Chem Chapter 12

The temperature dependence of the solubility of solids

∙The solubility of most solids in water increases with increasing temperature. In some cases, such as with sugar, the higher temperature increases how fast the solute dissolves and how much of the solute dissolves. ∙The solubility of solids increases with increasing temperature, e.g. 37 g at 20°C to 100g at 50°C. ∙Recrystallization: enough solid is added to a solvent to create a started solution at an elevated temperature; as the solution cools, it becomes supersaturated and the excess solid precipitates out of the solution; if the solution cools slowly, the solid forms crystals as it comes out of the solution. This is a common way to purify a solid because the crystalline structure tends to reject impurities, resulting in a purer solid.

Factors affecting the solubility of gases in water

∙The solubility of a gas in a solution is affected by both temperature and pressure. ∙Temperature: Unlike solids, whose solubility generally increases with increasing temperature, the solubility of gases in liquids decreases with increasing temperature. E.g. soda has more bubbles at room temperature than in the refrigerator. More gas comes out of solutions at room temperature than at a lower temperature because the gas is less soluble at room temperature. There is a decreasing solubility of gases with increasing temperature. When a solution is cooled, solids will precipitate out while gases become more soluble. When a solution is heated, gases will evaporate out while solids become more soluble. ∙Pressure: The higher the pressure of a gas above a liquid, the more soluble the gas is in the liquid. In a soda can, for example, carbon dioxide is maintained in the solution by a high pressure of carbon dioxide in the can. When the can is opened, the pressure is released and the solubility of carbon dioxide decreases, resulting in bubbling. At lower pressures, gases are less soluble in solutions. When volume is decreases, pressure increases, which cues the rate of molecule entering a solution to rise. The number of molecules in a solution increases until equilibrium is established again. However, the amount of gas in the solution is now greater. ∙We can quantify the solubility of gases with increasing pressure with Henry's Law: Sgas = kH x Pgas. Gas is the solubility of the gas (usually in M), kH is a constant of proportionality called the Henry's law constant that depends on the specific solute and solvent and also on temperature and is measured in M/atm, and Pgas is the partial pressure of the gas (usually in atm). The equation shows that the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. ∙The Henry's law constant is larger for polar molecules because it has a greater solubility in water than other nonpolar gases do.

Types of solutions and solubility

∙A solution may be composed of a solid and a liquid (e.g. salt and water), a gas and a liquid, 2 different liquids, or other combinations. ∙Aqueous solution: water is the solvent, and a solid, liquid, or gas is the solute. ∙Solubility: the amount of the substance that will dissolve in a given amount of solvent; ranges from 0 up; measured in grams of solute per grams of solvent (e.g. 36 g NaCl per 100g H₂O). Solubility of one substance in another depends on the tendency toward mixing and on the types of intermolecular forces. ∙Gaseous solution: gas (solute) + gas (solvent) ∙Liquid solution: gas (solute) + liquid (solvent); liquid (solute) + liquid (solvent); solid (solute) + liquid (solvent) ∙Solid solution: solid (solute) + solid (solvent)

Colligative properties: vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure

∙Colligative property: a property that depends on the number of particles dissolved in a solution, not on the type of particle. ∙4 colligative properties: vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. ∙Since these properties depend on the number of dissolved particles, nonelectrolytes are treated slightly differently than electrolytes when determine colligative properties. When 1 mol of a nonelectrolyte dissolves in a solution, it forms 1 mol of dissolved particles. When 1 mol of an electrolyte dissolves in a solution, however, it usually forms more than 1 mol of dissolved particles. For example, when 1 mol of NaCl dissolves in water, it forms 1 mol of dissolved Na⁺ and 1 mol of dissolved Cl⁻ ions. Therefore, the resulting solution has 2 mol of dissolved particles. The colligative properties of electrolyte solutions reflect this higher concentration of dissolved particles.

Colloids

∙Colloidal dispersion (or a colloid): a mixture in which a dispersed substance (which is solute-like) is finely divided in a dispersing medium (which is solvent-like). E.g. fog, smoke, whipped cream, air. ∙Whether or not a mixture is a colloid is determined by the size of the particles it contains. If the particles are small, then the mixture is a solution. If the particles have a diameter greater than 1 μm, then the mixture is a heterogeneous mixture; these particles usually settle out. If the particles are between 1 nm and 1000 nm in size, the mixture is a colloid. ∙Colloidal particles are small enough that they stay dispersed throughout the dispersing medium by collisions with other molecules or atoms. ∙When you view a colloidal particle dispersed in a liquid under a microscope, you can see its jittery motion, which proceeds along a random path; this motion is called Brownian motion, and it's caused by collisions with molecules in the liquid. ∙A colloid's dispersing substance (solute-like) and its dispersing medium (solvent-like) can both be either a solid liquid or gas. ∙Tyndall effect: the scattering of light by a colloidal dispersion. When a beam of light passes through a colloidal suspension, it's visible because the colloid particles scatter some of the light. The beam isn't visible in a noncolloidal solution. The Tyndall effect can be seen in fog or dust.

Expressing solution concentration

∙Dilute solution: contains small amounts of solute relative to the amount of solvent. For example, drinking a dilute solution of sodium chloride won't cause dehydration. ∙Concentrated solution: contains large amounts of solute relative to the amount of solvent. For example, drinking a concentrated solution of sodium chloride will cause dehydration.

Energetics of solution formation

∙Heat evolved = exothermic. Heat absorbed = endothermic. ∙Separating a solute into its constituent particles is endothermic (ΔHsolute > 0). Separating a solvent's particles from each other to make room for the solute particles is endothermic (ΔHsolvent > 0). These processes are endothermic because energy is needed to overcome the intermolecular forces holding the particles together. ∙Mixing the solute particles with the solvent particles is exothermic (ΔHmix < 0) because energy is released when the solute particles interact (through intermolecular forces) with the solvent particles. ∙According to Hess's Law, the overall enthalpy change upon solution formation, called the enthalpy of solution (ΔHsoln) is the sum of the changes in enthalpy for each step: ΔHsoln = ΔHsolute (endothermic) + ΔHsolvent (endothermic) + ΔHmix (exothermic). Since the first 2 terms are endothermic (positive ΔH), the overall sign of ΔHsoln depends on the magnitude of the individual terms. (1) If the sum of the endothermic terms is roughly equal in magnitude to the exothermic term, then ΔHsoln is about 0. The increasing entropy upon mixing drives the formation of a solution while the overall energy of the system remains nearly constant. (2) If the sum of the endothermic terms is smaller in magnitude than the exothermic term (ΔHmix > ΔHsolute + ΔHsolution), then ΔHsoln is negative and the solution process is exothermic. In this case, both the tendency toward lower energy and the tendency toward greater entropy drive the formation of the solution. (3) If the sum of the endothermic terms is greater in magnitude than the exothermic term (ΔHmix < ΔHsolute + ΔHsolution), then ΔHsoln is positive and the solution process is endothermic. In this case, as long as ΔHsoln is not too large, the tendency toward greater entropy still drives the formation of a solution. If, however, ΔHsoln is too large, a solution doesn't form.

Introduction

∙Homogenous mixtures = solutions. In solutions, atoms and molecules intermingle on the molecular and atomic scale. E.g. ocean water, gasoline, air. ∙Solution: a homogenous mixture of 2 or more substances or components. The majority component of a solution is usually a solvent, and the minority component is usually the solute. However, in some cases, a homogenous mixture will contain equal amounts of both components, and neither component can then be identified as the solvent. ∙In most solutions, the particles of the solute interact with the particles of the solvent through intermolecular forces. ∙Unless it is highly energetically unfavorable, substances tend to combine into uniform mixtures, not separate into pure substances. The tendency towards mixing results in a uniform concentration of the final solution.

Colligative properties and medical solutions

∙Hyperosmotic: solution having osmotic pressures greater than the pressure of the surrounding environment. These solutions take fluid away from the surrounding environment. ∙Hyposmotic: solutions having osmotic pressures less than those of the surrounding environment. These solutions release fluid into their surrounding environment. ∙Isosmotic (or isotonic): solutions that have osmotic pressures equal to that of their surroundings. ∙Solution concentrations are often reported in units that indicate the mass of the solute per given volume of solution or in percent mass to volume, which is the mass of the solute in arms divided by the volume of the solution in milliliters multiplied by 100%.

The effect of intermolecular forces

∙In the absence of intermolecular forces, 2 substances spontaneously mix to form a homogeneous mixture. Intermolecular forces can either promote or prevent the formation of a solution depending on the nature of the forces in the particular combination of solute and solvent. ∙Solvent-solute interactions are the interaction between a solvent particle and a solute particle. Solvent-solvent interactions are interactions between 2 or more solvent particles. Solute-solute interactions interactions are interactions between a solute particle and another solute particle. ∙Solvent-solute interactions > solvent-solvent and solute-solute interaction = solution forms ∙Solvent-solute interactions = solvent-solvent and solute-solute interactions = solution forms ∙Solvent-solute interactions < solvent-solvent and solute-solute interactions = solution may or may not form depending on relative disparity ∙Miscible: when the interactions within and between solute and solvent particles are of similar magnitude so the 2 substances are solute in each other in all proportions. E.g. hexane and pentane. ∙ If solvent-solute interactions are less than solvent-solvent and solute-solute interactions, then a solution may or may not form depending on relative disparity. If the disparity is small, the tendency to mix causes the solution to form even though the process is energetically uphill. If the disparity is large, however, a solution doesn't form, e.g. hexane and water. Although the tendency to mix is strong, it can't overcome the large energy disparity between the powerful solvent-solvent and solute-solute interactions. ∙Like dissolves like. Polar solvents tend to dissolve polar or ionic solutions. Nonpolar solvents tend dissolve nonpolar solutes. Similar kinds of solvents dissolve similar kinds of solutes.

Using parts by mass (or parts by volume) in calculations

∙We can use the parts by mass (or parts by volume) concentration of a solution as a conversion factor between mass (or volume) of the solute and mass (or volume) of the solution.

Mole fraction and mole percent

∙When the ratio of solute to solvent can vary widely, it is useful to express concentration as the amount of solute (in moles) divided by the total amount of solute and solvent (in moles). This ratio is the mole fraction, written as χsolute. χsolute = (amount solute, mol) / (total amount of solute and solvent, mol) = (nsolute) / (nsolute + nsolvent) The mole fraction can also be defined for the solvent: χsolvent = (nsolvent) / (nsolute + nsolvent) ∙Mole percent (mol %) is the mole fraction multiplied by 100%. mol % = χsolute x 100%

Aqueous solutions and heats of hydration

∙Many solutions contain ionic compounds dissolved in water. In these aqueous solutions, ΔHsolvent and ΔHmix can be combined into a single term called the heat of hydration (ΔHhydration). ∙Heat of hydration: the enthalpy change that occurs when 1 mole of the gaseous solute ions is dissolved in water, e.g. K⁺(g) + F⁻(g); the heat emitted when 1 mol of gaseous solute ions is dissolved in water. The sum of the negative of the lattice energy (which is ΔHsolute) and the heat of hydration is the heat of solution. ∙ΔHsolulte = - ΔHlattice. ΔHsolute is positive and endothermic. ΔHhdyration is negative and exothermic. ∙Because the ion-dipole interactions that occur between a dissolved ion and the surrounding water molecules are much stronger than the hydrogen bonds in water, ΔHhydration is always largely negative (exothermic) for ionic compounds. ∙Using the heat of hydration, we can write the enthalpy of solution as a sum of just 2 terms, one endothermic and one exothermic: ΔHsoln = ΔHsolute + ΔHsolvent + ΔHmix ΔHsolvent + ΔHmix = ΔHhydration ΔHsoln = ΔHsolute + ΔHhydration ∙For ionic compounds, ΔHsolute, the energy needed to separate the solute into its constituent particles is the negative of the solute's lattice energy (ΔHsolute = -ΔHlattice). For ionic solutions, then, the overall enthalpy of solution depends on the relative magnitudes of ΔHsolute and ΔHhydration, with 3 possible scenarios (in each case we refer to the magnitude, or absolute value, of ΔH): (1) Absolute value of ΔHsolute < absolute value of ΔHhydration. The amount of energy needed to separate the solute into its constituent ions is less than the energy given off when the ions are hydrated. ΔHsoln is therefore negative (e.g. -48 kJ/mol), and the solution process is exothermic. Solutes with negative enthalpies of solution include lithium bromide and potassium hydroxide. When these solutes dissolve in water [e.g. LiBr(s) ↔ Li⁺(aq) + Br⁻(aq)], the resulting solutions feel warm to the touch. (2) Absolute value of ΔHsolute > absolute value of ΔHhydration. The amount of energy needed to separate the solute into its constituent ions is greater than the energy given off when the ions are hydrated. ΔHsoln is therefore positive (e.g. +25 kJ/mol), and the solution process is endothermic (if a solution forms at all). Solute that form aqueous solutions with positive enthalpies of solution include ammonium nitrate and silver nitrate. When these solutes dissolve in water [e.g. NH₄NO₃(s) ↔ NH₄⁺(aq) + NO₃⁻(aq)], the resulting solutions feel cool to the touch. (3) Absolute value of ΔHsolute = absolute value of ΔHhydration. The amount of energy needed to separate the solute into its constituent ions is roughly equal to the energy given off when the ions are hydrated. ΔHsoln is therefore approximately 0, and the solution process is neither appreciably exothermic nor appreciably endothermic. Solutes with enthalpies of solution near 0 (e.g. 0.91 kJ/mol) include sodium chloride and sodium fluoride. When these solutes dissolve in water [e.g. NaF(s) ↔ Na⁺(aq) + F⁻(aq)], the resulting solution doesn't undergo a noticeable change in temperature.

Molality (m)

∙Molarity: the amount of solute (in moles) divided by the mass of solvent (in kilograms); a concentration unit that is independent of temperature; particularly useful when comparing concentrations over a range of different temperatures. Molality (m) = (amount of solute, mol) / (mass of solvent, kg) Units are mol/kg

Molarity (M)

∙Molarity: the amount of solute (in moles) divided by the volume of a solution (in liters). Molarity (M) = (amount of solute, mol) / (volume of solution, L) ∙Units are mol/L ∙Molarity is moles of solute per liter of solution, not per liter of solvent. To make a solution of a specified molarity, we usually put the solute into a flask and then add the solvent to the desired volume of the solution. E.g. to make a 1 M NaCl solution, we add 1 mol of NaCl to a flask and diet with water to make 1 L of solution. ∙Molarity depends on volume, and because volume varies with temperature, molarity also varies with temperature. For example, a 1 M aqueous solution at room temperature will be slightly less than 1 M at an elevated temperature because the volume of the solution is greater at the elevated temperature.

Osmotic pressure

∙Osmosis: the flow of solvent from a solution of lower solute concentration to one of higher solute concentration. Concentrated solutions draw solvent from more dilute solutions because of nature's tendency. ∙Equilibrium: pressure of excess fluid = osmotic pressure of solution. Osmosis cause the water level to rise in the solute solution and fall in the pure solvent side. ∙Semipermeable membrane: a membrane that selectively allows some substances to pass through but not others; it can be used to separate 2 halves of a cell, each half containing a liquid with different concentrations on each side. ∙Osmotic pressure: the pressure required to stop the osmotic flow. The equation for osmotic pressure: Π = MRT. M is the molarity of the solution (g/mol), R is the ideal gas constant (0.08206 L ∙atm / mol ∙ K), T is the temperature (K), and Π is the osmotic pressure (atm). 760 torr = 1 atm

Parts by mass and pays by volume

∙Parts by mass: the ratio of the mass of the solute to the mass of the solution, all multiplied by a multiplication factor. (mass solute / mass solution) x multiplication factor. ∙The particular parts by mass unit used determines the size of the multiplication factor and depends on the concentration of the solution. For example, for percent by mass, the multiplication factor is 100: percent by mass = (mass solute / mass solution) x 100. Percent means per hundred; a solution with a concentration of 14% by mass contains 14 g of solute per 100 g of solution. ∙Parts per million, which has a multiplication factor of 10⁶, or parts per billion, which has a multiplication factor of 10⁹ are used for more dilute solutions. ppm = (mass solute / mass solution) x 10⁶ ppb = (mass solute / mass solution) x 10⁹ A solution with a concentration of 15 ppm by mass has 15 g of solute per 10⁶ of solution. ∙You can report concentrations as a ratio of volumes, especially for solutions in which both the solute and the solvent are liquids. A parts by volume concentration is usually the ratio of the volume of the solute to the volume of the solution, all multiplied by a multiplication factor. (volume solute / volume solution) x multiplication factor For example, a 22% ethanol solution by volume has 22 mL of ethanol for every 100 mL of solution. ∙The units of ppm are equal to milligrams solute per liter of solution. 1 g/mL so 1 L has a mass of 1000 g.

Nature's tendency towards mixing: entropy

∙Physical systems tend toward lower potential energy; for example, 2 particles with opposite charges move toward each other because their potential energy lowers as their separation decreases (Coulomb's law). The formation of a solution, however, doesn't necessarily lower the potential energy of its constituent particles, e.g. the formation of a homogenous mixture (solution) of 2 ideal gases, where their potential energy remains unchanged upon mixing. The tendency of 2 ideal gases to mix is called entropy. ∙Entropy: a measure of energy randomization or energy dispersal in a system. Gas at any temperature above 0 K has kinetic energy due to the motion of its atoms, so when ideal gases are confined to compartments, their kinetic energies are also compartmentalized. When the barrier between the 2 compartments is removed, each gas (and its kinetic energy) becomes spread out or dispersed over a larger volume. Thus, the mixture of the 2 gases has greater energy dispersal, or greater entropy, than the separated components. - The pervasive tendency for energy to spread out, or disperse, whenever it's not restarted from doing so is the reason that 2 ideal gases mix. The transfer of thermal energy from hot to cold is another example of the tendency toward energy dispersal: heat will spread across a substance, distributing the thermal energy over a larger number of particles.

Common laboratory solvents

∙Polar: Water, Acetone (CH₃COCH₃), Methanol (CH₃OH), and Ethanol (CH₃CH₂OH). ∙Nonpolar: Hexane (C₆H₁₄), Diethyl ether (CH₃CH₂OCH₂CH₃), Toulene (C₇H₈), and Carbon tetrachloride (CCl₄). ∙-OH bonds are highly polar. ∙C-O bonds are polar. ∙N-H bonds are polar. ∙C-H bonds are nearly nonpolar. ∙Water soluble = polar. Fat soluble = nonpolar. Vitamins C and B₅ are water soluble. Vitamins K and A are fat soluble. ∙As the nonpolar chain in a hydrocarbon becomes longer, the OH groups become less important to its polarity. Thus, as a hydrocarbon chain lengthens, it becomes more nonpolar even though it originally started out as polar.

Colligative properties of strong electrolyte solutions

∙Since colligative properties depend on the number of dissolved particles in a solution, electrolytes must therefore be treated slightly differently than non electrolytes when determining colligative properties. For example, 1 mol of sodium chloride dissociates into nearly 2 mol of ions in a outline. ∙The ratio of moles of particles in solution to moles of formula until dissolved is called the van't Hoff factor (i): i = (moles of particle in solution) / (moles of formula units dissolved). ∙The van't Hoff factor only occurs exactly in very dilute solutions; typically, the measured i value is less than the expected i value. The van't Hoff factor approaches the expected value at infinite dilution (as the concentration approaches 0). ∙The reason measured van't Hoff factors don't exactly equal expected values is that some ions effectively pair in solution. We expect the dissociation of an ionic solution to be complete in solution, but in reality the dissociation isn't complete: at any moment, some cations pair with anions, slightly reducing the number of particles in solution and lowering the concentration of particles below what would be expected. ∙To calculate freezing point depression, boiling point elevation, and osmotic pressure of ionic solutions we use the van' Hoff factor in each equation as follows: ΔTf = im x Kf (freezing point depression) ΔTb = im x Kb (boiling point elevation) Π = iMRT (osmotic pressure)

Vapor pressures of solutions containing a volatile (nonelectrolyte) solute

∙Some solutions contain volatile solvents AND volatile solutes. In this case, both the solvent and the solute contribute to the overall vapor pressure of the solution. A solution like this may be an ideal solution (in which case its behavior follows Raoult's law at all concentrations for both the solvent and the solute) or it may be nonideal (in which case it doesn't follow Raoult's law). ∙In an ideal solution, the solute-solvent interactions are similar in magnitude to the solute-solute and solvent-solvent interactions. In this type of solution, the solute simply dilutes the solvent and ideal behavior is observed. The vapor pressure of each of the solution components is described by Raoult's law throughout the entire composition range of the solution. In an ideal solution, both components follow Raoult's law. For a two-component solution containing liquids A and B, we can write: PA = (χA)(P°A) PB = (χB)(P°B) P° and P are measured in torr; χ is mol, but its units cancel out. ∙The total pressure above such a solution is the sum of the partial pressures of the components: Ptot = PA + PB ∙In a nonideal solution, the solute-solvent interactions are either stronger or weaker than the solvent-solvent interactions. If the solute-solvent interactions are stronger, then the solute tends to prevent the solvent from vaporizing as readily as it would otherwise. If the solution is sufficiently dilute, then the effect will be small and Raoult's law works as an approximation. However, if the solution isn't dilute, then the effect will be significant and the vapor pressure of the solution (strong solute-solvent interactions) will be less than that predicted by Raoult's law; it experiences negative deviations from Raoult's law (Ptot experimentally measured < Ptot ideal). If, on the other hand, the solute-solvent interactions are weaker than the solvent-solvent interactions, then the solute tends to allow more vaporization than would occur with just the solvent. If the solution is not dilute, the effect will be significant and the vapor pressure of the solution will be greater than predicted by Raoult's law; it displays positive deviations from Raoult's law (Ptot experimentally measured > Ptot ideal). ∙A solution contains equal amounts (in moles) of liquid components A and B. The vapor pressure of pure A is 100 mmHg and that of pure B is 200 mmHg. The experimentally measured vapor pressure of the solution is 120 mmHg. What are the relative strengths of the solute-solute, solute-solvent, and solvent-solvent interactions in this solution? The solute-solvent interactions must be stronger than the solute-solute and solvent-solvent interactions. The stronger interactions lower the vapor pressure form the expected ideal value of 150 mmHg.

Solution equilibrium and factors affecting solubility

∙The dissolution of a solute in a solvent is a equilibrium process. Initially, the solvent molecules rapidly solvate the cations and anions of the solute, resulting in a noticeable decrease in the amount of solid ionic solute in the water. Over time, however, the concentration of the dissolved form of the ionic compound in the solution increases. This dissolved compound then begins to recrystallize as a solid. Initially the rate of dissolution far exceeds the rate of recrystallization, but as the concentration of the dissolved ionic compound increases, the rate of recrystallization also increase. Eventually the rates of dissolution and recrystallization become equal, and dynamic equilibrium has been reached: NaCl ⇌ Na⁺(aq) + Cl⁻(aq) ∙When a solute is first added to a solvent, the solute ions dissolve into the solvent. As the solution become more concentrated, some of the ions recrystallize as the solid form of the ionic compound. When the rate of dissolution equals the rate of recrystallization, dynamic equilibrium has been reached. ∙3 steps: (1) Initial, (2) Dissolving: rate of dissolution > rate of recrystallization, (3) Dynamic equilibrium: rate of dissolution = rate of recrystallization. ∙Saturated solution: a solution in which the dissolved solute is in dynamic equilibrium with the solid (undissolved) solute. If you add additional solute to a saturated solution, it won't dissolve. ∙Unsaturated solution: a solution containing less than the equilibrium amount of solute. If you add additional solute to an unsaturated solution, it will dissolve. ∙Supersaturated solution: a solution containing more than the equilibrium amount of solute; forms under certain circumstances; unstable and the excess solute normally precipitates out of the solution. I some cases, if left undisturbed, a supersaturated solution can exist for an extended period of time, e.g. a small piece of solid sodium acetate added to a supersaturated solution of sodium acetate, triggering the precipitation of the solute, which crystallizes out of the solution in a dramatic way.

Strong electrolytes and vapor pressure

∙The freezing point depression of a solution containing an electrolyte solute is greater than that of a solution containing the same concentration of non electrolyte solute. In the same way, vapor pressure lowering is greater for the same reasons. The vapor pressure for a sodium chloride (NaCl) solution is lowered about twice as much as it is for a nonelectrolyte solution of the same concentration. To calculate the vapor pressure of a solution containing an ionic solute, we must account for the dissociation of the solute when we calculate the mole fraction of the solvent. ∙To find the mole fraction of the solvent, we multiply the solute by how many ions it dissociates it into. We divide the moles of the solvent by the moles of solute multiplied by the number of ions it dissociates into and add that value to the moles of solvent. We multiply the mole fraction we obtain for the solvent by the vapor pressure of the solvent to obtain the vapor pressure of the solution.

Vapor pressure lowering

∙The vapor pressure of a liquid is the pressure of the gas above the liquid when the 2 are in dynamic equilibrium (i.e. when the rate of vaporization equals the rate of condensation). The vapor pressure of a nonvolatile nonelectrolyte solution is lower than the vapor pressure of a pure solvent. In other words, the vapor pressure of a solution is lower than the vapor pressure of a pure solvent. ∙Solute particles interfere with the ability of a solvent to vaporize, diminishing the rate of vaporization of a solution in comparison to the pure solvent. The change in the rate of vaporization creates an imbalance in the rates; the rate of condensation is now grater than the rate of vaporization. The net effect is that some of the gas molecules condense into the liquid state. As they condense, the reduced number of molecules in the gas state causes the rate of condensation to decrease. Eventually the 2 states reach equilibrium, but with fewer molecules in the gas phase/after the concentration of solvent molecules in the gas state has decreased. The result is a lower vapor pressure for the solution compared to the pure solvent. ∙A concentrated solution is thirsty, meaning it has the ability to draw solvent to itself. Since nature's tendency is to mix, if a pure solvent and concentrated solution are combined in a beaker, they naturally form a mixture in which the concentrated solution becomes less concentrated than it was initially. Similarity, if a pure solvent and concentrated solution are combined in a sealed container (even though they're in separate beakers), the 2 mix so that the concentrated solution becomes less concentrated. The net transfer of solvent form the beaker containing pure solvent to the one containing the solution shows that the vapor pressure of the solution is lower than that of the pure solvent. As solvent molecules vaporize, the vapor pressure in the sealed container rises. Before dynamic equilibrium is reached, the pressure exceeds the vapor pressure of the solution, causing molecules to condense into the solution. There, molecules constantly vaporize fro meh pure solvent, but the solvent's vapor pressure is never reached because molecules are constantly condensing into the solution. The result is a continuous transfer of solvent molecules from the pure solvent to the solution. The level of pure solvent drops, while the level of solution rises. ∙Raoult's law: Psolution = (χsolvent)(P°solvent) In this equation, Psolution is the vapor pressure of the solution, χsolvent is the mole fraction of the solvent, and P°solvent is the vapor pressure of the pure solvent at the same temperature. Psolution and P°solvent are measured in torr; χsolvent is measured in mol, but has no units. ∙The vapor pressure of a solution is directly proportional to the amount of solvent in the solution, e.g. the vapor pressure of the solvent is the mole fraction of the vapor pressure of the solution. ∙Vapor pressure lowering (ΔP): the difference in vapor pressure between the pure solvent and the solution; shows how much vapor pressure is lowered by a solute. ΔP = P°solvent - Psolution ∙For a 2-component solution, we substitute χsolvent for 1 - solute into Raoult's law. ΔP = (χsolute)(P°solvent) This equation shows that the lowering of the vapor pressure is directly proportional to the mole fraction of the solute. ∙1 g = 1 mL

Freezing point depression and boiling point elevation

∙Vapor pressure lowering occurs at all temperature. Vapor pressure is shifted downward compared to a pure solvent. Consequently, the vapor pressure cure intersects the solid-gas curve at a lower temperature. The net effect is that the solution has a lower melting point and a higher boiling point than the pure solvent. A nonvolatile solute lowers the vapor pressure of a solution, resulting in a lower freezing point and an elevated boiling point. These effects are called freezing point depression and boiling point elevation, both of which are colligative properties (like vapor pressure lowering). ∙The freezing point of a solution containing a nonvolatile solute is lower than the freezing point of the pure solvent, e.g. antifreeze. The more concentrated the solution, the lower the freezing point becomes. The amount that the freezing point decreases is given by this equation: ΔTf = m x Kf ΔTf is the change in temperature of the freezing point in Celsius (relative to the freezing point of the pure solvent), usually reported as a positive number. m is the molality of the solution in moles solute per kilogram solvent (m/kg). And Kf is the freezing point depression constant for the solvent (°C/m). ∙When an aqueous solution containing a dissolved solid solute freezes slowly, the ice that forms doesn't normally contain much of the solute. E.g. the ice that forms in an ocean isn't salt water, but it is fresh water. As ice forms, the crystal structure tends to exclude solute particles. ∙The boiling point of a solution containing a nonvolatile solute is higher than the boiling point of a pure solvent. The amount that the bowling point rises in solutions is given by the equation: ΔTb = m x Kb ΔTb is the change in temperature of the boiling point in Celsius (relative to the boiling point of the pure solvent). m is the molality of the solution in moles solute per kilogram solvent (m/kg). And Kb is the boiling point elevation constant for the solvent (°C/m).