ANALYTICAL CHEMISTRY CHEM 3811

CHAPTER 12

DR. AUGUSTINE OFORI AGYEMANAssistant professor of chemistryDepartment of natural sciences

Clayton state university

CHAPTER 12

CHEMICAL EQUILIBRIUM CALCULATIONS

- A measure of how much of a solute can be dissolved in a solvent

- Units: grams/100 mL

Three factors that affect solubility- Temperature

- Pressure- Polarity

SOLUBILITY

- Most nitrate (NO3-) salts are soluble

- Most salts of alkali metals (Group 1A) and ammonium (NH4

+) are soluble

- Most salts containing Cl-, Br-, and I- soluble Exceptions: salts of Ag+, Hg2

2+, Pb2+

SOLUBILITY OF SALTS

- Most sulfate salts are solubleExceptions: BaSO4, PbSO4, Hg2SO4

- Most hydroxides are slightly solubleHydroxides of Ba2+, Sr2+, and Ca2+ are marginally soluble

- Most salts containing S2-, CO32-, PO4

3-, CrO42- are insoluble

Exceptions: salts of alkali metals and NH4+

SOLUBILITY OF SALTS

- Solubility increases when soluble salts are addedto solutions of marginally soluble salts

- Cations are surrounded by anions to create a netnegative ionic atmosphere

- Anions are surrounded by cations to create a netpositive ionic atmosphere

- The net charges are less than those of the cation or anion alone

SOLUBILITY OF SALTS

- The attraction between ions in solution is decreasedwhich increases solubility

- Increasing the concentration of ions in solution decreasesthe attraction between ions and increases solubility

- Increasing concentration of ions increases ion dissociation

SOLUBILITY OF SALTS

IONIC STRENGTH

- A measure of the total concentration of ions in solution

.........zczczc21zc

21μ 2

ii2ii

2ii

i

2ii

µ = the ionic strengthci = the concentration of the ith species

zi = the charge on the ith species

IONIC STRENGTH

Find the ionic strength of 0.0250 M Na2SO4

Na2SO4 ↔ 2Na+ + SO42-

[Na+] = 2 x 0.0250 M = 0.0500 M

[SO42-] = 0.0250 M

0750.0)2)(0250.0(1)(0.0500)(21μ 22

IONIC STRENGTH

For 1:1 electrolytes (NaCl, NaNO3, KBr)

The ionic strength is equal to the molarity1:1 µ = molarity

For any other stoichiometryThe ionic strength is greater than the molarity

2:1 µ = 3 x molarity3:1 µ = 6 x molarity2:2 µ = 4 x molarity

ACTIVITY COEFFICIENT

Consider the equilibrium for the reaction

aA + bB ↔ cC + dD

The equilibrium constant (K) is given by

ba

dc

[B][A][D][C]K

K does not account for the effect of ionic strength

ACTIVITY COEFFICIENT- Activities (A) are used in place of concentrations

to account for ionic strength

A = [ ] x γ

where γ is the activity coefficient

- Activity coefficient depends on ionic strength

- Activity coefficient is 1 when there is no effect of ionic strength

- Activity coefficient decreases with increasing ionic strength

ACTIVITY COEFFICIENT

bB

baA

a

dD

dcC

c

bB

aA

dD

cC

γ[B]γ[A]γ[D]γ[C]

AAAAK

- K is generally expressed as follows

Debye-Hückel Equation

- Relates activity coefficients to ionic strength (at 25 oC)

/305)μ(α1μ0.51z

γlog2

γ = activity coefficientz = ion charge (±)

α = ion size in picometers (1 pm = 10-12 m)µ = ionic strength

ACTIVITY COEFFICIENT

ACTIVITY COEFFICIENT

Effects (limited to dilute aqueous solutions)

- Activity coefficient increases with decreasing ionic strength(approaches unity as ionic strength approaches zero)

- Activity coefficient depends on the magnitude of the chargebut not on the sign

(departs from unity as charge increases)

- Effect of activity on ions increases with decreasing ion size

ACTIVITY COEFFICIENT

Neutral Molecules

- Activity coefficient is assumed unity(no charge and no ionic atmosphere)

- Activity is assumed to be equal to its concentration

ACTIVITY COEFFICIENTGases

Activity (called fugacity) is written as

Agas = Pgas x γgas

P = pressure in bars

γgas = fugacity coefficient of a gas

For most gases at or below 1 barγgas ≈ 1

ACTIVITY COEFFICIENT

pH = negative logarithm of the hydrogen ion activitypH electrodes measure activity of hydrogen ions

HH]γ[HloglogApH

- Ionic strength of pure water is very low

- Activity coefficient of pure water is very close to unity

OHHw ]γ[OH]γ[HK

CHARGE BALANCE

- In a given solutionsum of positive charges = sum of negative charges

- The coefficient of each term equals the magnitude of thecharge on the respective ion

- 1 mole of an ion An+/n- contributes n moles of positive/negative charge

CHARGE BALANCE

n1[C1] + n2[C2] + ….. = m1[A1] + m2[A2] +…..

[C] = concentration of a cationn = magnitude of the charge on the cation

[A] = concentration of an anionm = magnitude of the charge on the anion

- Activity coefficient do not appear in charge balance

CHARGE BALANCE

Consider a solution containing the following speciesNa+, CO3

2-, HCO3-, H+, Ca2+, OH-, PO4

3-, HPO42-

total positive charge = total negative charge

[Na+] + [H+] + 2[Ca2+] =

2[CO32-] + [HCO3

-] + [OH-] + 3[PO43-] + 2[HPO4

2-]

MASS BALANCE

- Also called the material balance

- Conservation of matter

the quantity of a particular atom (or group of atoms)equals

the amount of that atom (or group of atoms) delivered

- Mass balance includes all products of compoundsthat dissociate in several ways

MASS BALANCE

Consider 0.0200 mol of H3AsO4 in 1.00 L of solution0.0200 M = [H3AsO4] + [H2AsO4

-] + [HAsO42-] + [AsO4

3-]

For KH2AsO4 in water[K+] = [H3AsO4] + [H2AsO4

-] + [HAsO42-] + [AsO4

3-]

For K2HAsO4 in water[K+] = 2 x {[H3AsO4] + [H2AsO4

-] + [HAsO42-] + [AsO4

3-]}

For K3AsO4 in water[K+] = 3 x {[H3AsO4] + [H2AsO4

-] + [HAsO42-] + [AsO4

3-]}

FRACTIONAL COMPOSITION

aHA K][H

][HF

[HA]α

a

a-

A K][H][K

F][Aα -

F = initial concentration of acid HA (formal concentration)

Fraction of species in the form HA

Fraction of species in the form A-

1ααAHA