Solutions and Chemical Equilibrium

Preparation for College ChemistryColumbia UniversityDepartment of Chemistry

Chapter Outline

Concentration of Solutions

Colligative Properties

Chemical Equilibrium

Osmosis and Osmotic Pressure

Ion Product of Water

Types of Solutions

Phase Solute Solvent Example

Gas

Liquid

Liquid

Solid alloys

H2 in Pt

Coke

antifreeze

Coke

airgas

liquid

liquid

liquid

solid

solidsolid

gas

solid

liquid

gas

gas

Liquid

Solid

Concentration of Solutions

Units Symbol Definition

Mass percent

Parts per million

Mass/volume percent

Volume percent

% m/m

% v/v

% m/v

ppm

(msolute/msolution ) x100

(vsolute/vsolution ) x100

(msolute/vsolution ) x100

mgsolute/Lsolution

Parts per billion ppb µgsolute/Lsolution

Molarity

Molality

M

m

molsolute/Lsolution

molsolute/kgsolvent

Mass % Solutemass solute

Total mass solutionMass % solute = x 100

ppb solute = mass % x 10 9

mass solutetotal mass solution

ppm solute = x 10 6

ppm solute(aqueous solutions) = mg solute / Lsolution

ppb solute (aqueous solutions) = µg solute / Lsolution

http://pubs.acs.org:80/hotartcl/est/99/oct/oct-news5.html

When concentration is so low that the d ~ dwater:

Molarity

moles soluteLiter solution

mol L

=

What volume of a 0.035 M AgNO3 solution can be made from 5.0 g AgNO3 ?

5.0 g AgNO3 x 0.035 mole AgNO3

L

169.91g

1 mole AgNO3 x = 840 mL

M =[solute] =

250mL

Dilution Equation

Ci,mol×L−1

()Vi,L ()=Ci×Vi,mol=chemical amount of solute

Only solvent is added

Preparing a dilute solution of specified concentration

=Ci Vi Cf Vf

Ci ViCf

Vf

=

Raoult’s Law

Ideal

Positive

Negative

P1

0

P1

10 X1

P1 =X1P10

X1 =n1

n1 +n2 +n3 +...

Basis for four properties of DILUTE SOLUTIONS

Colligative Properties

Freezing point depression. Kf (°C kgsolvent mol -1solute)

Boiling point elevation Kb (°C kgsolvent mol -1solute)

Osmotic Pressure (atm)

Depend on the concentration of solute species and not on its nature

Vapor-pressure lowering (atm)

0 20 40 60 80 100 120

Temperature(°C)

200

400

600

800

1000

Vap

or p

ress

ure

(to

rr)

Vapor-pressure of liquids

Pressure exerted by a vapor in equilibrium with its liquid

Atmospheric pressure

boi

lin

g p

oin

t

For water:

Vapor-pressure lowering

ΔP1 =P1 −P10 =X1P1

0 −P10 =−X2P1

0

For a two component system : solvent 1, solute 2:

X1 =1−X2

P1 =X1P10

Raoult Law:

The vapor pressure lowering is

The change in vapor pressure of the solvent is proportional to the mole fraction of the solute (< 0)

Boiling Point Elevation (∆Tb) Vapor Pressure lowering (∆P1)

Sol

ven

t vap

or p

ress

ure

1 atmP0

solvent

∆P1

∆Tb

Temperature

P0solution

Tb T’b

∆Tb and ∆Tf

∆Tb =Tb’ - Tb = Kbm ∆Tf = Tf’ - Tf = -Kfm

m=mol solutekg solvent

=mol solute

1000g solvent

∆Tb = b.p. elevation

∆Tf = f.p. depression

Kf = f.p. depression constant

Kb = b.p. elevation constant

Solvent

Acetic acid

Benzene

Camphor

m.p (°C) Kf b.p.(°C) Kb

Water 0.00 1.86 100.0 0.512

16.6 3.90 118.5 3.07

5.5 5.1 80.1 2.53

178 40 208.1 5.95

Kf and Kb (°C kgsolvent mol -1solute)

Osmosis and Osmotic Pressure, π =cRTJacobus van’t Hoff in 1887

c = M; R = universal gas constant; T absolute temperature

Pure water Solution

Semipermeable membrane

Chemical Equilibrium

2NO2N2O4

2NO2N2O4

2NO2N2O4

forward

reverse

PRODUCTSREACTANTS

REVERSIBLE REACTION:

T

T

Kinetics. Rates of Reaction

RATEforward

RATEreverse

RATEforward = RATEreverse

EquilibriumRea

ctio

n r

ate

Time

A + B C + D

C + D A + B

Chemical EquilibriumSaturated solution

Weak electrolyte dissociation

NaCl (s) Na+(aq) + Cl -(aq)

HC2H3O2 (aq) H3O+(aq) + C2H3O2 -(aq)

Complex ion formation

Fe 3+ (aq) + SCN - (aq) Fe(SCN)2+ ( aq)

Le’Chatelier’s Principle

“A system in equilibrium that is subjected to a stresswill react in ways that counteract the stress”

Four ways to stress a chemical system:

• Concentration Change

• Volume Change

• Temperature Change

• Presence of a Catalyst

Equilibrium Constants, Keq

aA + bB cC + dD

Keq =[A] a[B] b

[C] c [D] d

aA(g) + bB(g) cC(g) + dD(g)

Keq =(PC) c (PD) d

(PA) a (PB) b

Kc

Kp

LAW OF MASS ACTION. Guldberg and Waage. 1867

RATEforward

Q > K

Rea

ctio

n q

uot

ien

t

Time

Reaction Quotient, Q

RATEreverse

Q < K

Q = K

Q =[A] a[B] b

[C] c [D] d

Keq =[A] a[B] b

[C] c [D] d

• Gases enter equilibrium expressions as partial pressures in atm

• Dissolved species enter as concentrations in M

• Pure solids and pure liquids are represented by the number 1 (unity)

• A solvent in a chemical reaction is represented by 1, provided the solution is diluted

Writing Equilibrium Constants

Ion Product Constant for Water, KW

H2O + H2O H3O+(aq) + OH -(aq)

Keq =[H2O] 2

[H3O +] [OH -]

= 55.5 M1kg H2O

103 g H2Ox x18 g H2O

1 mol H2O

1L H2O

1kg H2O

Keq [H2O] 2 = [H3O +] [OH -]Kw = = 1x 10 -14

Autoionization of Water

[H3O +] = [OH -] = 1x 10 -7 M

[H2O] =