Chapter 11 Properties of Solutions
Solutions Homogeneous mixtures of two or more substances Composition is uniform throughout the sample No chemical reaction between the components of the mixture
Solvents and Solutes
Types of Solution
Solution always has the physical state of the solvent! The solvent is water in an aqueous solution
Solution Composition Measure of the amount of solute dissolved in a given amount of solution
Dilute Solutions Small amounts of solute are dissolved Concentrated Solutions Large amounts of solute are dissolved
Molarity (M) The number of moles of solute in exactly 1 L of solution: molarity = moles solute / liters of solution A direct measure of the number of particles (ions, atoms or molecules) of solute present
Mass Percent The percent by mass of the solute in the solution: mass % = (mass solute / mass solution) x 100% where: mass solution = mass solute + mass solvent
Mole Fraction ( ) The ratio of the number of moles of a particular component to the total number of moles of solution: A n A n n A B...
Molality (m) The number of moles of solute in exactly 1 kg of solvent: molality = moles solute / kilograms of solvent
Equivalent Mass Definition depends on the type of reaction being studied: 1. Acid-Base Reactions the mass of acid or base which can produce or accept one mole of protons 2. Redox Reactions the mass of oxidizing or reducing agent which can produce or accept one mole of electrons Cr 2 O 7 2- (aq) + 14H + + 6e - 2Cr 3+ (aq) + 7H 2 O(l) 1 mole K 2 Cr 2 O 7 (aq) = 294.20 g = 6 mol e - equivalent mass K 2 Cr 2 O 7 = molar mass / 6 = 49.033 g
Normality (N) The number of equivalents of solute in exactly 1 L of solution: normality = equivalents solute / liters of solution where: equivalents solute = mass solute / equivalent mass
Relationship between Normality and Molarity normality = n x molarity where: n = number of protons or electrons transferred
Solubility
Many ionic compounds readily dissolve in water because it is polar
Methanol dissolves in water also because they are both polar
While oil does not dissolve in water since oil is non-polar and water is polar
Like Dissolves Like For a solution to form the polarities of the solvent and solute must be similar
Example
Thermodynamics of Solution Formation
Formation of a Solutions Step 1: expand the solute Step 2: expand the solvent Step 3: form the solution enthalpy of solution, H soln = H 1 + H 2 + H 3 H 1 and H 2 are endothermic H 3 is normally exothermic H soln can be exothermic or endothermic
Exothermic H soln Occurs when energy released in step 3 (solution formation) is greater than energy absorbed in steps 1 and 2 (solute and solvent expansion) Example: polar solute in polar solvent H 1 > 0 since the intermolecular forces between the solute molecules have to be broken H 2 > 0 (large) since the intermolecular forces between the solvent molecules (e.g. hydrogen bonds) have to be broken H 3 < 0 (large) due to strong attraction of solute and solvent
Endothermic H soln Occurs when energy released in step 3 (solution formation) is less than energy absorbed in steps 1 and 2 (solute and solvent expansion) Example: non-polar solute in polar solvent H 1 > 0 (small) since the weak intermolecular (dispersion) forces between the solute molecules have to be broken H 2 > 0 (large) since the intermolecular forces between the solvent molecules (e.g. hydrogen bonds) have to be broken H 3 < 0 (small) due to weak attraction of solute and solvent
If H soln is negative, a solution will readily form! S univ = S sys + S surr Both S sys is positive (due to positional entropy) and S surr are positive (negative H soln ) so S univ positive (spontaneous)
If H soln is small and positive, a solution can still form! Still dissolves due to increase in positional entropy: S univ = S sys + S surr S sys more positive than S surr negative (small positive H soln ) so S univ positive (spontaneous)
However, if H soln is large and positive, a solution is very unlikely to form! S univ = S sys + S surr S surr more negative (large positive H soln ) is than S sys positive so S univ negative (non-spontaneous)
Summary
Factors Affecting Solubility
Solubility and Structure Molecules with many polar bonds tend to be soluble in water (hydrophillic) while molecules with few polar bonds are generally insoluble in water (hydrophobic) non-polar polar
Surfactants Some molecules are amphiphillic in that they are both hydrophilic and hydrophobic with one polar end and one non-polar end The hydrophobic ends dissolve in non-polar substances like oil forming a polar outer shell which can then dissolve in water Detergents work using this principle
Solubility and Pressure The solubility of gases in liquids increase with pressure
Can of Soda
William Henry (1774-1836)
Henry s Law The amount of gas dissolved in a solution is directly proportional to the pressure of that gas above the solution: C = kp where: C = concentration of dissolved gas (moll -1 ) P = pressure of gaseous solute above solution (atm) k = Henry s Law constant - a constant characteristic of a particular solution (moll -1 atm -1 )
Limitations of Henry s Law Henry s Law only applies when there is no chemical reaction between the solute and solvent (dilute solutions of gases which do not dissociate in or react with the solvent) Examples: Henry s Law is obeyed for oxygen gas dissolving in water Henry s Law is NOT obeyed for hydrogen chloride gas dissolving in water since it dissociates: HCl g H aq Cl aq HOl 2 () ( ) ( ) ( )
Solubility and Temperature While solids dissolve more rapidly at higher temperatures, the amount of solid dissolving normally increases but can sometimes decrease (retrograde solubility)
The solubility of gases in water always decrease with increasing temperature:
Colligative Properties Colligative properties of solutions depend only on the number of particles of solute and not on their identities The most important colligative properties are vapor pressure lowering, boiling point elevation, freezing point depression and osmotic pressure. These properties yield information on the number of solute particles in solution and so can be used to obtain the molecular weight of the solute Example: Equal amounts of Na 2 SO 4 and CaCl 2 would exhibit the same colligative properties (vapor pressure lowering, boiling point elevation, freezing point depression and osmotic pressure) since each compound dissolves to form the same number of ions
Vapor Pressure of Solutions
Addition of a non-volatile solute lowers the vapor pressure of a solvent: Why? The solute decreases the number of solvent molecules per unit volume and hence the probability of their escape
Aqueous Solution and Water in Closed Container Since the vapor pressure of the pure solvent is greater than the vapor pressure of the solution, the solution absorbs vapor and the solvent emits vapor until all the solvent is transferred into the solution and equilibrium is reached
François-Marie Raoult (1830-1901)
Raoult s Law The vapor pressure of a solution containing a non-volatile solute is directly proportional to the mole fraction of the solvent present: P 0 soln solvent solvent where: P soln = vapor pressure of the solution soln = mole fraction of the solvent P 0 solvent = vapor pressure of the pure solvent P
Raoult s Law is another Linear Equation! P P 0 soln solvent solvent
Molar Mass from Vapor Pressure Since the lowering of vapor pressure depends on the number of solute particles present in the solution, by dissolving a known mass of solute in a solvent and measuring the resultant vapor pressure we can use Raoult s Law to determine the number of moles of solute present and from that calculate its molar mass
Characterizing Ionic Solutions Since ionic compounds dissolve to form multiple ions, the lowering of the vapor pressure is greater than if the compound dissolved in its undissociated form This gives us important information on the nature of the solution after it dissolves Example: Sodium chloride when dissolved in water lowers the vapor pressure approximately twice as much as expected since it forms two ions in solution
Predict the vapor pressure of a solution prepared by mixing 24.5 g of solid sodium phosphate with 256 g of water at 25 C. The vapor pressure of pure water at 25 C is 23.76 torr
Non-volatile Solutes In most solutions, the solute cannot be assumed to be non-volatile For liquid-liquid solutions where both components are volatile, a modified form of Raoult s Law must be used: P P P P P 0 0 total A B A A B B where: P total = total vapor pressure of the solution P A and P B = partial pressures of A and B A and B = mole fractions of A and B P 0 A and P 0 B = vapor pressures of pure A and pure B
Ideal Solutions Obey Raoult s Law perfectly Ideal behavior is rare but can be approached when the solute-solute, solvent-solvent and solute-solvent interactions are very similar ( H soln = 0, T = 0) Example:
Non-ideal Solutions Deviate from Raoult s Law due to interactions between the solute and the solvent in solution
Negative Deviations from Raoult s Law Observed vapor pressure is lower than expected If the solvent has a strong affinity for the solute (e.g. forms hydrogen bonds), the solvent molecules will not be able to escape as easily ( H soln < 0, T > 0) Example: acetone water
Positive Deviations from Raoult s Law Observed vapor pressure is higher than expected If the solvent-solute interactions are weaker than the solvent-solvent and solute-solute interactions, the solvent molecules will be able to escape more easily ( H soln > 0, T < 0) Example:
Summary
What deviation, if any, from Raoult s Law would you expect when the following pairs of liquids are mixed? a) NH 3 and H 2 O b) CH 3 Cl and CCl 4 c) O 2 and N 2
Boiling-point Elevation The normal boiling point of a liquid occurs at a temperature where the vapor pressure equals 1 atm Since non-volatile solutes lower the vapor pressure of a solvent, the solution has to be heated to a higher temperature in order for it to boil
Calculating Changes in Boiling-point The magnitude of the elevation depends on the concentration of the solute: T b = K b m solute where: T b = the boiling point elevation ( C) = T b (solution) T b (solvent) K b = molal boiling-point elevation constant ( C kg mol -1 ) m solute = molality of the solute in the solution By measuring the boiling-point elevation produced from a given mass of solute (and assuming K b is known), it is possible to calculate the molality of the solute and hence its molar mass
Boiling-point Elevation Constants (K b )
Freezing-point Depression The vapor pressures of a solid and a liquid are the same at the normal freezing point Since non-volatile solutes lower the vapor pressure of a solvent, the solution has to be cooled to a lower temperature in order for it to freeze
Road Salting sodium chloride and calcium chloride are spread on roads and pavements to prevent ice from forming during freezing weather
Calculating Changes in Freezing-point The magnitude of the depression depends on the concentration of the solute: T f = K f m solute where: T b = the freezing point depression ( C) = T f (solvent) T f (solution) K f = molal freezing-point depression constant ( C kg mol -1 ) m solute = molality of the solute in the solution By measuring the freezing-point depression produced from a given mass of solute (and assuming K f is known), it is possible to calculate the molality of the solute and hence its molar mass
Freezing-point Depression Constants (K f )
Osmosis When a solution and a pure solvent are separated by a semipermeable membrane (allowing solvent but not solute molecules to pass) the volume of solvent decreases and the volume of solution increases as the solvent crosses the membrane until equilibrium is reached At equilibrium, the liquid level of the solution is higher than the liquid level of the solvent so it experiences a higher hydrostatic pressure This excess pressure is called the osmotic pressure
Explaining Osmotic Pressure Initially, the rate of transfer from the solution to the solvent is slower than the rate of transfer of from the solvent to the solution due to the solute molecules interfering with the passage of the solvent causing a net transfer of solvent molecules into the solution As the solution level rises, the resulting pressure forces the solvent molecules back through the membrane until the rate of solvent transfer is equal in both directions and equilibrium is reached
Measuring Osmotic Pressure Osmotic pressure can be measured by applying an external pressure of increasing magnitude until osmosis stops The minimum pressure that stops the osmosis is equal to the osmotic pressure of the solution
Calculating Osmotic Pressure The magnitude of the osmotic pressure depends on the concentration of the solute: = MRT where: = the osmotic pressure (atm) M = the molarity of the solution (moll -1 ) R = the gas law constant (0.08206 L atm mol -1 K -1 ) T = the temperature (K) By measuring the osmotic pressure produced from a given mass of solute, it is possible to calculate the molarity of the solute and hence its molar mass
Kidney Dialysis A type of osmosis occurring at the walls of animal and plant cells which allow the transfer of both solvent molecules and small solute molecules and ions This is technique is used in dialysis machines which pass blood from a patient with kidney failure through a cellophane tube (acting as a semi-permeable membrane) which is then immersed in a dialyzing solution containing the same concentrations of ions and small molecules as blood but none of the waste products The resulting transfer into the dialyzing solution cleans the blood of waste
Intravenous Administration of Fluids to the Body Fluids administered to the body intravenously must have identical osmotic pressures to body fluids Such fluids are said to be isotonic If fluids are administered to the body with a higher osmotic pressure than that of body fluids, the cells will shrivel due to a net transfer of water out of the cells (crenation) Such fluids are said to be hypertonic If fluids are administered to the body with a lower osmotic pressure than that of body fluids, the cells will rupture due to a net transfer of water into of the cells (hemolysis) Such fluids are said to be hypotonic
Osmosis and Red Blood Cells isotonic hypertonic hypotonic
Reverse Osmosis Occurs when a solution in contact with pure solvent is subjected to an external pressure which is larger than its osmotic pressure causing a net flow of solvent from the solution to the solvent Here the semi-permeable membrane acts as a filter to remove solute particles
Desalination The removal of dissolved salts from seawater to produce drinking water can be achieved by reverse osmosis
Jacobus Henricus van t Hoff (1852-1911) First Nobel Laureate in Chemistry (1901)
Colligative Properties of Electrolyte Solutions Since colligative properties depend on the number of solute particles, solutes that dissociate into several ions will have an effect proportional to the number of ions which they form The relationship between the number of moles of solute dissolved and the number of particles in solution is expressed by the van t Hoff factor, i: i moles of particles in solution moles of solute dissolved The colligative properties of electrolyte solutions are then described by including the van t Hoff factor in the appropriate equation: T b = ik b m solute T f = ik f m solute = imrt
Experimental van t Hoff Factors Theoretically, the value for i should always be equal to the number of ions produced by each formula unit of solute However, in practice the observed factors are generally smaller:
Ion Pairing (Association) The theoretical value of i assumes that when a salt dissolves, it completely dissolves into its ions which move independently However, in practice ion pairing probably occurs where at a given instant a small percentage of the ions are paired and therefore count as a single particle (which has the effect of lowering i) Ion pairing is most important in concentrated solutions and when highly charged ions are present (e.g. Fe 3+ ) As a solution becomes more dilute less ion pairing occurs
Colloidal Dispersions Colloidal Dispersions (or colloids for short) are suspensions of tiny particles in a solid, liquid or gas The suspended particles are single large molecules or molecular/ionic aggregates ranging in size from 1-1000 nm Colloids are classified according to the states of the dispersed phase and the dispersing medium:
The Tyndall Effect Used to distinguish a colloid from a solution since only in a colloid will the scattering of light by suspended particles be observed
Stabilization of Colloids Why do colloidal particles remain in suspension rather than form larger aggregates which then precipitate out? Most likely this is due to colloidal particles (which are initially neutral) attracting from the medium, layers of ions all of the same charge These charged particles in turn attract another layer of oppositely charged ions Since the colloidal particles all have an outer layer of ions with the same charge, they repel each other and do not aggregate
The haze seen in Titan s atmosphere (the largest moon of the planet Saturn) consists of tiny droplets of liquid hydrocarbons suspended in its nitrogen-rich atmosphere: Which kind of colloid is this?