1

Chapter 6

Solutions

27 March 2014

Representation of Concentration of Ions in Solution

Two common ways of expressing concentration of ions in solution:

1. Moles per liter (molarity)• Molarity emphasizes the number of

individual ions

2. Equivalents per liter (eq/l)• Emphasis on charge

2

ionon charges ofnumber (g)ion of massmolar ionan of equivalent One =

Comparison of Molarity and Equivalents

1 mol/l Na3PO4

• What would the concentration of PO43- ions be?

• 1 mol/l

• Equivalent is defined by the charge

• One Equivalent of an ion is the number of grams of the ion corresponding to Avogadro’s number of electrical charges

Molarity vs. Equivalents – 1 mol/l Na3PO4

• 1 mol Na+ = 1 equivalent Na+

• 1 mol PO43- = 3 equivalents PO4

3-

• Equivalents of Na+?– 3 mol Na+ = 3 equivalents of Na+

• Equivalents of PO43-?

– 1 mol PO43- = 3 equivalents of PO4

3-

3

Calculating Ion Concentration• Calculate eq/l of phosphate ion, PO4

3- in a solution with 5.0 x 10-3 mol/l phosphate

• Need to use two conversion factors:– mol PO4

3- mol charge

– mol charge eq PO43-

5.0 x 10-3 mol PO43- x 3 mol charge x 1 eq

1 l 1 mol PO43- 1mol charge

= 1.5 x 10-2 eq PO43- /l

Concentration-Dependent Solution Properties

• Colligative properties - properties of solutions that depend on the concentration of the solute particles, rather than the identity of the solute

• Four colligative properties of solutions1. vapor pressure lowering2. boiling point elevation3. freezing point depression4. osmotic pressure

4

Raoult’s LawTotal vapor pressure p above

the solution is sum of the partial pressures of the individual components

* * * ...A A B B C Cp p x p x p x= + + +

Ax

*ip vapor pressure of the pure component i

mole fraction of the component i in the mixture

Note that this is similar to the Dalton’s Law

Vapor Pressure of a LiquidConsider Raoult’s law in molecular

terms• Vapor pressure of a solution results

from escape of solvent molecules from liquid to gas phase

• Partial pressure of gas phase solvent molecules increases until equilibrium vapor pressure is reached

• Presence of solute molecules hinders escape of solvent molecules, lowering equilibrium vapor pressure

5

Vapor Pressure Lowering• Raoult’s law - when a nonvolatile solute is added to a

solvent, vapor pressure of the solvent decreases in proportion to the concentration of the solute

• Solute molecules (red below) serve as a barrier to the escape of solvent molecules resulting in a decrease in the vapor pressure

• Freezing point depression (ΔTf) - is proportional to the number of solute particles – Solute particles, not just solute

• How does an electrolyte behave?– Dissociate into ions

• An equal concentration of NaCl will affect the freezing point twice as much as glucose (a nonelectrolyte)

• Each solvent has a unique freezing point depression constant or proportionality factor

ΔTf=kf m

Freezing Point Depression

Cryoscopy

6

• Boiling point elevation (ΔTb) - is proportional to the number of solute particles

• An electrolyte will affect boiling point to a greater degree than a nonelectrolyte of the same concentration

• Each solvent has a unique boiling point elevation constant

ΔTb=kb m

Boiling Point Elevation

Ebullioscopy

• Boiling point elevation (ΔTb) - is proportional to the number of solute particles

• An electrolyte will affect boiling point to a greater degree than a nonelectrolyte of the same concentration

• Each solvent has a unique boiling point elevation constant

ΔTb=kb m

Boiling Point Elevation

Ebullioscopy

7

Osmotic Pressure• Some types of membranes appear impervious to

matter, but actually have a network of small holes called pores

• These pores may be large enough to permit small solvent molecules to move from one side of the membrane to the other

• Solute molecules cannot cross the membrane as they are too large

• Semipermeable membrane - allows solvent but not solute to diffuse from one side to another

Osmotic Pressure

• Osmosis - the movement of solvent from a dilute solution to a more concentratedsolution through a semipermeable membrane

• Requires pressure to stop this flow

8

• Osmotic pressure (π) - the amount of pressure required to stop the flow across a semipermeable membrane

• Osmolarity - the molarity of particles in solution– Osmol, used for osmotic pressure

calculation

π=cMRT

Osmotic Pressure

Calculating OsmolarityCalculate the osmolarity of 5.0 x 10-3 mol/l Na3PO4

Na3PO4 is an ionic compound forming electrolytes

1 mol Na3PO4 yields 4 product ions[5.0 x 10-3 mol Na3PO4 / l] x 4 mol particles

1 mol Na3PO4

= 2.0 x 10-2 mol particles / l2.0 x 10-2 mol particles / l = 2.0 x 10–2 osmol

9

Calculating Osmotic PressureCalculate the osmotic pressure of a 5.0 x 10-2 mol/lsolution of NaCl at 25 °C (298 K)

Definition of osmotic pressure, π=cMRTcM is osmolarity =[5.0 x 10-2 mol NaCl / l] x 2 mol particles

1 mol NaCl = 1.0 x 10-1 mol particles / l

Substitute into osmotic pressure equation:π = 1.0 x 10-1 mol particles x 0.0821 l x atm x 298 K

liter K x mol= 2.4 atm

Tonicity and the Cell• Living cells contain aqueous solution and these cells are also

surrounded by aqueous solution• Cell function requires maintenance of the same osmotic

pressure inside and outside the cell• Solute concentration of fluid surrounding cells higher than

inside results in a hypertonic solution causing water to flow into the surroundings, causing collapse = crenation

• Solute concentration of fluid surrounding cells too low, resultsin a hypotonic solution causing water to flow into the cell, causing rupture = hemolysis

• Isotonic solutions have identical osmotic pressures and no osmotic pressure difference across the cell membrane

10

Hemolysis Crenation

Tonicity and the Cell

Tonicity and the Cell

Isotonic solution 0.9% w/v of NaCl

11

Pickling Cucumber in HypertonicBrine Due to Osmosis

Cracked tomatoes in hypotonicenvironment (rain water) due to osmosis

12

Water as a Solvent• Water is often referred to as the “universal

solvent”• Excellent solvent for polar molecules • Most abundant liquid on earth• 60% of the human body is water

– transports ions, nutrients, and waste into and out of cells

– solvent for biochemical reactions in cells and digestive tract

– reactant or product in some biochemical processes

Electrolytes in Body FluidsCATIONS IN THE BLOOD and CELLS• Na+ and K+ two most important cations

Na+

K+

Blood Cells

135 meq/l 3.5 – 5.0 meq/l

10 meq/l 125 meq/l