January 24, 2012
CH-112
Chapter 13
Properties of Solutions
*A Solution is formed when one substance disperses uniformly throughout another.
The ability of substances to form solutions depends on two factors:
1. the natural tendency of substances to mix and spread into larger volumes when unrestrained
2. types of intermolecular interactions involved in the solution process
Mixing of gases is spontaneous- it occurs without any input of energy from outside the system.
The formation of solutions is favored by the increase in entropy that accompanies mixing.
It is the balance of the tendencies of systems to increase their entropy and decrease their enthalpy that determines whether a process is spontaneous.
Mixing occurs spontaneously when molecules of different types are brought together, unless intermolecular forces are strong enough to oppose this mixing.
Dispersion forces dominate when one non-polar substance dissolves in another.
Ion-dipole forces dominate in solutions of ionic substances in water.
In addition to these there are also dipole-dipole and hydrogen bond forces that operate between solute and solvent particles in solution.
Three kinds of intermolecular interactions are involved in solution formation:
Solute-solute: interactions between solute particles must be overcome in order to disperse the solute particles through the solvent.L
Solvent-solvent: interactions between solvent particles must be overcome to make room for the solute particles in the solvent.
Solvent-solute: interactions between solvent and solute particles occur as the particles mix.
The extent to which a substance is able to be dissolved in another is dependent on the magnitude of these forces.
Solvation: interactions between solute and solvent molecules.
Hydration: interactions in which the solvent is water.
Solution processes are typically accompanied by changes in enthalpy.
Hess' Law is used to analyze how solute-solute, solvent-solvent, and solute-solvent interactions influence the enthalpy of a solution.
-Solute particles separate from one another: ΔHsolute
-Solvent particles separate from one another: ΔHsolvent
-Solute and solvent particles mix: ΔHmix
Producing overall enthalpy change: ΔHsoln
ΔHsoln = ΔHsolute + ΔHsolvent + ΔHmix
Separation of particles from one another always requires input of energy to overcome their attractive forces, making these processes endothermic ( ΔH > zero), whereas the mixing of solute and solvent particles arises from attractive forces, in which the system loses heat and therefore is an exothermic process ( ΔH < zero).
For solutions to form the solvent-solute interaction must be strong enough to make the exothermic process comparable in magnitude to the endothermic processes.
Crystallization: the process in which some solute particles collide with the surface of the solid in a solution and reattach.
The equation is represented by half arrows to show that the solute is both being crystallized and dissolved simultaneously. Because I don't have the ability to actually draw here, I will type it in like this <=====>.
Dynamic Equilibrium: when the rates of opposing processes become equal.
Saturated: a solution that is in equilibrium with undissolved solute.
Solubility: the maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature given that excess solute is present.
Unsaturated: a solution containing less solute than needed to be saturated.
Supersaturated: solutions that contain a greater amount of solute than needed to form a saturated solution.
*Supersaturation can be accomplished by heating a saturated solution to high temperatures and then allowing it to slowly cool.
When a seed crystal is introduced to a supersaturated solution, crystallization of the excess solute occurs.
Attractive forces between gas molecules and solvent molecules are mainly dispersion forces, which increase with increasing size and molecular mass.
The stronger the attractions between solvent and solute molecules, the greater the solubility of the solute in that solvent.
Like dissolves like: polar liquids tend to dissolve in polar solvents.
*Water is both polar and able to form hydrogen bonds, thus polar molecules, especially those that are able to form hydrogen bonds with water molecules, tend to be soluble in water.
Miscible: pairs of liquids that mix in all proportions.
Immiscible: pairs of liquids that do not dissolve in one another.
*Substances with similar intermolecular attractive forces tend to be soluble in one another. Another way of saying "like dissolves like".
Network solids are not soluble in either polar or non-polar solvents because of the strong bonding forces within the solid.
Pressure Effects
-The solubility of a gas in any solvent is increased as the partial pressure of the gas above the solvent increases.
-The solubility of a gas in a liquid solvent increases in direct proportion to the partial pressure of the gas above the solution.
The relationship between pressure and gas solubility is expressed by Henry's Law:
Sg = kPg
Sg is the solubility of the gas in the solvent (expressed in molarity)
k is a proportionality constant known as Henry's law constant
Pg is the partial pressure of the gas over the solution.
EXERCISE: HENRY'S LAW CALCULATION
1.) Calculate the concentration of CO2 in a soft drink that is bottled with a partial pressure of CO2 of 4.0atm over the liquid at 25 degrees Celsius. The Henry's law constant for CO2 in water at this temperature is 3.4 x 10^-2 mol/L-atm.
Sg = kPg
So we're given the values for k and Pg and are being asked to find concentration of CO2, which we know is usually expressed in molarity, and can thus infer that will be the value of Sg (which represents molarity). This is a plug & play problem:
S-CO2 = kP-CO2
S-CO2 = (3.4 x 10^-2 mol/L-atm)(4.0atm)
The unit 'atm' will cancel out leaving the value for concentration (molarity) of CO2:
0.14mol/L (remember sig-figs when rounding, in this case, we round to 2 significant figures)
2.) Calculate the concentration of CO2 in a soft drink after the bottle is opened and equilibrates at 25 degrees Celsius under a CO2 partial pressure of 3.0 x 10^-4atm.
We know that we are looking for Sg (concentration), and we are given the partial pressure of the CO2 after the bottle has been opened and equilibrated.
We also know that the Henry's law constant for CO2 at 25 degrees Celsius is 3.4 x 10^-2 from our last problem so we can, once again, just plug and play... these problems are a bit too easy.....
Sg = (3.4 x 10^-2 mol/L-atm)(3.0 x 10^-4 atm)
The unit 'atm' will cancel out, leaving unit for concentration: mol/L:
1.02 x 10^-5 mol/L remembering sig-figs, we can round this number to
1.0 x 10^-5 mol/L or 1.0 x 10^-5M
Eaaaaaaaaaaaasy.
*The solubility of most solid solutes in water increases as the solution temperature increases.
Like we stated previously: a solvent can dissolve more solute when the solution is heated, in most cases.
*Conversely, the solubility of gases in water decreases with increasing temperature.
Think of the bubbles that form on the sides of a pot when the water within it is being heated on a stove, this is dissolved air coming out of solution.
Which, to my amusement, is the next "Give It Some Thought" question in the book: why do bubbles form on the inside wall of a cooking pot when the water is heated on the stove, even though the water temperature is well below boiling point?
Hah.
Solution concentration is expressed qualitatively as well as quantitatively using the terms "dilute" and "concentrated".
Dilute: a relatively small concentration of solute.
Concentrated: a relatively large concentration of solute.
Mass percentage of a component in solution is given by:
Mass % of component = mass of component in solution / total mass of solution x 100
That is: the percent of mass of any component in a solution is found by dividing the mass of the component by the total mass of the solution and multiplying the answer by one hundred (to get percent, or "per hundred").
Concentrations of very dilute solutions is measured in parts per million (ppm) or parts per billion (ppb):
ppm of component = mass of component in solution / total mass of solution x 10^6
That is: parts per million of a component in a solution is found by dividing the mass of the component by the total mass of the solution and multiplying the answer by 10^6
***For ppb, multiply by 10^9***
ppm means that for each million (10^6) grams of solution, there is 1 gram of solute.
ppm also corresponds to 1mg of solute per liter of aqueous solution.
EXERCISE: CALCULATION OF MASS-RELATED CONCENTRATIONS
1.) A solution is made by dissolving 13.5g of glucose (C6H12O6) in 0.100kg of water. What is the mass percentage of solute in this solution?
The first aspect of the problem is fairly simple, we're given everything we need to plug into the mass percentage equation and solve. The only flag here is that the units don't match so we need to convert the kg of water to grams, simple enough:
0.100kg x 1000g/1kg = 100g
Now plug the numbers into the equation:
Mass % of component = 13.5g / 13.5g + 100g x 100 = 11.9% (remember sig-figs)
2.) A 2.5g sample of groundwater was found to contain 5.4 micrograms of Zn^2+. What is the concentration of Zn^2+ in ppm?
Knowing, by now I hope, that micro indicated a subscript of 10^-6, we can determine that 5.4 micrograms is equivalent to 5.4 x 10^-6g, thus making out units of measurement for both groundwater and Zn grams. After that, we merely plug in the numbers to the ppm formula:
ppm = mass solute/mass soln x 10^6
ppm = 5.4 x 10^-6g / 2.5 g x 10^6 = 2.16ppm
once again, remembering sig-figs we round the above number to 2 significant figures based on the calculation, making the final solution to the problem 2.2ppm.
Other formulas:
Mole fraction of a component = moles of component/total moles of all components
Molarity = moles of solute/liters of solution
Molality (not to be confused with the above, Molarity) = moles of solute/kilograms of solvent
*Molarity depends on the volume of the solution, whereas molality depends on the mass of the solvent.
*When water is the solvent, molality and molarity of dilute solutions will be numerically about the same.
*Molality does not vary with temperature because masses do not vary with temperature.
Colligative properties: properties that depend on the quantity but not the kind or identity of solute particles. Ie: boiling point/freezing point, vapor-pressure lowering, and osmotic pressure.
Vapor Pressure: the pressure exerted by the vapor when it is at equilibrium with the liquid.
Nonvolatile substance: a substance that exhibits no measurable vapor pressure.
Volatile substance: a substance that does exhibit measurable vapor pressure.
*A solution consisting of a volatile liquid solvent and a nonvolatile solute forms spontaneously because of the increase in entropy that accompanies their mixing. Solvent molecules are stabilized in their liquid state and have a lower tendency to escape into the vapor state. Therefore:
**When a nonvolatile solute is present, the vapor pressure of the solvent is lower than the vapore pressure of the pure solvent.
Raoult's Law: states that the partial pressure exerted by solvent vapor above the solution, Psolution, equals the product of the mole fraction of the solvent, Xsolvent, times the vapor pressure of the pure solvent, P`solvent:
Psolution = (Xsolvent)(P`solvent)
The vapor-pressure lowering caused by adding a nonvolatile solute depends on the total concentration of solute particles, regardless of whether they are molecules or ions.
Note to Self: remember that ionic molecules break apart into their constituent elements, ie: NaCl is not counted as one, but two, because in aqueous solution it is present as Na+ and Cl- rather than the molecule NaCl. Glucose, on the other hand, C6H12O6 is counted as one molecule because it is not ionic and therefore will not break apart in solutions where water is the solvent.
An ideal solution is defined as one that obeys Raoult's Law. It implies total uniformity of interaction. The molecules/particles in an ideal solution all influence each other in some way- solute-solute, solvent-solvent, and solute-solvent interactions are indistinguishable from one another.
Not all solutions obey Raoult's law exactly and are therefore not ideal.
The normal boiling point of a liquid is the temperature at which its vapor pressure is equal to 1 atm, therefore a solution in which the vapor pressure of a solvent has been lowered by the addition of a nonvolatile solute will have a higher boiling point than that of the pure solvent.
The increase in boiling point of solution relative to that of pure solvent is given by:
ΔTb = Kbm
Where ΔTb is the increase in boiling point relative to pure solvent
Kb is the molal boiling-point-elevation constant
and m is molality
Likewise, freezing point of a solution is lower than that of the pure liquid. The decrease in freezing point of the solution from the freezing point of a pure solvent is given by:
ΔTf = Kfm
Molal Boiling-Point-Elevation and Freezing-Point-Depression Constants:
Water, H2O}}} | Boiling point: 100C | Kb: 0.51C/m | Freezing point: 0C | Kf: 1.86C/m |
Benzene, C6H6 | 80.1C | 2.53C/m | 5.5C | 5.12C/m |
Ethanol, C2H5OH | 78.4C | 1.22C/m | -114.6 | 1.99C/m |
Osmosis: The net movement of solvent through a semipermeable membrane toward the solution with greater solute concentration.
*the net movement of solvent is always toward the solution with the higher solute concentration
Osmotic pressure: the pressure required to stop osmosis from a pure solvent to a solution
*Osmotic pressure obeys the law: ΠV = nRT (similar to the ideal-gas law)
Where Π is the osmotic pressure
V is the volume of solution
n is the number of moles of solute
R is the ideal-gas constant
and T is the temperature (always in Kelvin)
To further complicate it and make one's head spin about in some kind of informational orbit, that equation is rearranged to become this one:
Π = (n/v)RT = MRT
Where M is the molarity of the solution
*Osmotic pressure is a colligative property because osmotic pressure for any solution is dependent on the solution concentration.
Isotonic solutions: two solutions of identical osmotic pressure
Hypotonic solution: in two solutions of differing osmotic pressure, the hypotonic solution is the one with lower osmotic pressure.
Hypertonic solution: in two solutions of differing osmotic pressure, the hypertonic solution is the one with higher osmotic pressure.
It goes without saying that osmosis plays a critical role in bodily functions, with particular importance to our blood, therefore I am not going to summarize that portion of the section, I will note, however, that:
Crenation is when water flows out of a cell, as when placed in a hypertonic environment, causing the cell to shrink or shrivel.
Hemolysis is when water flows into a cell, as when placed in a hypotonic environment, causing the cell to swell.
**Movement of a substance from an area where its concentration is high to an area where it is low is spontaneous. Biological cells transport water and other select materials through their membranes, permitting nutrients to enter and waste materials to exit. In some cases substances must be moved across the cell membrane from an area of low concentration to one of high concentration. This movement is called active transport and is not spontaneous- it requires cells to expend energy.
Colloids: mixtures containing particles larger than normal solutes but small enough to remain suspended in the dispersing medium.
*Colloids may be either hydrophobic or hydrophilic. A hydrophilic molecules folds in such a way that its hydrophobic groups are away from the water molecules, think phospholipid bilayer cellular membranes.
*Hydrophobic colloids can be dispersed in water only if they are stabilized in some way, otherwise they will naturally separate. One method is adsorption, adhering ions on the surface of hydrophobic particles.
Coagulation: a process used to remove colloids from solution. This can be done by heating or adding an electrolyte.
*A semipermeable membrane may also be used to remove ions from colloids (think dialysis).
CHEESEBURGER.
