ANALYTICAL CHEMISTRY CHEM 3811 CHAPTER 12 DR. AUGUSTINE OFORI AGYEMAN Assistant professor of chemistry Department 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 (NO 3 - ) salts are soluble - Most salts of alkali metals (Group 1A) and ammonium (NH 4 + ) are soluble - Most salts containing Cl -, Br -, and I - soluble Exceptions: salts of Ag +, Hg 2 2+, Pb 2+ SOLUBILITY OF SALTS

- Most sulfate salts are soluble Exceptions: BaSO 4, PbSO 4, Hg 2 SO 4 - Most hydroxides are slightly soluble Hydroxides of Ba 2+, Sr 2+, and Ca 2+ are marginally soluble - Most salts containing S 2-, CO 3 2-, PO 4 3-, CrO 4 2- are insoluble Exceptions: salts of alkali metals and NH 4 + SOLUBILITY OF SALTS

- Solubility increases when soluble salts are added to solutions of marginally soluble salts - Cations are surrounded by anions to create a net negative ionic atmosphere - Anions are surrounded by cations to create a net positive 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 decreased which increases solubility - Increasing the concentration of ions in solution decreases the 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 µ = the ionic strength c i = the concentration of the ith species z i = the charge on the ith species

IONIC STRENGTH Find the ionic strength of M Na 2 SO 4 Na 2 SO 4 ↔ 2Na + + SO 4 2- [Na + ] = 2 x M = M [SO 4 2- ] = M

IONIC STRENGTH For 1:1 electrolytes (NaCl, NaNO 3, KBr) The ionic strength is equal to the molarity 1:1 µ = molarity For any other stoichiometry The ionic strength is greater than the molarity 2:1 µ = 3 x molarity 3:1 µ = 6 x molarity 2:2 µ = 4 x molarity

ACTIVITY COEFFICIENT Consider the equilibrium for the reaction aA + bB ↔ cC + dD The equilibrium constant (K) is given by 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 - K is generally expressed as follows

Debye-Hückel Equation - Relates activity coefficients to ionic strength (at 25 o C) γ = activity coefficient z = ion charge (±) α = ion size in picometers (1 pm = m) µ = ionic strength 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 charge but 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 COEFFICIENT Gases Activity (called fugacity) is written as A gas = P gas x γ gas P = pressure in bars γ gas = fugacity coefficient of a gas For most gases at or below 1 bar γ gas ≈ 1

ACTIVITY COEFFICIENT pH = negative logarithm of the hydrogen ion activity pH electrodes measure activity of hydrogen ions - Ionic strength of pure water is very low - Activity coefficient of pure water is very close to unity

CHARGE BALANCE - In a given solution sum of positive charges = sum of negative charges - The coefficient of each term equals the magnitude of the charge on the respective ion - 1 mole of an ion A n+/n- contributes n moles of positive/negative charge

CHARGE BALANCE n 1 [C 1 ] + n 2 [C 2 ] + ….. = m 1 [A 1 ] + m 2 [A 2 ] +….. [C] = concentration of a cation n = magnitude of the charge on the cation [A] = concentration of an anion m = magnitude of the charge on the anion - Activity coefficient do not appear in charge balance

CHARGE BALANCE Consider a solution containing the following species Na +, CO 3 2-, HCO 3 -, H +, Ca 2+, OH -, PO 4 3-, HPO 4 2- total positive charge = total negative charge [Na + ] + [H + ] + 2[Ca 2+ ] = 2[CO 3 2- ] + [HCO 3 - ] + [OH - ] + 3[PO 4 3- ] + 2[HPO 4 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 compounds that dissociate in several ways

MASS BALANCE Consider mol of H 3 AsO 4 in 1.00 L of solution M = [H 3 AsO 4 ] + [H 2 AsO 4 - ] + [HAsO 4 2- ] + [AsO 4 3- ] For KH 2 AsO 4 in water [K + ] = [H 3 AsO 4 ] + [H 2 AsO 4 - ] + [HAsO 4 2- ] + [AsO 4 3- ] For K 2 HAsO 4 in water [K + ] = 2 x {[H 3 AsO 4 ] + [H 2 AsO 4 - ] + [HAsO 4 2- ] + [AsO 4 3- ]} For K 3 AsO 4 in water [K + ] = 3 x {[H 3 AsO 4 ] + [H 2 AsO 4 - ] + [HAsO 4 2- ] + [AsO 4 3- ]}

FRACTIONAL COMPOSITION F = initial concentration of acid HA (formal concentration) Fraction of species in the form HA Fraction of species in the form A -