# Solutions

When the components of a mixture are uniformly intermingled, or when a mixture is homogeneous, it is called a solution.  Aqueous solutions, those containing water, are the most common solutions.

There are several to define the concentration of a solution depending on the application:

1. Weight percent (wt/wt) = (mass of solute / mass of solution) * 102
• Parts per thousand = (mass of solute / mass of solution) * 103
• Parts per million = (mass of solute / mass of solution) * 106
• Parts per billion = (mass of solute / mass of solution) * 109
2. Volume percent (v/v) = (volume of solute / volume of solution) * 102 ; only if both are liquids
3. Mole Fraction (Xsolute) = (moles of solute / moles of solute + moles of solvent)
• Xsolvent = (moles of solvent / moles of solute + moles of solvent)
4. Molality (m) = (moles of solute / kilograms of solvent)
5. Molarity (M) = (moles of solute / liters of solution)
Factors Affecting Solubility

1. Solute/Solute, Solvent/Solvent and Solute/Solvent Intermolecular Forces - In order for a solute to be soluble in a particular solvent, three things need to be considered.  First, the intermolecular forces holding the solvent molecules together must be broken to make room for the solute.  This requires energy (bond breaking always takes energy).  Second, the intermolecular forces holding the solute together must be broken.  Again, this requires energy.  Finally, the solute and solvent can interact through whatever forces are available.  This releases energy (bond formation gives off energy), and is called solvation energy.  If the energy needed in the first two steps is not too great and the solvation energy is sufficiently large, the overall energy will be negative or slightly positive, a solution will be formed.  The more random or disordered nature of a solution (entropy) provides the additional push if the energy is a little positive.  The rule "like dissolves like" refers to the fact that if the intermolecular forces in the solvent and the solute are similar (H-bonding, dipole-dipole or London forces), solute/solvent interactions are probably similar as well.

 Solute (A) Solvent (B) A-A B-B A-B Solution? CH3OH H2O H-Bonding H-Bonding H-Bonding Yes C6H6 H2O London H-Bonding Dipole-Induced Dipole No NaCl H2O Ionic H-Bonding Ion - Dipole Yes NaCl C6H6 Ionic London Ion-Induced Dipole No CHCl3 C6H6 Dipole - Dipole London Dipole-Induced Dipole Yes
Color coding of A-A, B-B, and A-B columns: red = strong attractions, pink = moderately strong, yellow = intermediate attractions, green = weak attractions.

2.  Temperature - Generally speaking the water solubility of a liquid or solid will increase with increasing temperature.  However, there are some exceptions to this.  Some solutes like solid Ce2(SO4)3 is less soluble with increasing temperature. The thermodynamics of the solution process is again responsible.  Since a solution that has reached the solubility limit is in equilibrium, the various laws of equilibrium apply to that system. There is a principle that will be more completely discussed in a future chapter called Le Chatlier's Principle.  The principle says that when a stress is applied externally to an equilibrium, the equilibrium is disrupted temporarily and will shift in such a way as to undo the stress that had been applied.  One such stress that can be applied is temperature change.  According to the Principle, increasing the temperature of an equilibrium will always favor the endothermic process of an equilibrium since it is the endothermic process that can absorb the added energy resulting from the increase in temperature.  That effectively counteracts the temperature increase.  Since most liquid and solid solutes dissolved in water have the solution formation process endothermic (see above), that would be favored when the temperature was increased resulting in an increase in the solubility limit.  However some solutes like Ce2(SO4)3 have an exothermic heat of solution.  Since increasing the temperature will always favor the endothermic process the dissolution (solution breakdown) process endothermic) will be favored and the solubility will decrease.  Gaseous solutes always have an exothermic heat of solution.  Consequently, the solubility of all gases in water decrease with increasing temperature.  That is why carbonated drinks that have carbon dioxide gas dissolved in them will become "flat" tasting when heated.  The sparkle of the drink will have disappeared along with the carbon dioxide gas.

3.  Pressure - Pressure changes above the solution do not affect the solubility limits of solids or liquids dissolved in water. However gaseous solutes are affected.  If the pressure of the gas is increased above the gaseous solution, then the solubility will be increased in a linear fashion.  This was investigated by William Henry (c. 1774-1836) and is now called Henry's Law.
Henry noted that when you increased the pressure of a gas above a gaseous solution, the concentration of the gas in the solution would increase in a linear fashion.

Cgas = kPgas

where Cgas = molar concentration of the gas in the solution; k = Henry's law constant for that gas at a particular temperature; and P = partial pressure of the gas above the solution.

 Gas Solubility (mol/l atm) N2 6.8 x 10-4 O2 1.4 x 10-3 CO2 3.2 x 10-2 SO2 1.5 x 10-1 CO 1.0 x 10-3 He 3.8 x 10-4 Ne 4.7 x 10-4 Ar 1.5 x 10-3 Kr 2.8 x 10-3 Xe 4.8 x 10-3 Rn 1.0 x 10-2

Colligative Properties

Colligative Properties are those properties of a liquid that may be altered by the presence of a solute.  Colligative means "depending on the collection" because the magnitude of the change is due to the number of particles in the solution and not their chemical identity.  Examples of properties that fall under this category are the vapor pressure, melting and boiling points, and osmotic pressure.  All of these properties ultimately relate to the vapor pressure.  The diagram below shows the phase diagram for a pure solvent (black equilibrium lines) superimposed on the phase diagram of a solution (blue eqilibrium lines).  Note the liquid phase is the only phase containing solute.  The melting point and the boiling point curves are both effected by the presence of solute.  In a solution, a fraction of the molecules with energy in excess of the intermolecular force are nonvolatile solute molecules, or another way of saying this is that the number of solvent molecules with energies above the intermolecular force has been reduced.  Because of this the solution has a lower vapor pressure than the pure solvent at all temperatures, and, therefore, a higher normal boiling point.  The presence of solute particles interferes with the crystallization process and thus the normal melting point is lower (more energy needs to be removed to favor crystallization). The quatitative relationships are given below.  In all of these, we must take into account the total number of particles produced by strong electrolyes such as NaCl.  When one mole of NaCl dissolves in water, two moles of particles (Na+ and Cl-) are formed.  1 mole of MgCl2 would give 3 moles of particles (Mg2+ and 2 Cl-).  This factor of ionization is usually expressed using the vant Hoff factor (i):

i = moles of particles in solution/moles of solute dissolved

Vapor Pressure Lowering of Solutions

In a solution, a fraction of the molecules with energy in excess of the intermolecular force are nonvolatile solute molecules, or another way of saying this is that the number of solvent molecules with energies above the intermolecular force has been reduced.  Because of this the solution has a lower vapor pressure than the pure solvent.  Experiments on the vapor pressures of solutions containing nonvolatile solutes were carried out by Francois Marie Raoult (1830-1901). His results are described by the equation known as Raoults law:

Psolution  =  XsolventPosolvent

where Psolution is the observed vapor pressure of the solution, Xsolvent is the mole fraction of solvent, and Posolvent is the vapor pressure of the pure solvent.

Any solution that obeys Raoults law is called an ideal solution. Raoults law is to solutions what the ideal gas law is to gases. Yet, some strong solute-solvent interactions do not behave ideally, and gives a vapor pressure lower than that predicted by Raoults law.  When this happens, a negative deviation from Raoults law results. When liquid-liquid solutions with both components being volatile, a modified form of Raoults law applies:

Ptotal = Pa + Pb = XaPoa + XbPob

where Ptotal represents the total vapor pressure of a solution containing A and B. Xa and Xb are the mole fractions of A and B. Poa and Pob are the vapor pressures of pure A and B, and Pa and Pb are the partial pressures resulting from molecules of A and B in the vapor above the solution.

Boiling-Point Elevation and Freezing-Point Depression

Because changes of state depend on vapor pressure, the presence of a solute affects the freezing point and boiling point of a solvent.  The normal boiling point of a liquid occurs at the temperature where the vapor pressure is equal to 1 atmosphere. A nonvolatile solute elevates the boiling point of the solvent.  The magnitude of the boiling-point elevation depends on the concentration of the particles of solute.  The change in boiling point can be represented by the equation: Tb = iKbmsolute

where Tb is the boiling-point elevation, or the difference between the boiling point of the solution and that of the pure solvent; i is the vant Hoff factor; Kb is a constant that is characteristic of the solvent and is called the molal boiling-point elevation constant; and msolute is the molality of the solute in the solution.

When a solute is dissolved in a solvent, the freezing point of the solution is lower than that of the pure solvent. The equation for freezing-point depression is analogous to that for boiling-point elevation: Tf = iKf msolute

wher Tf  is the freezing-point depression, or the difference between the freezing point of the pure solvent and that of the solution;  i is the vant Hoff factor; Kf is a constant that is characteristic of a particular solvent and is the called the molal freezing-point depression constant; and msolute is the molality of the solute in the solution.

 Compound Normal bp Kb (oC/m) Normal mp Kf (oC/m) Water, H2O 100.0 0.52 0.0 1.86 Benzene, C6H6 80.1 2.53 5.5 5.12 Ethanol, C2H5OH 78.4 1.22 -114.6 1.99 Carbon tetrachloride, CCl4 76.8 5.02 -22.3 29.8 Chloroform, CHCl3 61.2 3.63 -63.5 4.68

Osmotic Pressure

A solution and pure solvent are separated by a semipermeable membrane, which allows solvent but not solute molecules to pass through. As time passes, the volume of the solution increases and that of the solvent decreases.  This flow of solvent into the solution through the semipermeable membrane is called osmosis. Because liquid levels are different when the liquid levels stop changing, there is a greater hydrostatic pressure on the solution than on the pure solvent. This excess pressure is called the osmotic pressure. Experiments show that the dependence of the osmotic pressure on solution concentration is represented by the equation: = MRT

where is the osmotic pressure in atmospheres, M is the molarity of the solute, R is the gas law constant, and T is the Kelvin temperature.

Solutions that have identical osmotic pressures are said to be isotonic solutions.  If a solution in contact with pure solvent across a semipermeable membranes subjected to an external pressure larger than its osmotic pressure, reverse osmosis occurs. The pressure will cause a net flow of solvent from the solution to solvent.