Chapter 9:

Effects of Electrolytes on Chemical Equilibria: Activities

Please do problems: 1,2,3,6,7,8,12

Exam II February 13 Chemistry Is Not Ideal

● The ideal gas law: PV = nRT works only under “ideal situations when when pressures are low and temperatures not too low. Under non-ideal conditons we must use the Van der Wals equation to get accurate results.

● Ideal to non-ideal formalisms are common in science ● With equilibrium constants we see the same. Our idealistic case is dilute solutions. As we move away from dilute situation our equilibrium expressions become unreliable. We deal with this using a new way to express “effective concentration” called “activity” Our Ideal Equilbrium Constants Don’t Always Work

[C]c[D]d aA + bB cC + dD Kc = [A]a[B]b

3+ - 3+ - 3 Al(OH)3(s) Al (aq) + 3OH (aq) Ksp = [Al ][OH ]

[H+] HCOOH (aq) H+ (aq) + HCOO- (aq) K = a [A-] [HA]

+ - [H3O ][OH ] H O(l) + H O(l) H O+ + OH– K = 2 2 3 w 2 [H2O] Electrolyte Concentrations Impact Kc Values

Must Use Activity

Molarity Works Fine Here [Electrolytes] Affect Equilibrium

● Addition of an electrolyte (as concentration increase) tends to increase solubility.

● We need a better Kc than one using molarities. We use “effective concentration” which is called activity. Activity of An Ion is “effective concentration”

aA + bB cC + dD

c d equilibrium [C] [D] constatnt in Kc = a b terms of molar [A] [B] concentration

c d equilibrium ay az constant in Ka = a b terms of aw bx activities Activity of An Ion is “effective concentration”

In order to take into the effects of electrolytes on chemical equilibria we use “activity” instead of “concentration”.

The activity of an ion is defined as: Activity coefficient Varies with ionic strength Activity of an ion ai = [Xi] ϒi

th where [Ci] is the molarity of the i ion and ϒi is the ion’s activity coefficient (a dimensionless quantity). ϒi depends on the ionic strength of the solution. What is the Effect of Ionic Strength on Equilibria

The ionic strength of a solution is a measure of the total electrolyte concentration and is a function of both concentration and charge of the ions in solution.

1 ionic strength = µ = [A]Z2 + [B]Z2 + [C]Z2 + ... 2 A B C ! "

where [X] is the molarity of a ions A, B, C, ....and ZA, ZB, ZC

Recognize that the total ionic strength of a solution is the sum of all ions in solution! Ionic Strength Worked Example

Calculate the ionic strength of (a) 0.1M solution of KNO3 and (b) 0.1M solution of Na2SO4

1 ionic strength = µ = [A]Z2 + [B]Z2 + [C]Z2 + ... 2 A B C ! " Ionic Strength Worked Example

Calculate the ionic strength of (a) 0.1M solution of KNO3 and (b) 0.1M solution of Na2SO4

+ - (a) For the KNO3 solution [K ] = [NO3 ] = 0.1M, the charge z = +1 and -1. We can substitute: + 2- (b) For the Na2SO4 solution [Na ] = 0.2M and [SO4 ] = 0.1M, the charge z = +1 and -2, respectively. We can substitute: 1 ionic strength = µ = [A]Z2 + [B]Z2 + [C]Z2 + ... 2 A B C ! " 1 (a) µ = [0.1]12 + [0.1]( 1)2 = 0.1M 2 − 1 ! " (b) µ = [0.2]12 + [0.1]( 2)2 = 0.3M 2 − ! " Ionic Strength = Molar Concentration for Mono

Type Ionic Example Electrolyte Strength 1:1 NaCl c

1:2 Ba(NO3)2 Na2(SO4) 3c

1:3 Al(NO3)3 Na3(PO4) 6c

2:2 Mg(SO4) 4c

Ionic strength increases rapidly with charge of ions (increases as the square of the charge. Activity of An Ion is “effective concentration”

aA + bB cC + dD

c d equilibrium [C] [D] constatnt in Kc = a b terms of molar [A] [B] concentration

c d equilibrium ay az constatnt in Ka = a b terms of aw bx activities

Activity ai = [Xi] ϒi definition Activity of An Ion is “effective concentration” [C]c[D]d aA + bB cC + dD Kc = [A]a[B]b

thermodynamic concentration equilibrium activity constant equilibrium coefficients (tables) constant

c d c d c d ay az ([C]γc) ([D]γd) γc γd K◦ = = = K c a b a b c a b aw bx ([A]γa) ([B]γb) × γa γb Properties of Activity Coefficients

● Activity coefficient is a measure of effectiveness of that species to influence an equilbrium. When ionic strength ==> 0, then ϒ ==> 1 and activities = [X]. ● Ionic strength varies with charge of ion, thus activities vary significantly with ionic strength. Activities of uncharged molecules ~1 no matter how concentrated. ● At any given ionic strength the activity coefficients ϒ are about the same for a given charge. Activity of An Ion is “effective concentration”

c d aA + bB cC + dD [C] [D] Kc = [A]a[B]b

Concentrations ai = [Xi] ϒi expressed in molarity!

if we now substitute for [ai] we get:

c d c d Kc expressed in ay az ([C]γc) ([D]γd) activity Kc = a b = a b coefficients aw bx ([A]γa) ([B]γb) and [X] Activity of An Ion is “effective concentration”

c d aA + bB cC + dD [C] [D] Kc = [A]a[B]b

thermodynamic equilibrium concentration constant activity equilibrium (tables) coefficients constant

c d c d c d ay az ([C]γc) ([D]γd) γc γd K◦ = = = K c a b a b c a b aw bx ([A]γa) ([B]γb) × γa γb The Debye-Huckel Equation Calculates Activity Coefficients

● 1923--Debye and Huckel derive an expression that allows calculation of activity coefficients, ϒχ for ions from knowledge of charge, Z, the ionic strength of the solution, μ and average diameter of hydrated ion in nm, α (at 25˚C). Charge of the ion, χ 2 0.51 Zχ √µ log γχ = − 1 + 3.3 αχ √µ

Activity Coefficient, Ionic strength ϒχ for ion χ diameter of ion in of solution nanometers Activity Coefficients For Ions 25˚C

NOTE: Deybye-Huckel fails beyond ionic strengths of 0.1M. We then must use experimentally derived activity coefficients. Properties of Activity Coefficients

● Activity coefficients is a measure of the effectiveness with which a species influences a system of equilibrium. ● With dilute solutions ionic strength is small and the activity coefficient = 1, the activity = Molar concentration in expressions. ● As electrolyte concentrations increase so does ionic strength ● Precipitates won’t be so insoluble is net concentrations decrease ==> increase solubility observed. ● Increase dissociation of weak electrolytes Equilibrium Calculations With Activities

+ 2- Calculate the activity coefficients for K and SO4 in a 0.20 M solution of K2SO4. Assume αK+ = 0.3nm and αSO4 = 4.0 nm

2 calculate 0.51 Zχ √µ this first log γχ = − 1 + 3.3 αχ √µ

get this from a table provided or given data Equilibrium Calculations With Activities + 2- Calculate the activity coefficients for K and SO4 in a 0.020 M solution of K2SO4. 1 µ = [A]Z2 + [B]Z2 + [C]Z2 + ... 2 A B C 1 ! " µ = [K]12 + [SO ]( 2)2 2 4 − 1 ! " µ = [2 0.020]12 + [0.020]( 2)2 = 0.060 2 × − ! "

2 0.51 1 √0.060 0.101 log γK+ = = 0.1005 γK+ = 10− = 0.79 − 1 + 3.3 0.3 √0.060

0.51 ( 2)2 √0.060 0.463 log γSO4 = − = 0.463 γ = 10 = 0.344 − 1 + 3.3 0.4 √0.060 SO4 − Equilibrium Calculations With Activities + Use activities to calculate the H3O concentration in a 0.120M solutioin of HNO2 that is also 0.050M NaCl (The -4 thermodynamic equilibrium constant K˚a = 7.1 X 10 ) 1 2 2 2 µ = [A]ZA + [B]ZB + [C]ZC + ... we neglect the 2 dissociation of 1 2 2 µ =  + [0.050]( 1) = 0".0500 HNO2 2 − We look up! in the table the activity coef"ficients based on this ionic strength: ϒH3O+ = 0.85 and ϒNO2 = 0.81 and ϒHNO2 = 1.00 (rule 3)

+ - HNO2 <==> H + NO3

+ aH+ a [H ]γH+ [NO−]γ γH+ γ NO2− 2 NO3− NO3− Ka◦ = = = Ka aHNO2 [HNO2]γHNO2 × γHNO2

γHNO2 4 1 3 Ka = Ka◦ = 7.1 10− = 1.03 10− × γH+ γ × × 0.85 0.81 × NO3− × Equilibrium Calculations With Activities

Calculate the pH of pure water using activities and do the same thing when pure water has 0.10 M KCl at 25˚C.

+ Kw = aH+ aOH = [H ]γH+ [OH−]γOH − −

Because KCl is monvalent its ionics strength = molarity = 0.10. If + - we now look up the ϒi for H and OH we find their values to be 0.83 and 0.76 respectively. We can now solve as we did before.

14 7 1.0 10− = (x)0.83(x)0.76 = 1.26 10− × × + 7 pH = log[H ] = log[1.26 10− ] = 6.98 − − × Activity Coefficients For Ions 25˚C

NOTE: Deybye-Huckel fails beyond ionic strengths of 0.1M. We then must use experimentally derived activity coefficients.