CHM 1046 - General Chemistry 2

Summer A 2014

Dr. Jeff Joens

Classroom: CP 145 Time: M, W, F noon to 2:15pm

Office: CP 331 phone 348-3121 email: joensj@fiu.edu

web page: www.joenschem.com

CHAPTER 13

Physical Properties of Solutions

Solutions

A solution is a homogeneous mixture. The major component of a solution is called the solvent, while the minor components are called solutes.

There are several common kinds of solutions

kind of solution example

gas in gas air (78% N2, 21 % O2, 0.9 % Ar + others)

gas in liquid O2 in water

liquid in liquid ethanol in water

solid in liquid NaCl in water

solid in solid alloys (bronze - copper + tin)

We will usually focus on solutions where the solvent is a liquid, but all of the above combinations represent possible types of solutions.

Solubility

The term solubility means the amount of a particular solute that will dissolve in a given amount of solvent (usually a liquid). There are two common ways in which solubility is given.

1) Mass solute per mass solvent. Indicates the maximum mass of solute that will dissolve in a given mass of solvent.

Example: At 25 C the solubility of sodium chloride in water is 36. g NaCl per 100. g water.

2) Molar solubility. The maximum number of moles of solute per liter of solution.

Example: The molar solubility of silver chloride (AgCl) in pure water at 25 C is 1.3 x 10-5 mol/L. (Equivalent to 1.9 x 10-4 g per 100 g water).

There are other ways of expressing solubility, including mass per volume of solvent, and solubility product.

Soluble and Insoluble

There are several common terms that refer to the ability of a solid solute to dissolve in a liquid solvent.

Soluble - Indicates that a large amount of solute will dissolve in a given amount of solvent.

Insoluble - Indicates that a small amount, or no, solute will dissolve in a given amount of solvent.

In our above examples sodium chloride is soluble in water and silver chloride is insoluble in water.

In fact, many substances classified as “insoluble” will dissolve to a small extent in water or other solvents. We will discuss this in more detail later in the semester.

Thermodynamics of Solution Formation

Consider the following general process for the formation of a solution by mixing two liquids.

Liquid A + Liquid B Solution

There are two factors that favor formation of a solution:

1) A decrease in the energy of the system.

2) An increase in the randomness of the system.

Enthalpy of Solution (Hsoln)

1) A decrease in the energy of the system. If mixing lowers the energy of a system then it is more likely to occur. Since solutions are usually prepared under conditions of constant pressure, we look at the enthalpy of solution, Hsoln, defined as the change in enthalpy for the process of solution formation (the change in enthalpy and the change in energy are approximately equal for forming a solution).

Liquid A + Liquid B Solution Hsoln

There are two possibilities:

The energy decreases when the two liquids mix to form a solution. Then mixing is exothermic (Hsoln < 0). Lowering the energy favors formation of solution.

The energy increases when the two liquids mix to form a solution. Then mixing is endothermic (Hsoln > 0). Raising the energy favors not forming a solution.

Energy Diagram for Solution Formation

Lowering the energy (Hsoln < 0) favors formation of a solution.

Entropy of Solution (Ssoln)

2) An increase in the randomness of the system. In thermodynamics randomness is measured in terms of entropy. For solutions the change in entropy is called Ssoln.

Consider the mixing of two liquids. We would expect that the solution is less ordered than the starting pure liquids. Therefore, we expect Ssoln > 0 (randomness increases).

Solution Formation

Hsoln Ssoln Will a solution form?

negative positive Yes.

(exothermic) (more random)

positive positive Maybe.

(endothermic) (more random)

If solution formation is exothermic we expect a solution to form. If solution formation is endothermic then a solution might form, depending on which factor in solution formation is more important - the increase in randomness or the increase in energy when the solution forms. This mainly depends on the magnitude of Hsoln.

Examples of Solvent-Solute Attractive Forces

Hsoln For Various Liquid + Liquid Combinations

Liquid A nonpolar polar nonpolar polar

Liquid B nonpolar nonpolar polar polar

liquid A-liquid A attraction weak strong weak strong

liquid B-liquid B attraction weak weak strong strong

liquid A-liquid B attraction weak weak weak strong

enthalpy change (Hsoln) ~ 0 positive positive ~ 0

(large) (large)

Conclusion - For mixing of liquids “like dissolves like”.

Miscible and Immiscible Liquids

We can classify liquids in terms of their ability to form solutions when mixed.

Two liquids are miscible if any amounts of the two liquids will combine to form a solution (water + ethyl alcohol).

Two liquids are immiscible if they do not mix (water + gasoline).

Application to Other Types of Solutions

Mixing of gases. The particles making up a gas are generally far apart relative to the size of the gas particles, and so Hsoln 0. Since randomness increases, a solution will always form when gases are mixed. (example - nitrogen + oxygen)

Polar molecular solid + water. The same factors apply as for mixing of two polar liquids, and so a solution will almost always form (example - glucose+water)

Nonpolar molecular solid + water - The same factors apply as for mixing of a nonpolar liquid + water, and so a solution will almost never form (example - naphthalene+water)

Ionic solid + water - Because the forces involved are all very strong, it is not easy to predict whether the process will be exothermic or endothermic, and how large the value will be for Hsoln. So a solution might form or might not form, depending on the compound.

Classification of Solutions

Solutions can be classified according to the relative amount of dissolved solute.

Unsaturated solution - Contains less than the maximum equilibrium amount of dissolved solute.

Saturated solution - Contains the max-imum equilibrium amount of dissolved solute.

Supersaturated solution - Contains more than the maximum equilibrium amount of dissolved solute.

Note that a supersaturated solution is unstable. It will spontaneously form a preci-pitate until it becomes a saturated solution.

Preparing a Saturated Solution

We can prepare a saturated solution of a solid substance as follows:

1) Add an excess amount of the solid substance being dissolved.

2) Stir the mixture.

3) Filter the excess undissolved solid.

Effect of Temperature On Solubility

Note that the solubility of most solids in water or other liquids increases with increasing temperature.

Recrystallization

The increase in the solubility of a solid in a liquid solvent with increasing temperature is the basis of a purification technique called recrystal-lization. The solid is dissolved in a minimum amount of hot solvent. When the solvent cools, the solute precipitates to form pure crystals.

Gas Solubility

Gases can also dissolve in liquids. Gas solubility is described by Henry’s law

[A] = k pA [A] = concentration of dissolved A (in mol/L)

pA = partial pressure of A above the solution

k = Henry’s law constant

The value for the Henry’s law constant depends on the solvent, the gas, and temperature. For most gases solubil-ity is low (exceptions are gases that can chemically interact with the solvent) and solubility decreases as temperature in-creases.

Example:

The Henry’s law constant for water is k = 2.02 x 10-3 mol/L.atm at T = 20 C. What is the concentration of dissolved oxygen in water in equilibrium with the Earth’s atmosphere (pO2 = 0.21 atm)?

Example:

The Henry’s law constant for water is kH = 2.02 x 10-3 mol/L.atm at T = 20 C. What is the concentration of dissolved oxygen in water in equilibrium with the Earth’s atmosphere (pO2 = 0.21 atm)?

[O2] = k pO2 = (2.02 x 10-3 mol/L.atm) (0.21 atm)

= 4.2 x 10-4 mol/L (or 0.0135 g/L)

While small, this is enough dissolved oxygen to support fish life.

Concentration Units - Molarity

There are several common units for solutions.

Molarity (M) = moles solute

liters solution

Molarity is the most common concentration unit used for solutions because it is easy to prepare solutions with know values of molarity.

Note that molarity depends on temperature, because the volume occupied by a solution changes when temperature changes.

Concentration Units - Molality and Mole Fraction

Solution concentrations can also be given in terms of molality and mole fraction. (Note - Some books use b to indicate molality)

Molality (m) = moles solute

kg solvent

Mole fraction (Xi) = ni = moles of ith substance

ntotal total number of moles

Molality and mole fraction are used in some specialized applications, such as in equations for some of the colligative properties of solutions and in Dalton’s law of partial pressure. Note that molality and mole fraction are temperature independent.

Concentration Units - Percent By Mass, Parts Per

Million By Mass and Related Units

We can also give solution concentrations in terms of the masses of substances present in the solution.

Percent by mass (mass %) = mass of solute x 100 %

mass of solution

Parts per million by mass (ppm) = mass of solute x 106

mass of solution

By analogy with ppm (parts per million) we can also define ppb (parts per billion; multiply by 109) or parts per trillion (ppt; multiply by 1012).

Since there are other ways of using part per million (parts per million by number, for example) we should always indicate which type of parts per million we are using.

Solution Calculations

There are two general types of problems you should be able to do in connection with solutions.

1) Given information on how a solution is prepared, you should be able to find the solute concentration (molarity, molality, mole fraction, mass percent, and so forth).

2) Conversion from one concentration unit to a different concentration unit.

Example: A solution is prepared that is 40.0 % by mass ethylene glycol (C2H6O2, MW = 62.07 g/mol) in water (H2O, MW = 18.02 g/mol). The density of the solution is D = 1.0514 g/mL. What are the molarity, molality, and mole fraction ethylene glycol in the solution?

Example: A solution is prepared that is 40.0 % by mass ethylene glycol (C2H6O2, MW = 62.07 g/mol) in water (H2O, MW = 18.02 g/mol). The density of the solution is D = 1.0514 g/mL. What are the molarity, molality, and mole fraction ethylene glycol in the solution?

Assume that you have 100.0 g of solution. Then you have 40.00 g of ethylene glycol and 60.00 g water.

nE = 40.00 g 1 mol = 0.6444 mol E

62.07 g

nW = 60.00 g 1 mol = 3.3296 mol W

18.02 g

XE = nE = (0.6444 mol) = 0.1622

nE + nW (0.6444 + 3.3296)mol

The molality ethylene glycol in the solution is

mE = mol E = 0.6444 mol = 10.74 mol/kg

kg H2O 0.06000 kg

The total mass of solution is m = 40.00 g + 60.00 g = 100.00 g. Since the density of the solution is D = 1.0514 g/mL, the volume of the solution is

V = 100.00 g 1 mL = 95.11 mL

1.0514 g

So ME = 0.6444 mol = 6.775 mol/L

0.09511 L

Volatile Liquids and Vapor Pressure

A volatile liquid is a liquid that has a significant vapor pressure. A volatile liquid will, if left exposed in the atmosphere, evaporate. Liquids that do not have a significant vapor pressure are called nonvolatile.

Vapor pressure is defined as the equilibrium pressure of gas above a sample of pure liquid. The value for the vapor pressure depends on temperature, and increases when temperature increases.

Solutions of Volatile Liquids - Raoult’s Law

Raoult’s law is a relationship that applies to some solutions of volatile liquids. A solution that obeys Raoult’s law is considered an ideal solution.

Consider a solution consisting of two volatile liquids A and B. Raoult’s law predicts that the partial pressure of vapor from each liquid above the solution is given by the relationships

pA = XA pA pB = XB pB

where pA, pB are the partial pressures of A and B above the solution

XA, XB are the mole fraction of A and B in the solution

pA, pB are the vapor pressures of pure A and pure B

Example: At 20C the vapor pressure of pure benzene is 24. torr and the vapor pressure of pure toluene is 76. torr. Consider a solution with XB = 0.40. Assuming that benzene and toluene form an ideal solution, find the partial pressure of benzene and toluene and the total pressure above the solution.

Example: At 20C the vapor pressure of pure benzene (B) is 24. torr and the vapor pressure of pure toluene (T) is 76. torr. Consider a solution with XB = 0.40. Assuming that benzene and toluene form an ideal solution, find the partial pressure of benzene and toluene and the total pressure above the solution.

From Raoult’s law, pA = XApA

XB + XT = 1, so XT = 1 – XB = 1 – 0.40 = 0.60

So pB = (0.40)(24. torr) = 9.6 torr

pT = (0.60)(76. torr) = 45.6 torr

ptotal = psoln = pB + pT = 9.6 torr + 45.6 torr = 55.2 torr

Ideal Solution

An ideal solution is a solution whose components obey Raoult’s law.

The solvent in a solution will always obey Raoult’s law in the limit XA 1.

In a mixture of two liquids A and B there are three types of inter-molecular forces

A --- A molecules of A with A

B --- B molecules of B with B

A --- B molecules of A with B

Solutions will generally be close to ideal if they are composed of similar molecules with similar intermolecular attractive forces (so usually molecules that are both nonpolar).

Ideal and Nonideal Solution

For an ideal solution a plot of pressure vs mole fraction will be linear. If such a plot is not linear, then we have a nonideal solution.

A = CH3COCH3; B = CS2

Colligative Property

A colligative property is any property of a solution consisting of a volatile solvent and a nonvolatile solute that depends at most on two things:

1) The physical properties of the solvent

2) The number or concentration of solute particles

There are four colligative properties

- vapor pressure lowering

- boiling point elevation

- freezing point depression

- osmotic pressure

The equations given for colligative properties apply to ideal conditions (dilute solutions).

Vapor Pressure Lowering

Consider the situation below. The left side contains pure solvent A, while the right side contains a solution of A and a nonvolatile solute.

pleft = pA pright = XA pA

We may define the vapor pressure lowering p = pleft - pright, and so

p = pA - XA pA = (1 - XA) pA

But XA + XB = 1, so 1 - XA = XB, and so

p = XB pA , the final expression for vapor pressure lowering.

Measurement of Vapor Pressure Lowering

The apparatus shown below can be used to accurately measure the vapor pressure of a solution relative to that of a pure liquid. Note that the working fluid in the manometer is often chosen to be a non-volatile liquid of lower density than mercury, such as sulfuric acid or mineral oil.

Boiling Point Elevation and Freezing Point Depression

Consider the situation below. The left side contains pure solvent A, while the right side contains a solution of A and a nonvolatile solute. The boiling point of the solution will be higher than the boiling point of the pure liquid, and the freezing point of the solution will be lower than the freezing point of the pure liquid.

Tb = Tb - Tb° = Kb mB boiling point elevation

Tf = Tf° - Tf = Kf mB freezing point depression

Kb, Kf = boiling point elevation and freezing point depression constantsTb, Tf = boiling and freezing point for the solution

Tb°, Tf ° = boiling and freez-ing point for the pure liquid

mB = molality of solute par-ticles

Example

A solution is prepared by dissolving 1.00 mol glucose (C6H12O6) in 2500. g of water. What are the normal freezing point and normal boiling point for this solution?

A solution is prepared by dissolving 1.00 mol glucose (C6H12O6) in 2500. g of water. What are the normal freezing point and normal boiling point for this solution?

glucose(s) glucose(aq)

Tb = 100.00 C Tf = 0.00 C

Kb = 0.52 C/m Kf = 1.86 C/m

molality glucose = 1.00 mol glucose = 0.400 mol particles = 0.400 m

2.500 kg water kg water

So Tb = (0.52 C/m) (0.400 m) = 0.208 C

Tf = (1.86 C/m) (0.400 m) = 0.744 C

Tb = 100.00 C + 0.208 C = 100.21 C

Tf = 0.00 C - 0.744 C = - 0.74 C

Phase Diagram For Solutions

We can picture the differences between the behavior of a pure liquid and a solution of the liquid and a nonvolative solute in terms of the corresponding phase diagram.

In a sense all that has changed for the solution is the location of the triple point, which affects the locations of the phase boundaries, as indicated in the phase diagram at right.

Osmotic Pressure

Consider the apparatus below. The right chamber contains a pure liquid, while the left chamber contains a solution of the liquid and a non-volatile solute. The two chambers are separated by a semipermeable membrane that allows solvent molecules to pass but prevents the passage of solute molecules.

The osmotic pressure, , is defined as the additional pressure that must be applied to the solution to keep the level of liquid in both cham-bers the same.

Semipermeable Membrane

A semipermeable membrane is a barrier that allows some particles to pass through but which prevents the passage of other particles. The discrimination is usually based on the size of the particles (or, for ions, the size of the hydrated or solvated ions).

Calculation of Osmotic Pressure

For dilute solutions the osmotic pressure is given by the relationship

= MBRT , where MB is the molarity of solute particles (mol/L)

Example: What is the osmotic pressure for a 0.0100 M solution of naphthalene (C10H8) in benzene (C6H6) at T = 25. C?

What is the osmotic pressure for a 0.0100 M solution of naphtha-lene (C10H8) in benzene (C6H6) at T = 25. C?

= MBRT , where MB molarity of solute particles (mol/L)

For naphthalene, MB = 0.0100 M, T = 273. + 25. = 298. K

(naph.) = (0.0100 mol/L)(0.08206 L.atm/mol.K)(298 K)

= 0.245 atm ( = 186. Torr)

Note that we use absolute temperature (Kelvin) in the equation for osmotic pressure.

Solutions With a Nonvolative Ionic Solute

For a solution containing a nonvolatile ionic solute (or any nonvolatile solute that can dissociate into smaller particles) there is one additional complicating factor. As before, there will only be solvent molecules above the solution.

If the solvent obeys Raoult’s law (true if dilute solution), then

pA = psoln = XA pA

However, we must take into account the ionization or dissociation of the solute in calculating the mole fraction of solvent.

XA = moles of solvent particles

total moles of particles

XB = moles of solute particles total moles of particles

Finding the Moles of Particles (Examples)

Consider the following three substances:

C6H12O6 (sugar)

NaCl (sodium chloride)

K2SO4 (potassium sulfate)

When 1.000 moles of each of the above substances are dissolved in water how many moles of particles will form?

Finding the Moles of Particles (Examples)

C6H12O6 (glucose)

C6H12O6(s) C6H12O6(aq)

mol particles = 1.00 mole glu. 1 mole particle = 1.00 mol particles

1 mol glu.

NaCl (sodium chloride)

NaCl(s) Na+(aq) + Cl-(aq)

mol particles = 1.00 mol NaCl 2 mol particles = 2.00 mol particles

1 mol NaCl

K2SO4 (potassium sulfate)

K2SO4(s) 2 K+(aq) + SO42-(aq)

mol particles = 1.00 mol K2SO4 3 mol particles = 3.00 mol particles

1 mol K2SO4

Van’t Hoff Factor (i)

The van’t Hoff factor, i, is defined as

i = moles of particles

moles of solute

So moles of particles = i (moles of solute)

For the above examples:

C6H12O6(s) C6H12O6(aq) i = 1

NaCl(s) Na+(aq) + Cl-(aq) i = 2

K2SO4(s) 2 K+(aq) + SO42-(aq) i = 3

Modified Equations For

Colligative Properties

We may modify our expressions for the colligative properties to account for ionization (or similar behavior) using the van’t Hoff factor.

Vapor pressure lowering p = iXB pA

Boiling point elevation Tb = Tb - Tb° = iKb mB

Freezing point depression Tf = Tf° - Tf = iKf mB

Osmotic pressure = iMBRT

Experimental Values for theVan’t Hoff Factor

The value for the van't Hoff factor can be found experimentally. For dilute solutions the experimental value for the van’t Hoff factor is close to the value predicted from theory. However, for more concentrated solutions the experimental value is lower than that expected.

For example, for NaCl

NaCl(s) Na+(aq) + Cl-(aq)

Molality NaCl itheory iexperimental

0.0001 2.00 1.99

0.001 2.00 1.97

0.01 2.00 1.94

0.1 2.00 1.87

Unless otherwise stated we will use the theoretical value for i.

Colligative Properties With Several Solutes

If we have a solution containing several nonvolatile solutes the easiest way to proceed is to use our original equations for the colligative properties, but express solute concentration in terms of the total concentration of solute particles.

Example: Consider the following two solutions:

A) 1.000 L of an aqueous solution containing 0.200 moles of Ca(NO3)2.

B) 1.000 L of an aqueous solution containing 0.200 moles of Ca(NO3)2, and 0.200 moles of glucose.

What is the osmotic pressure for each of the above solutions at T = 37. C?

Example: Consider the following two solutions:

A) 1.000 L of an aqueous solution containing 0.200 moles of Ca(NO3)2.

B) 1.000 L of an aqueous solution containing 0.200 moles of Ca(NO3)2, and 0.200 moles of glucose.

What is the osmotic pressure for each of the above solutions at T = 37. C?

For solution A (Ca(NO3)2(s) Ca2+(aq) + 2 NO3-(aq) ; i = 3)

mol particles = 0.200 mol Ca(NO3)2 . 3 mol particles

1 mol Ca(NO3)2.

= 0.600 mole particles

For solution B

mol particles = (0.600 + 0.200) = 0.800 mol particles

For solution A

MsolA = 0.600 mol particles = 0.600 M

1.000 L soln

= MsolART = (0.600 mol/L)(0.08206 L.atm/mol.K)(310. K)

= 15.3 atm

For solution B

MsolB = 0.800 mol particles = 0.800 M

1.000 L soln

= MsolBRT = (0.800 mol/L)(0.08206 L.atm/mol.K)(310. K)

= 20.4 atm

Note that we could have found the osmotic pressure for solution A using our modified equation for osmotic pressure, = iMRT

Applications to Molecular Mass Determination

Any of the four colligative properties may be used to determine the molecular mass of a nonvolative solute. In practice osmotic pressure or vapor pressure lowering are usually used, as they are more sensitive and can be used to find the molecular mass of high molecular mass molecules.

Example: A solution is prepared by dissolving 0.1438 g of a nonvolatile and nonionizing solute in water to form a solution of final volume V = 25.00 mL. The osmotic pressure of the solution, measured at T = 37.0 C, is 21.6 torr. What is the molecular mass of the solute?

Example: A solution is prepared by dissolving 0.1438 g of a nonvolatile and nonionizing solute in water to form a solution of final volume V = 25.00 mL. The osmotic pressure of the solution, measured at T = 37.0 C, is 21.6 torr. What is the molecular mass of the solute?

MW = m/n = grams/moles

= MBRT = 21.6 torr (1 atm/760 torr) = 0.02842 atm

MB = = 0.02842 atm = 1.117 x 10-3 mol/L

RT (0.08206 L.atm/mol.K) (310. K)

n = MBV = (1.117 x 10-3 mol/L) (0.02500 L) = 2.792 x 10-5 mol

M = 0.1438 g = 5150. g/mol

2.792 x 10-5 mol

Reverse Osmosis

One interesting application of a colligative property is the use of reverse osmosis to purify seawater. The high pressure forces water through the semipermeable membrane while trapping ions and larger molecules. The process is usually more expensive than other sources of potable water, but can be economically viable in some cases.

Medical Applications of Osmotic Pressure

The membranes of red blood cells are semipermeable membranes. Therefore, these cells can experience an osmotic pressure when placed in a liquid with a different molality than blood plasma, which has a molality m 0.30 mol/kg, about the same molality as a 0.9 g NaCl per 100. g water solution.

Colloid

A colloid is a mixture of small particles suspended within a substance. The particles in a colloid are larger than the solute molecules or ions in a solution. The size of colloid particles is generally in the range 1 - 1000 nm.

Types of Colloid

End of Chapter 13

“If you're not part of the solution, you're part of the precipitate.”- unknown

“How can you distinguish science from junk? Science posits hypothesis and tests them. Pseudoscience assumes conclusions and finds evidence to back them up.” - Wendy Kaminer, Sleeping With Extra-Terrestrials