Solutions: formation, properties, and units

CHM116Dr. Mencer

Energetics

Energetics

Solution energetics Illustrated

If the solute is a solid or liquid, it must first be dispersed — that is, its molecular units must be pulled apart. This requires energy, and so this step always works against solution formation.

The solute must then be introduced into the solvent. Whether this is energetically favorable or unfavorable depends on the nature of the solute and solvent.

Exothermic if A-B attractions stronger than A-A + B-BEndothermic if attractions between like molecules are stronger than those between unlike molecules.

Ionic CompoundSolubility:temperature dependence

Henry’s Law: cg = kPg

Henry’s Law works for idealCases: note that in the real World, there can be deviationsFrom ideal behavior.

Gas Solubility: temperature

Suspensions, Colloids, Solutions

A Suspension and a Colloid

Suspended SiO2 (sand) settles very quickly.

Each colloidal particle of SiO2 (Ludox®) attains a (–) charge, which repels other colloidal particles.

Why are there no gas-in-gas colloids?

Colloidal charges

• Net charge on colloidal particles

• Balanced by other particles (ions) . . . But

• Colloidal particles repel one another– Stay in solution– Do not sediment

Formation and Coagulationof a Colloid

When a strong electrolyte is added to colloidal iron oxide, the charge on the surface of each particle is partially neutralized …

… and the colloidal particles coalesce into a suspension that quickly settles.

Tyndall Effect

Light of visible wavelengths scatter from colloidal particles due to similar size scale.

Soap in action

Various micelle and bilayer interactions

Reverse Micelle

• Molarity: moles of solute/liter of solution• Percent by mass: grams of solute/grams of

solution (then multiplied by 100%)• Percent by volume: milliliters of solute/milliliters

of solution (then multiplied by 100%)• Mass/volume percent: grams of solute/milliliters

of solution (then multiplied by 100%)

Most concentration units are expressed as:

Solution Concentration

Amount of solvent or solutionAmount of solute

Example 1 How would you prepare 750 g of an aqueous

solution that is 2.5% NaOH by mass?

Answer: 19 g of NaOH and 731 g of water.

Example 2 At 20 °C, pure ethanol has a density of 0.789 g/mL

and USP ethanol has a density of 0.813 g/mL. What is the mass percent ethanol in USP ethanol (which is 95% v/v)?

Answer: 92.3% by mass EtOH in USP ethanol.

• Parts per million (ppm): grams of solute/grams of solution (then multiplied by 106 or 1 million)

• Parts per billion (ppb): grams of solute/grams of solution (then multiplied by 109 or 1 billion)

• Parts per trillion (ppt): grams of solute/grams of solution (then multiplied by 1012 or 1 trillion)

• ppm, ppb, ppt ordinarily are used when expressing extremely low concentrations (a liter of H2O that is 1 ppm fluoride contains only 1 mg F–!)

Solution Concentration (cont’d)

Most concentration units are expressed as: Amount of solvent or solution

Amount of solute

Example 3 The maximum allowable level of nitrates in

drinking water in the United States is 45 mg NO3

–/L. What is this level expressed in parts per million (ppm)?

Answer: For dilute aqueous solutions (i.e. solutions that are nearly pure water) the density is so close to 1.00 gcm-3 that we can say that –

ppm = mg per Lso 45 mg NO3

–/L = 45 ppm NO3–

Molality (m): moles of solute/kilograms of solvent.

• Molarity varies with temperature (expansion or contraction of solution).

• Molality is based on mass of solvent and is independent of temperature.

• We will use molality in describing certain properties of solutions.

Solution Concentration (cont’d)

Most concentration units are expressed as: Amount of solvent or solution

Amount of solute

Example 4 What is the molality of a solution prepared by

dissolving 5.05 g naphthalene [C10H8(s)] in 75.0 mL of benzene, C6H6 (d = 0.879 g/mL)?Answer: 0.598 m C6H6

Example 5 How many grams of benzoic acid, C6H5COOH,

must be dissolved in 50.0 mL of benzene, C6H6 (d = 0.879 g/mL), to produce 0.150 m C6H5COOH?

Answer: 0.805 g C6H5COOH

• Mole fraction (xi): moles of component i per moles of all components (the solution).

• The sum of the mole fractions of all components of a solution is ____.

• Mole percent: mole fraction times 100%.

Solution Concentration (cont’d)

Most concentration units are expressed as: Amount of solvent or solution

Amount of solute

Example 6 An aqueous solution of ethylene glycol HOCH2CH2OH

used as an automobile engine coolant is 40.0% HOCH2CH2OH by mass and has a density of 1.05 g/mL. What are the (a) molarity, (b) molality, and (c) mole fraction of HOCH2CH2OH in this solution?

Example 7 An Estimation Example Without doing detailed calculations, determine which

aqueous solution has the greatest mole fraction of CH3OH: (a) 1.0 m CH3OH, (b)10.0% CH3OH by mass, or (c) xCH3OH = 0.10.

Colligative Properties

How solutes affect the properties of solutions.

Solution: Solute dispersed in a solvent.

Some Types of Solutions

• An ideal solution exists when all intermolecular forces are of comparable strength, DHsoln = 0 and DVsoln = 0.

• When solute–solvent intermolecular forces are somewhat stronger than other intermolecular forces, DHsoln < 0 and DVsoln < 0 .

• When solute–solvent intermolecular forces are somewhat weaker than other intermolecular forces, DHsoln > 0 and DVsoln > 0.

• When solute–solvent intermolecular forces are much weaker than other intermolecular forces, the solute does not dissolve in the solvent (no mixing = immiscible).– Energy released by solute–solvent interactions is

insufficient to separate solute particles or solvent particles.

Intermolecular Forcesin Solution Formation

Physical vs Chemical

• Mixing is physical process; chemical properties don’t change

• Properties of solutions are similar to those of the pure solvent

• Addition of a foreign substance to water alters the properties slightly

Three (plus one) Effects of Solute

• Reduces the vapor pressure of the solvent in the solution.

• Lowers the freezing point of the solution.

• Raises the boiling point of the solution.

• Generates Osmotic Pressure

Colligative: particles are particles• Colligative comes from colligate – to tie

together

• Colligative properties depend on amount of solute but do not depend on its chemical identity (as a first order approximation)

• Solute particles exert their effect merely by being rather than doing

Colligative Properties

Colligative properties for nonvolatile solutes: take it to the bank

• Vapour pressure is always lower

• Boiling point is always higher

• Freezing point is always lower

• Osmotic pressure drives solvent from lower concentration to higher concentration

Why does vapor pressure of the solvent decrease?

The surface area of the water exposed to the vapor phase is reduced By the presence of the solute particles at that boundary.

Molecular view of Raoult’s law:Boiling point elevation

• Vapor pressure of solvent in solution containing solute is always lower than vapor pressure of pure solvent at same T– At equilibrium rate of vaporization = rate of condensation– Solute particles occupy volume reducing rate of evaporation

the number of solvent molecules at the surface– The rate of evaporation decreases and so the vapor pressure

above the solution must decrease to recover the equilibrium

Raoult’s Law – nonvolatile solute

• Vapor pressure above solution is vapor pressure of solvent times mole fraction of solvent in solution

• Vapour pressure lowering follows:

We will return to Raoult’s law later for mixtures that contains two volatile components.

Solution Deviants

• Like ideal gas law, Raoult’s Law works for an ideal solution

• Real solutions deviate from the ideal– Concentration gets larger– Solute – solvent interactions are unequal

• Solvent – solvent interactions are stronger than the solute – solvent: Pvap is higher

• Solvent – solute interactions are stronger than solvent – solvent interactions: Pvap is lower

Colligative Properties

Two other colligative properties

• Blue curves are phase boundaries for pure solvent

• Red curves are phase boundaries for solvent in solution

• Freezing point depression– Pure solid separates out at freezing – negative ΔTf

• Boiling point elevation– Vapour pressure in solution is lower, so higher

temperature is required to reach atmospheric – positive ΔTb

Counting particles

• The influence of the solute depends only on the number of particles

• Molecular and ionic compounds will produce different numbers of particles per mole of substance (ideal behavior shown here)– 1 mole of a molecular solid → 1 mole of particles– 1 mole of NaCl → 2 moles of particles– 1 mole of CaCl2 → 3 moles of particles

Incomplete dissociation

• Not all ionic substances dissociate completely• Others form ion pairs• Still others have non-ideal solvent interactions• Van’t Hoff factor accounts for this

Van‘t Hoff factor: i = moles of particles in sol’n/moles of solute dissolved

(can be non-ideal)

At very low concentrations, the “theoretical” values of i are reached.

At higher concentrations, the values of i are significantly lower than the theoretical values; ion pairs form in solution.

Magnitude of depression

• Analagous to boiling point, the freezing point depression is proportional to the molal concentration of solute particles

• To account for dissociation, the van’t Hoff factor is applied to modify m:

mKT ff D

imKT ff D

Molecular view of Freezing point depression

• Depends on the solute only being in the liquid phase– Fewer water molecules at surface: rate of freezing drops– Ice turns into liquid– Lower temperature to regain balance– Depression of freezing point

Magnitude of elevation

• Depends on the number of particles present• Concentration is measured in molality

(independent of T)• Kb is the molal boiling point elevation constant• Note: it is the number of particles (use i as

needed)

DTf = –Kf × m DTb = Kb × m

Freezing Point Depression and Boiling Point Elevation

Osmosis: molecular discrimination

• A semi-permeable membrane discriminates on the basis of molecular type– Solvent molecules pass through– Large molecules or ions are blocked

• Solvent molecules will pass from a place of lower solute concentration to higher concentration to achieve equilibrium

Osmotic pressure

• Solvent passes into more conc solution increasing its volume

• The passage of the solvent can be prevented by application of a pressure

• The pressure to prevent transport is the osmotic pressure

Ordinarily a patient must be given intravenous fluids that are isotonic—have the same osmotic pressure as blood.

Practical Applications of Osmosis

External solution is hypertonic; produces osmotic pressure > πint. Net flow of water out of the cell.

External solution is hypotonic; produces osmotic pressure < πint. Net flow of water into the cell.

Red blood cell in isotonic solution remains the same size.

Calculating osmotic pressure

• The ideal gas law states

• But n/V = M and so

• i is this the Van’t Hoff factor• Where M is the molar concentration of

particles and Π is the osmotic pressure• Note: molarity is used not molality

nRTPV

Osmotic pressure and molecular mass

• Molar mass can be computed from any of the colligative properties

• Osmotic pressure provides the most accurate determination because of the magnitude of Π– 0.0200 M solution of glucose exerts an osmotic

pressure of 374.2 mm Hg but a freezing point depression of only 0.02ºC

Determining molar mass• A solution contains 20.0 mg insulin in 5.00 mL

develops an osmotic pressure of 12.5 mm Hg at 300 K

Assuming the species does not dissociate (i = 1)

• Moles insulin = MxV = 3.34x10-3 mmol

• Molar mass = mass of insulin/moles of insulin = 20.0 mg/3.34x10-3 mmol = 5,990 g/mol

Raoult’s Law Revisited

• Volatile solute in volatile solvent• Total pressure is the sum of the pressures of

the two components

BAtotal PPP

BBAAtotal XPXPP

Ideal behaviour of liquid mixture

• Total pressure in a mixture of toluene (b.p. = 110.6ºC) and benzene (b.p. = 80.1ºC) equals sum of vapor pressures of components

toltolbenbentotal XPXPP

Deviations from ideal

• Real solutions can deviate from the ideal:– Positive (Pvap > ideal) solute-solvent

interactions weaker– Negative (Pvap < ideal) solute-solvent

interactions stronger

Fractional distillation: separation of liquids with different boiling points

• The vapor above a liquid is richer in the more volatile component

• Boiling the mixture will give a distillate more concentrated in the volatile component

• The residue will be richer in the less volatile component

Fractional Distillation

The vapor here …

… is richer in the more volatile component than the original liquid here …

… so the liquid that condenses here will also be richer in the more volatile component.

The practice of fractional distillation

• In practice, it is not necessary to do the distillation in individual steps

• The vapor rising up the column condenses and re-evaporates continuously, progressively becoming enriched in the volatile component higher up the tube

• If the column is high enough, pure liquid will be collected in the receiver