1. Colligative Properties
Lecture 7 (Ch 16)
Assigned Reading: Chapter 15.6,

2. Expressing Solute Concentration
Colligative properties are physical properties of solutions that vary depending on ratio of solute to solvent
There are 4 methods for expressing these ratios:
Molarity
Percent mass
Mole fraction
Molality

3. Disadvantage of Molarity
The major disadvantage of molarity as a measure of solute/solvent ratio is that molarity changes with temperature due to fluctuations of density.
Increasing the temperature of a solution LOWERS its molarity.
Solute concentrations expressed as % mass, mole fractions, and molality are all independent of temperature.

4. % 𝐦𝐚𝐬𝐬= 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞 𝐭𝐨𝐭𝐚𝐥 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐱 𝟏𝟎𝟎%
% Mass
% mass is used when the molar mass of the solute is unknown, or if the solute is a mixture of various substances (e.g. plant extract).
Ex g of a solute is dissolved in g of water. What is the %mass of the solute?
% 𝐦𝐚𝐬𝐬= 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞 𝐭𝐨𝐭𝐚𝐥 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧 𝐱 𝟏𝟎𝟎%
% 𝑚𝑎𝑠𝑠= 5.85 𝑔 𝑔 𝑥 100%=5.53%
GP1,2

5. Mole Fraction
Mole fraction is defined as the ratio of moles of a given species (xa) to the total number of moles of all components in solution (ntot).
Ex. Calculate the mole fraction of NaCl in a solution containing 1.0 g of NaCl in 100 g of water.
𝒙 𝒂 = 𝒙 𝒂 𝒏 𝒕𝒐𝒕
x Na = mol NaCl (.017 mol NaCl+5.55 mol H 2 O) x 100%=0.3%
GP 3,4

6. Molality
For dilute solutions containing solutes of known molar mass, it may be convenient to use molalilty (m), especially if a solution will be used over a wide range of temperatures. Molality is NOT molarity!
Ex. Calculate the molality of a solution prepared by dissolving 20.0g of sucrose into 500 g of water (see GP 4)
𝒎= 𝐦𝐨𝐥𝐞𝐬 𝐨𝐟 𝐬𝐨𝐥𝐮𝐭𝐞 𝐤𝐠 𝐬𝐨𝐥𝐯𝐞𝐧𝐭
𝑚= mol kg =0.117𝑚

7. Colligative Molality
It is essential for the understanding of colligative properties to realize that it is the ratio of solute species to solvent species that determines the magnitude of a colligative effect.
For example, a 0.10m NaCl(aq) solution has twice as many solute species as a 0.10m sucrose (aq) solution because NaCl is a strong electrolyte that produces two ions in solution.
We can describe a secondary term called colligative molality (mc):
where i is the number of species produced when the solute is dissolved.
𝒎 𝒄 =𝒊𝒎
GP5

8. Colligative Properties: Vapor Pressure
Suppose we seal a beaker of liquid and remove all air from the headspace so that there is zero pressure.
The liquid molecules are in constant motion, and some at the surface of the liquid will break free and create vapor above the liquid, which exerts pressure.
The vapor pressure increases rapidly at first, then slows down until a constant pressure is attained, known as the equilibrium vapor pressure.

9. Colligative Properties: Vapor Pressure
The number of molecules that leave the surface is proportional to the surface area of the liquid. Since this does not change, the evaporation rate is constant.
As more vapor molecules form, there are more collisions between vapor and liquid molecules, which results in faster condensation.

10. Boiling Points as a Function of Pressure
At each temperature, a liquid has an exact equilibrium vapor pressure.
The normal boiling point is the temperature at which the vapor pressure of the liquid is the same as atmospheric pressure.
Ex. Vail, California is 8200 feet above sea level. The atmospheric pressure is atm. Estimate the boiling point of water there?

11. Colligative Effects on Vapor Pressure
The vapor pressure of the solvent over a solution is always less than the vapor pressure above pure solvent.
The presents of solute molecules decreases the number of solvent molecules at the surface, which means a lower surface area of the solvent.
Vapor pressure varies with mole fraction.

12. Raoult’s Law
The vapor pressure of a solution is related to the mole fraction of solute by Raoult’s Law:
where P1 is the vapor pressure of the solvent above the solution, x1 is the mole fraction of the solvent, and 𝑃 1 𝑜 is the equilibrium vapor pressure of the pure solvent.
The extent by which the vapor pressure is lowered ( P 1 o − P 1 , or ∆ 𝑃 1 ) is simply called the vapor pressure lowering.
𝐏 𝟏 = 𝐱 𝟏 𝐏 𝟏 𝐨
∆ 𝐏 𝟏 =(𝟏− 𝒙 𝟏 ) 𝐏 𝟏 𝐨

13. Example
The vapor pressure of water at 80oC is 355 mmHg. What is the vapor pressure of a solution prepared by dissolving 60.8g of sucrose in 100 g of water? What is the vapor pressure lowering ?
x water = mol water total mol = 5.55 mol 5.55 mol water mol sucrose =0.969
𝑃 𝑤𝑎𝑡𝑒𝑟 = 𝑚𝑚𝐻𝑔 =344 𝑚𝑚 𝐻𝑔
∆ 𝑃 𝑤𝑎𝑡𝑒𝑟 = 𝑚𝑚𝐻𝑔 =11 𝑚𝑚𝐻𝑔
GP 6

14. Colligative Properties: Boiling Point
Since the addition of solutes to a solvent lowers its equilibrium vapor pressure, the temperature required for boiling is higher for a solution than for the pure solvent. The extent of the increase (∆ 𝑇 𝑏 ) is the boiling point elevation.
where Kb is a constant which depends of the solvent and mc is the colligative molality.
∆ 𝐓 𝐛 = 𝐊 𝐛 𝒎 𝐜

15. GP 7

16. Colligative Properties: Freezing Point
Solutions have lower freezing points than pure solvents. The extent of the decrease, ∆ 𝑇 𝑏 , is the freezing point depression.
The freezing point depression of dissolved substances is the basis for antifreezes. For example, heavy duty automobile antifreeze is 50% ethylene glycol by mass in water. The freezing point is -30oC (-22oF)
∆ 𝐓 𝐅 = 𝐊 𝐅 𝒎 𝐜
GP8

17. Colligative Properties: Osmosis

18. Colligative Properties: Osmosis
Osmotic pressure is the pressure required to stop the flow of solvent across a permeable membrane. The higher vapor pressure on the water side pushes it through the membrane into the glucose (aq) side.

19. Colligative Properties: Osmosis
Osmotic pressure, П, is given by
where R is the gas constant and Mc is the colligative molarity.
Ex. What is the osmotic pressure of seawater (0.55M NaCl) at 15oC?
П=RT M c
П= 𝐿 𝑎𝑡𝑚 𝑚𝑜𝑙 𝐾 288𝐾 𝑚𝑜𝑙 𝐿 =26 𝑎𝑡𝑚 !!!

20. Reverse Osmosis for Purifying Water