Solutions

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Vapor Pressure

    The vapor pressure of a solvent is changed by the presence of a solute.  The nature of the change depends on whether the solute is volatile or non-volatile.

•    For a non-volatile solute in a volatile solvent:  P_soln = X_solvent P^o_solvent

    where P^o_solvent   is the vapor pressure of the pure solvent
 DP = X_soluteP^o_solvent
where X_solute is the mole fraction of particles (molecules, or ions) in solution. Problem:  4.0 g of NaOH is added to 96.0 g of water at 50^oC.  What is the vapor             pressure of the mixture? [Water has a vapor pressure of 92.51 mmHg at 50^oC.]

• For two volatile components:  Ideal solutions obey Raoult's Law:

 P_total = P_a + P_b = X_aP^o_a + X_bP^o_b      This applies to ideal solutions, where the intermolecular forces between a and a and b and b are similar to those between a and b.

      For non-ideal solutions, there can be negative deviations from Raoult's Law.  When the attraction between a and b is stronger than that between pure a or pure b,  the resulting solution exerts a lower vapor pressure than that based on ideal behavior.
      There can also be positive deviations from Raoult's Law when the attraction between pure a and pure b is greater than the attractions between a and b in the mixture.  This solution will have a greater vapor pressure than that based on ideal behavior.

Colligative Properties

     These are properties of solutions contain a non-volatile solute and a volatile solvent in which the property depends solely on the amount of solute particles dissolved, and not on their chemical nature.  As a result of a decrease in vapor pressure, a solution with a non-volatile solute will have an altered phase diagram as illustrated below.  An outcome of lowering the vapor pressure is an increase in boiling point and a decrease in freezing point (compared to pure solvent).

• Boiling Point Elevation - Since a non-volatile solute lowers the vapor pressure of the solvent, it follows that the boiling point of the solution will be greater than that of pure solvent.  The experimentally derived relationship is:

DT_b = K_bm
 where Kb is the boiling point elevation constant for the solvent
  m is the molality of the solute particles

• Freezing Point Depression - The freezing point of the solution decreases (due to the decrease in vapor pressure), and is described by the relationship:

DT_f = K_fm
 where Kf is the freezing point depression constant for the solvent
  m is the molality of the solute particles

Problem:  The solubility of NaNO₃ in water at 0^oC is 75 grams per 100g of water.  Calculate the freezing point of the solution.
Problem:  A solution of 2.5og of a compound with an empirical formula of C₆H₅P in 25.0 g of benzene has a freezing point of 4.3^oC.  Calculate the molar mass of the solute and its molecular formula.  [The normal freezing point of benzene is 5.5^oC, and K_f for benzene = 5.12 ^oC/m.]

• Osmosis and Osmotic Pressure
 osmosis - the flow of solvent through a semi-permeable membrane
 osmotic  pressure - the pressure required to just stop osmosis

P= MRT
 where P is osmotic pressure;  M = molarity of solute particles, R = gas law constant,
T= absolute temperature in Kelvin

• Applications of Colligative Properties - antifreeze, salting of ice, determining molar masses, desalination.

 Problem: 0.8750 g of a protein is dissolved in enough water to make 100. ml of solution.  The solution has an osmotic pressure of 3.8 mm Hg at 25^oC.  Calculate the molar mass of the protein.

 isotonic solutions - solutions with the same osmotic pressure as that of red blood cells.
hypotonic solutions - solutions with less osmotic pressure than red blood cells.  Exposure to blood can cause cells to undergo hemolysis, a bursting due to large amounts of water entering the cell.
hypertonic solutions - solutions with greater osmotic pressure than red blood cells.  Cells may undergo crenation - where they dehydrate and shrivel.
 

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Copyright ©1998 Beverly J. Volicer and Steven F. Tello, UMass Lowell.  You may freely edit these pages  for use in a non-profit, educational setting.  Please include this copyright notice on all pages.