Solutions. Solution Concentration Although molarity (M) is used for stoichiometry calculations, there are many other ways to express the concentration

SolutionsSolutions

Solution Concentration Solution Concentration

Although molarity (M) is used for Although molarity (M) is used for stoichiometry calculations, there are stoichiometry calculations, there are many other ways to express the many other ways to express the concentration of a solution.concentration of a solution.

Molarity will vary slightly with Molarity will vary slightly with changes in temperature as the volume changes in temperature as the volume expands or contracts. Units such as expands or contracts. Units such as mass percent, mole fraction, or molarity mass percent, mole fraction, or molarity remain constant as temperature remain constant as temperature changes.changes.

Solution ConcentrationSolution Concentration

Mass percent = (Mass percent = (mass of solute)mass of solute) (100%) (100%) (mass of solution)(mass of solution)

Mole fraction (XMole fraction (XAA) = () = (moles of A)moles of A)total # of molestotal # of moles

Molality (m) = Molality (m) = moles of solutemoles of solute kg of solventkg of solvent

The Solution ProcessThe Solution Process

We will focus on solid or liquid We will focus on solid or liquid solutes dissolved in a liquid solvent. solutes dissolved in a liquid solvent. Since all particles are in contact Since all particles are in contact with each other, the solute-solute with each other, the solute-solute and solvent-solvent forces of and solvent-solvent forces of attraction are disrupted, and new, attraction are disrupted, and new, solute-solvent forces of attraction solute-solvent forces of attraction are created.are created.


The disruption of solute-solute and The disruption of solute-solute and solvent-solvent forces of attraction solvent-solvent forces of attraction requires energy, and is endothermic. requires energy, and is endothermic. The interaction of solvent and solute The interaction of solvent and solute usually releases energy. The sum of the usually releases energy. The sum of the energy of all three steps is called the energy of all three steps is called the enthalpy of solutionenthalpy of solution, , ΔΔHHoo

solnsoln..

Note that solutions may form Note that solutions may form whether the net process is endothermic whether the net process is endothermic or exothermic.or exothermic.



The general rule on solution The general rule on solution formation is:formation is:

Like dissolves like.Like dissolves like.

Polar and ionic compounds dissolve Polar and ionic compounds dissolve in polar solvents. Non-polar in polar solvents. Non-polar compounds dissolve in non-polar compounds dissolve in non-polar solvents.solvents.

Like Dissolves LikeLike Dissolves Like

Vitamin A Vitamin A consists almost consists almost entirely of carbon entirely of carbon and hydrogen, and hydrogen, and is non-polar. and is non-polar. As a result, As a result, vitamin A is fat-vitamin A is fat-soluble, and can soluble, and can be stored in the be stored in the body.body.

Like Dissolves LikeLike Dissolves Like

Vitamin C Vitamin C contains polar contains polar C-O and O-H C-O and O-H bonds. It is bonds. It is water soluble, water soluble, and must be and must be consumed often, consumed often, as it is excreted as it is excreted easily.easily.

O-H bonds

C-O bond


In addition to the enthalpy of In addition to the enthalpy of solution, we must also consider the solution, we must also consider the entropy of mixingentropy of mixing. Entropy is a measure . Entropy is a measure of randomness or disorder. An increase of randomness or disorder. An increase in entropy makes a process more likely in entropy makes a process more likely to occur.to occur.

Since mixing pure substances Since mixing pure substances increases entropy, this factor makes increases entropy, this factor makes processes that are slightly endothermic processes that are slightly endothermic favorable.favorable.


Disrupt-ion of solute

Disrupt-ion of solvent

Solute/Solvent interact-ion

Factors Affecting Factors Affecting SolubilitySolubility

Molecular StructureMolecular Structure Pressure (for gaseous solutes)Pressure (for gaseous solutes) TemperatureTemperature

Liquid-Liquid SolutionsLiquid-Liquid Solutions

When two volatile liquids mix, When two volatile liquids mix, they form a solution. An they form a solution. An ideal ideal solutionsolution, similar to an ideal gas, will , similar to an ideal gas, will exert a vapor pressure which is exert a vapor pressure which is related to the vapor pressures of the related to the vapor pressures of the pure liquids and their relative pure liquids and their relative abundance in the mixture.abundance in the mixture.


The solution obeys The solution obeys Raoult’s law:Raoult’s law:

PPAA = = χχAAPPooAA

PPBB = = χχBBPPooBB

where where χχAA is the mole fraction of is the mole fraction of component Acomponent A

and Pand PooA A is the vapor pressure of pure A is the vapor pressure of pure A


Raoult’s law Raoult’s law is best seen is best seen graphically. The graphically. The vapor pressure vapor pressure of the mixture is of the mixture is the sum of the the sum of the vapor pressures vapor pressures of each of each component.component.


Ideal solutions Ideal solutions typically involve typically involve non-polar non-polar molecules with molecules with similar structures. similar structures. Mixtures of liquid Mixtures of liquid hydrocarbons hydrocarbons often form ideal often form ideal solutions.solutions.


If the two components of the If the two components of the mixture are strongly attracted to mixture are strongly attracted to each other, such as two polar each other, such as two polar molecules, the vapor pressure of molecules, the vapor pressure of the mixture is often the mixture is often lessless thanthan that predicted by Raoult’s law. that predicted by Raoult’s law.


This is known This is known as a as a negative negative deviationdeviation from from Raoult’s law. It Raoult’s law. It occurs with occurs with mixtures of liquid mixtures of liquid acids and water. As acids and water. As the acid ionizes, the the acid ionizes, the forces of attraction forces of attraction in the mixture in the mixture increase.increase.


If a mixture contains liquids If a mixture contains liquids that have stronger attractive that have stronger attractive forces when pure than when forces when pure than when mixed, the mixture will exert a mixed, the mixture will exert a vapor pressure that is greater vapor pressure that is greater than that predicted by Raoult’s than that predicted by Raoult’s law. This is called a law. This is called a positive positive deviationdeviation from Raoult’s law. from Raoult’s law.


A mixture of ethanol and water exhibits a positive deviation from Raoult’s law. The hydrogen bonding of each pure liquid is disrupted when the two liquids are mixed.

Pressure EffectsPressure Effects

Gases dissolved in a liquid solute Gases dissolved in a liquid solute obey obey Henry’s LawHenry’s Law::

C = kPC = kP

where C is the concentration, k is a where C is the concentration, k is a constant specific to solute and constant specific to solute and solvent, and P is the pressure of the solvent, and P is the pressure of the gas above the solutiongas above the solution


Gases dissolved in a liquid solute Gases dissolved in a liquid solute obey obey Henry’s LawHenry’s Law::

C = kPC = kP

The amount of a gas dissolved in The amount of a gas dissolved in a solution is directly proportional to a solution is directly proportional to the pressure of the gas above the the pressure of the gas above the solution.solution.


Temperature EffectsTemperature Effects

For gases For gases dissolved in liquids, dissolved in liquids, the solubility the solubility decreases as decreases as temperature temperature increases. That is, increases. That is, gases dissolve gases dissolve better in cold better in cold liquids than in liquids than in warmer liquids.warmer liquids.

Temperature EffectsTemperature Effects

For solid For solid solutes dissolved solutes dissolved in water, the in water, the effect of effect of temperature on temperature on solubility is solubility is difficult to difficult to predict. predict.

The Colligative The Colligative PropertiesProperties

The The colligative propertiescolligative properties are are properties that depend upon the properties that depend upon the concentration of particles (molecules concentration of particles (molecules or ions) dissolved in a volatile solvent, or ions) dissolved in a volatile solvent, and not on the nature of the particles. and not on the nature of the particles.

They include:They include: vapor pressurevapor pressure freezing pointfreezing point boiling pointboiling point osmotic pressureosmotic pressure

The Colligative The Colligative PropertiesProperties

Relatively simple mathematical Relatively simple mathematical relationships can be used to predict the relationships can be used to predict the changes in vapor pressure, freezing changes in vapor pressure, freezing and boiling point, etc. and boiling point, etc.

The properties can be predicted The properties can be predicted for for dilute solutionsdilute solutions (<0.1M) of (<0.1M) of non-non-volatilevolatile solute (usually solids) dissolved solute (usually solids) dissolved in a in a volatilevolatile solvent (usually a liquid). solvent (usually a liquid).

Vapor PressureVapor Pressure

The The addition of a addition of a non-volatile non-volatile solute to a solute to a volatile volatile solvent lowers solvent lowers the vapor the vapor pressure of pressure of the solvent.the solvent.


The decrease in vapor pressure The decrease in vapor pressure can be understood by looking at the can be understood by looking at the evaporation process. We need to evaporation process. We need to compare the enthalpy change (compare the enthalpy change (ΔΔHHvapvap) ) and entropy change of evaporation.and entropy change of evaporation.


The vapor pressure of the pure The vapor pressure of the pure solvent or the solution is the result of solvent or the solution is the result of solvent molecules escaping the liquid solvent molecules escaping the liquid surface and becoming gaseous. Since surface and becoming gaseous. Since the solute is the solute is non-volatilenon-volatile, it does not , it does not evaporate.evaporate.

Since only solvent molecules Since only solvent molecules evaporate, the enthalpy change for pure evaporate, the enthalpy change for pure solvent or the solution is the same.solvent or the solution is the same.

Vapor PressureVapor PressureThe The

decrease in decrease in vapor pressure vapor pressure of the solution is of the solution is the result of the result of changes in changes in entropy. The entropy. The vapor in either vapor in either container is container is disordered, due disordered, due to the random to the random motion of motion of gaseous solvent.gaseous solvent.


The liquid The liquid phases differ in phases differ in entropy. The entropy. The pure solvent is pure solvent is relatively relatively ordered since ordered since all of the all of the molecules are molecules are the same the same (solvent).(solvent).


The liquid The liquid phase of the phase of the solution is solution is much more much more random, random, since it is a since it is a mixture. mixture.


Upon Upon evaporation, evaporation, the pure the pure solvent solvent undergoes a undergoes a greater greater increase in increase in entropy than entropy than the solution. the solution.


Systems tend to Systems tend to maximize maximize entropy. The entropy. The pure solvent pure solvent evaporates more evaporates more readily, because readily, because it undergoes a it undergoes a greater increase greater increase in entropy.in entropy.

Vapor Pressure LoweringVapor Pressure LoweringThe change in vapor pressure can The change in vapor pressure can

be calculated as follows:be calculated as follows:

∆∆vp = -Xvp = -Xsolutesolute P Psolventsolvent

where X is the mole fraction of where X is the mole fraction of solute particlessolute particles

PPoosolvent solvent is the vapor pressure of the pure is the vapor pressure of the pure

solventsolvent

o

Vapor Pressure LoweringVapor Pressure Lowering

∆∆vp = -Xvp = -Xsolutesolute P Poosolventsolvent

The sign is negative because the The sign is negative because the vapor pressure decreases. vapor pressure decreases.

Vapor Pressure LoweringVapor Pressure Lowering

PPsolnsoln = X = Xsolventsolvent P Poosolventsolvent

The mole fraction of solvent, The mole fraction of solvent, XXsolvent solvent , = moles of solvent/total , = moles of solvent/total moles of moles of particlesparticles and solvent. and solvent.

Problem – Vapor Problem – Vapor PressurePressure

Water has a vapor pressure of 92.6 mmHg Water has a vapor pressure of 92.6 mmHg at 50at 50ooC. C.

a) Compare the vapor pressure of two a) Compare the vapor pressure of two aqueous solutions at 50aqueous solutions at 50ooC. One C. One contains .100 mole of sucrose dissolved in contains .100 mole of sucrose dissolved in 1.00 mol of water. The other contains .100 1.00 mol of water. The other contains .100 moles of CaClmoles of CaCl22 dissolved in 1.00 mol of dissolved in 1.00 mol of water. water.

b) Calculate the vapor pressure of the b) Calculate the vapor pressure of the CaClCaCl22 solution. solution.

Solution Phase DiagramsSolution Phase Diagrams

The lowering of the vapor pressure The lowering of the vapor pressure due to the presence of a non-volatile due to the presence of a non-volatile solute affects several properties. solute affects several properties. The phase diagram for the solution The phase diagram for the solution will be shifted, due to the lower will be shifted, due to the lower vapor pressure of the solution.vapor pressure of the solution.



As a result of the lower vapor pressure, the boiling point of the solution is greater than that of pure solvent.


Since the liquid-solid line is shifted to a lower temperature, the freezing point of the solution is lowered.

Properties of SolutionsProperties of Solutions

Solutions of non-volatile solutes Solutions of non-volatile solutes in a volatile solvent havein a volatile solvent have

- higher boiling points and- higher boiling points and- lower freezing points lower freezing points

than the pure solvent.than the pure solvent.

Boiling Point ElevationBoiling Point ElevationThe size of the increase in boiling point The size of the increase in boiling point depends upon the concentration of depends upon the concentration of solute particles.solute particles.

∆∆TTbb = K = Kbbm(m(i)i)

where Kwhere Kbb is the solvent dependent is the solvent dependent boiling boiling point elevation constant,point elevation constant,

m = molality of the solutem = molality of the solute

ii = van’t Hoff factor = van’t Hoff factor

The van’t Hoff Factor, The van’t Hoff Factor, ii

The van’t Hoff factor is the The van’t Hoff factor is the number of particles number of particles in solutionin solution compared to the number dissolved. compared to the number dissolved. If an ionic compound forms two ions If an ionic compound forms two ions per formula unit, its per formula unit, its ii value = 2. value = 2.

The van’t Hoff Factor, The van’t Hoff Factor, ii

If a molecule “pairs up” in If a molecule “pairs up” in solution, with two molecules uniting solution, with two molecules uniting to form one molecule, then the to form one molecule, then the ii factor will be 0.5.factor will be 0.5.

For non-electrolytes, the For non-electrolytes, the ii factor factor is usually 1, and is often ignored.is usually 1, and is often ignored.

Freezing Point Freezing Point DepressionDepression

The size of the decrease in freezing The size of the decrease in freezing point depends upon the concentration point depends upon the concentration of solute particles.of solute particles.

∆∆TTff = -K = -Kffm(m(i)i)

where Kwhere Kff is the solvent dependent is the solvent dependent freezing point freezing point depression depression constant,constant,

m = molality of the solutem = molality of the solute

ii = van’t Hoff factor = van’t Hoff factor

Constants for Common Constants for Common SolventsSolvents

ApplicationsApplications

Solutions of Solutions of sugar in water sugar in water or maple syrup or maple syrup (sap) have (sap) have boiling points boiling points that are higher that are higher than 100than 100ooC.C.


Salt is spread Salt is spread on roads to lower on roads to lower the freezing point the freezing point of ice and keep of ice and keep the roads from the roads from icing up at icing up at temperatures temperatures below 0below 0ooC.C.


Antifreeze Antifreeze keeps the keeps the radiators in cars radiators in cars from freezing from freezing during the during the winter and winter and overheating in overheating in the summer.the summer.

ProblemProblem

Which of the following aqueous Which of the following aqueous solutions will have the lowest solutions will have the lowest freezing point?freezing point?

0.015m calcium nitrate0.015m calcium nitrate

0.040m sodium chloride0.040m sodium chloride

0.040m sucrose0.040m sucrose

0.020m hydrochloric acid0.020m hydrochloric acid

ProblemProblem

The solubility of NaNOThe solubility of NaNO33 in water at in water at 00ooC is 75 grams per 100g of water. C is 75 grams per 100g of water. Calculate the freezing point of the Calculate the freezing point of the solution. Ksolution. Kff for water = 1.86 for water = 1.86ooC/m (or C/m (or ooC-kg/mol).C-kg/mol).

Applications – Molar Applications – Molar MassMass

Since boiling point or freezing point Since boiling point or freezing point changes are proportional to concentration changes are proportional to concentration (molality), it is possible to calculate molar (molality), it is possible to calculate molar masses of unknown solutes using a masses of unknown solutes using a measured temperature change.measured temperature change.

Solvents with greater values of KSolvents with greater values of Kff or or KKbb will provide the largest change in will provide the largest change in temperature for a given concentration.temperature for a given concentration.

Constants for Common Constants for Common SolventsSolvents


∆∆TTbb = K = Kbbm(m(ii))

where m = molality = moles of solute/kg where m = molality = moles of solute/kg of solventof solvent

∆∆TTbb = K = Kbbm(m(ii) = K) = Kbb(moles solute/kg (moles solute/kg solvent)(solvent)(ii))

oror

∆∆TTff = -K = -Kffm(m(ii) = K) = Kff(moles solute/kg (moles solute/kg solvent)(solvent)(ii))


∆∆TTbb = K = Kbbm(m(ii) = K) = Kbb(moles solute/kg solvent)(moles solute/kg solvent)((ii))oror

∆∆TTff = -K = -Kffm(m(ii) = K) = Kff(moles solute/kg solvent)(moles solute/kg solvent)((ii))

Using either relationship, moles of Using either relationship, moles of solute can be calculated. If the mass of the solute can be calculated. If the mass of the solute is also known, the molar mass is solute is also known, the molar mass is easily calculated.easily calculated.

Problem – Molar MassProblem – Molar Mass

A solution of 2.50g of a compound A solution of 2.50g of a compound with an empirical formula of Cwith an empirical formula of C66HH55P P in 25.0 g of benzene has a freezing in 25.0 g of benzene has a freezing point of 4.3point of 4.3ooC. Calculate the molar C. Calculate the molar mass of the solute and its molecular mass of the solute and its molecular formula. [The normal freezing point formula. [The normal freezing point of benzene is 5.5of benzene is 5.5ooC, and KC, and Kff for for benzene = 5.12 benzene = 5.12 ooC/m. Assume C/m. Assume ii =1] =1]

Osmotic PressureOsmotic Pressure

OsmosisOsmosis is the flow of solvent is the flow of solvent across a across a semipermeable membrane.semipermeable membrane. The membrane allows solvent molecules The membrane allows solvent molecules to pass through, but not solute particles.to pass through, but not solute particles.



The minimum The minimum pressure needed pressure needed to just stop to just stop osmosis is called osmosis is called the the osmotic osmotic pressure.pressure.


ΠΠ = MRT( = MRT(ii))

where where ΠΠ is the osmotic pressure is the osmotic pressure

M is molarity (mol solute/L M is molarity (mol solute/L of soln)of soln)

R = 0.08206 L-atm/mol-KR = 0.08206 L-atm/mol-K

T is temperature in KelvinsT is temperature in Kelvins

Osmotic Pressure - Osmotic Pressure - ApplicationsApplications

A relatively dilute solution A relatively dilute solution provides a fairly large osmotic provides a fairly large osmotic pressure. As a result, osmotic pressure. As a result, osmotic pressure is an excellent way to pressure is an excellent way to obtain molar masses of very dilute obtain molar masses of very dilute solutes such a proteins.solutes such a proteins.

ProblemProblem

0.8750 g of a protein is dissolved in 0.8750 g of a protein is dissolved in enough water to make 100. ml of enough water to make 100. ml of solution. The solution has an solution. The solution has an osmotic pressure of 3.8 mm Hg at osmotic pressure of 3.8 mm Hg at 2525ooC. Calculate the molar mass of C. Calculate the molar mass of the protein. the protein.


Renal dialysis Renal dialysis uses osmosis to uses osmosis to rid the blood of rid the blood of waste products waste products in people with in people with kidney failure.kidney failure.


Isotonic saline Isotonic saline is is a salt solution a salt solution with the same with the same osmotic osmotic pressure as pressure as blood cells. This blood cells. This maintains a fluid maintains a fluid balance within balance within the cell.the cell.


If a solution of If a solution of saline is too saline is too concentrated, concentrated, the cell will the cell will become become dehydrated and dehydrated and shrink (crenate).shrink (crenate).


If a solution of If a solution of saline is too saline is too dilute, the red dilute, the red blood cells blood cells become swollen become swollen with excess with excess water and water and eventually burst eventually burst (hemolysis).(hemolysis).


In reverse osmosis, In reverse osmosis, a pressure greater a pressure greater than the osmotic than the osmotic pressure is applied pressure is applied to a solution. Pure to a solution. Pure solvent can be solvent can be obtained on the obtained on the other side of the other side of the membrane.membrane.


Behavior of ElectrolytesBehavior of Electrolytes

The van’t Hoff factor, The van’t Hoff factor, ii, , represents the number of particles represents the number of particles formed in solution for each solute formed in solution for each solute particle dissolved.particle dissolved.

ii = = moles of particles in solutionmoles of particles in solutionmoles of solute dissolvedmoles of solute dissolved


For ionic solutes, we expect the For ionic solutes, we expect the value of value of ii to be 2 for NaCl, 3 for to be 2 for NaCl, 3 for MgClMgCl22, and 4 for FeCl, and 4 for FeCl33, etc. In , etc. In extremely dilute solutions, the extremely dilute solutions, the observed value of observed value of ii is very close to is very close to these expected values.these expected values.


However, as However, as solutions become solutions become more concentrated, more concentrated, ion pairingion pairing occurs, occurs, and some of the and some of the ions formed in ions formed in solution pair up and solution pair up and behave like a single behave like a single particle.particle.


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Solutions. Solution Concentration Although molarity (M) is used for stoichiometry calculations, there are many other ways to express the concentration