3 (only one free electron pair) and HF (only one H) can only participate in two hydrogen bonds: once as a donor, once as an acceptor

Structure and Properties of Water • Water has a high heat capacity because many hydrogen bonds need to be broken in order to increase the kinetic energy of the molecules • The high heat capacity of water is important • The simple fact that water absorbs a lot of heat when it warms up and that is also releases a lot of heat when it cools down explains how oceans and lakes can contribute to moderating the climate along coasts.

Structure and Properties of Water • H2O is one of the rare substances where the liquid has a higher density than the solid • The H2O molecules in ice form a unique three-dimensional network because each molecule can participate in four hydrogen bonds • The three-dimensional network introduces small cavities that reduce the density of the solid

Phase Changes • A phase is a homogenous part of a system in contact with other parts of that same system, separated by a well-defined boundary • For example, ice floating on water is a two phase system with a solid phase (ice) and a liquid phase (water) • A phase change is the change from one phase to another • A phase change (usually) involves a heat transfer and a change of disorder or entropy among the molecules (for example, the melting of ice is an endothermic process that increases the disorder in the H2O molecules)

Liquid-Vapor Equilibrium • At every temperature (even lower than the boiling temperature), there is a certain number of molecules in a liquid that contain enough kinetic energy to escape the surface and enter the gas phase • This process is called vaporization or evaporation • The pressure exerted by the molecules that have entered the gas phase is called the vapor pressure

Liquid-Vapor Equilibrium • When the liquid and gas phases reach an equilibrium, the measured vapor pressure is called the equilibrium vapor pressure, or simply: vapor pressure • The equilibrium vapor pressure is the maximal vapor pressure that can be exerted by a liquid at a given temperature • The equilibrium vapor pressure increases with temperature

Critical Temperature and Critical Pressure • A gas can be liquefied by lowering the temperature (the kinetic energy decreases to a point where the molecules cannot escape one another) or by increasing the pressure (the molecules get closer and mutual attraction becomes strong enough to bring them together) • However, it is sometimes impossible to liquefy a gas • The critical temperature (Tc) is the temperature above which a gas cannot be liquefied no matter what amount or pressure is applied • The critical pressure (Pc) is the minimal pressure that needs to be applied in order to liquefy a gas at its critical temperature • Above the critical temperature, the molecules always have sufficient kinetic energy to escape intramolecular forces

Liquid-Solid Equilibrium • The transition from liquid to solid is freezing • The transition from solid to liquid is melting (or fusion) • The melting point of a solid is the temperature at which the solid and liquid phases coexist in a dynamic equilibrium • The enthalpy of fusion (∆Hfus) is the energy required to melt one mole of a solid • ∆Hfus is typically much smaller than ∆Hvap because in the transition from solid to liquid, the molecules stay close to one another and the intermolecular attractions remain more or less intact • By going from liquid to gase, all intermolecular attractions are lost

Liquid-Solid Equilibrium • The direct transition from the solid phase to the gas phase is called sublimation • The direct transition from the gas phase to the solid phase is called deposition • The enthalpy of sublimation (∆Hsub) is the energy needed to sublime one mole of solid • As require by Hess’s law, ∆Hsub= ∆Hfus + ∆Hvap

Phase Diagrams • a phase diagram describes the conditions of temperature and pressure under which a substance is found in the solid, liquid, or gas phase • Each of the phases is called a domain (there is one domain per phase) • The curve defining two areas indicates the conditions under which the two phases can coexist in equilibrium

Phase Diagrams • The curve between liquid and vapor is the same as the curve for the vapor pressure as a function of temperature • The curve that separates ice from water has a negative slope because the lower density of ice makes it less stable than the higher density liquid at high pressure (the slope is almost always positive for other substances where the solid is denser than the liquid) • The triple point is the only temperature and pressure where solid, liquid and gaseous phases can coexist in equilibrium (for water, it is 0.01oC and 0.006 atm)

Phase diagrams • The phase diagram of CO2 shows why CO2(l) does not exist under normal pressure conditions • CO2(l) can only exist at pressures greater than 5.2 atm • This explains why dry ice, (i.e., CO2(s)) directly sublimes from solid to gas when heated under a normal pressure of roughly one atmosphere

Units of Concentration • Mass percent: • Molarity (M, mol/L): • Molality (m, mol/kg):

Units of Concentration • Example: Find the molarity, molar fraction, and mass percent of a 1.74 m solution of sucrose (C12H22O11, MW = 342.30 g/mol). The solution’s density is 1.12 g/mL.

Units of Concentration • Example: Find the molarity, molality and molar fraction of a 44.6% aqueous solution of NaCl (MW = 58.44 g/mol). The solution’s density is 1.17 g/mL.

Colligative Properties • A colligative property is a property of a solution that depends on the number of solute particles, but does not depend on their nature • Decrease of vapor pressure • Boiling point elevation • Freezing point depression • Osmotic pressure • If a given electrolyte dissociates into x particles, its effect will be x times greater than that of a non-electrolyte compound of the same concentration. • Note: The formulas to follow are more precise when the solute concentration is not very high, i.e: < 0.2 M

Vapor Pressure Decrease • Raoult’s law states that the partial vapor pressure of the solvent vapor above the solution, Psolvent, is given by the vapor pressure of the pure solvent , Posolvent, multiplied by the mole fraction of solvent in the solution, Xsolvent • Xsolvent = 1 - Xsolute , where Xsolute is the molar fraction of the solute (or the sum of the molar fractions if there is more than one solute) • The decrease of the vapor pressure, ∆P, is given by

Boiling Point Elevation • We have learned that the addition of a solute reduces the solution’s vapor pressure (essentially, it stabilizes the liquid with respect to the vapor) • For a liquid to boil, the vapor pressure must be equal to the atmospheric pressure • Therefore, we must reach a higher temperature for the liquid to start boiling

Boiling Point Elevation • The elevation of the boiling point, ∆Tb, is directly proportional to the solution’s molality • Kb is the ebullioscopic constant (K/m or oC/m ) • We use molality rather than molarity because the molarity changes with the temperature (molality does not) and we are trying to describe a temperature variation ∆Tb ∝ m ∆Tb = Kb m

Freezing Point Depression • Just like adding a solute stabilizes the liquid with respect to the vapor, the addition also stabilizes the liquid with respect to the solid • A solvent’s freezing point in a solution is lower than that of a pure solvent • The depression of the freezing point, ∆TF, is directly proportional to the molality of the solution • KF is the cryoscopic constant (K/m or oC/m) • This applies to volatile and non-volatile solvents ∆TF∝ m ∆TF = KF m

Boiling Point Elevation and Freezing Point Depression • Example: Find the boiling and freezing points of a solution made up of 478 g ethylene glycol, CH2(OH)CH2(OH), in 3202 g of water. The ebullioscopic and cryoscopic constants of water are respectively 0.52 K/m and1.86 K/m. • Solution: We have (478 g)/(62.07 g/mol) = 7.70 mol of glycol ethylene • The boiling point is 101.3oC A\and the freezing point is -4.47oC.

Colligative Properties and Electrolytes • For colligative properties, the number of solute particles is the crucial factor • As an example, for four different solutions : 0.1 M glucose, 0.1 M NaCl, 0.1 M CaCl2, and 0.1 M FeCl3: • the effects of the solute on ΔPsolvent,, ∆Tb,and ∆TF will be • 2 times greater for NaCl than for glucose • 3 times greater for CaCl2 than for glucose • 4 times greater for FeCl3 than for glucose

Colligative Properties and Electrolytes • We introduce the van’t Hoff factor, i, • The van’t Hoff factor would be 1,2,4 and 4 for glucose, NaCl, CaCl2, and FeCl3, respectively • Our formulas then become ∆Tb = i Kbm ∆TF = i KFm

Liquids and solutions