920116......34 slides 1 Activity & Activity Coefficients http:\\asadipour.kmu.ac.ir

$Page 1: 920116......34 slides 1 Activity & Activity Coefficients http:\\asadipour.kmu.ac.ir$
920116......34 slides 1

Activity & Activity Coefficients

http:\\asadipour.kmu.ac.ir

EFFECT OF ELECTROLYTES ON CHEMICAL EQUILIBRIA

H3AsO4 + 3I- + 2H+ H3AsO3 + I3- + H2O

The position of most solution equilibria depends on the electrolyte concentration of the medium, even when the added electrolyte contains no ion in common with those involved in the equilibrium.

........................................................................................ KI

H3AsO4 + 3I- + 2H+ H3AsO3 + I3- + H2O

........................................................................................KCl

H3AsO4 + 3I- + 2H+ H3AsO3 + I3- + H2O

920116......34 slides 2http:\\asadipour.kmu.ac.ir

920116......34 slides 3

Effect of Ions concentration on Solubility of Potassium tartarate

www.chem.wits.ac.za/chem212-213-280

↑ concentration with addition of an “inert” ion

↓ concentration with addition of common ion

“neutral” species


K2C

4H4O

6

Chemical Equilibrium Electrolyte Effects

Electrolytes: producing ions

1-Common 2-no common

Can electrolytes affect chemicalequilibria?

(A) “Common Ion Effect” Decreases solubility of BaSO4 with BaCl2Ba2+ is the “common ion”


Predicted effect of excess barium ion on solubility of BaSO4.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)


(B) No common ion:

“inert electrolyte effect”or

“diverse ion effect”


920116......34 slides 7

Adding an “inert” salt to a sparingly soluble salt increases the solubility of the sparingly soluble salt.

“inert” salt = a salt whose ions do not react with (e.g., chelate, or precipitate) the compound of interest

The Salt Effect


©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

Increases solubility of BaSO4 Why???shielding of dissociated ion species

Predicted effect of presense of Na2SO4 on solubility of

BaSO4.


920116......34 slides 9

Consider: BaSO4 Ba2+ + SO42-

BaSO4 (Ksp = 1.1x10-10) as the sparingly soluble salt and

NaNO3 → Na+ + NO3- as the “inert” salt.

The cation (Ba2+) is surrounded by anions (SO42-, NO3

-)net positive charge is reduced

attraction between oppositely charged ions (Ba2+, SO42-)

is decreased. Solubility is increased

How?


NO3-

Na+

The anion (SO42-) is surrounded by cations (Ba2+, Na+)

net negative charge is reduced

920116......34 slides 10

Concentration v.s. Activity

• For many substances the active mass per unit volume is directly proportional to the concentration. ai≈Ci

...but the approximation of activity being equal to concentration will not accurately reflect the actual behavior of matter under all conditions.

• ai=Ci :is a reasonably valid approximation for an

• u< 10-2 M

ba

dc

BA

DCK

][][

][][

Only an approximation of the equilibrium condition.


920116......34 slides 11

Activity Coefficients

• The activity coefficient accounts for available ‘acid’ species in solution at high concentrations

XX XA ][

ActivityConcentration

Activity Coefficient


920116......34 slides 12

Activity Coefficient

Effective concentration of decreases

1


920116......34 slides 13

Ionic Strength

• Ionic strength, , is a measure of the total ionic charges in solutions

where ci is the concentration of the iones species and zi is the associated charge.

i

iizczczc 22

22

2

11 2

1

2

1


920116......34 slides 14

Ionic Strength• Find the ionic strength of a KCl solution:

– At 0.10 M KCl…

– At 0.025 M KCl…

M

ClK

10.0110.0110.02

1

)1()1(2

1 22

M 025.01025.01025.02

1


920116......34 slides 15

Ionic Strength

• Find the ionic strength of a CaCl2 solution:– At 0.10 M CaCl2 …

– At 0.025 M CaCl2 …

M 30.0120.0410.02

1

)1(Cl)2(2

1 222

Ca

M 075.01050.04025.02

1



920116......34 slides 17

Calculation of Activity Coefficients

• Requires the Debye-Hückel equation:

• z is the charge of the ion• a is the effective hydrated radius of

the ion (in nm)

m is the ionic strength of the solution

(Valid at 25°C for 0.1M)

)(3.31

51.0log

2

z


920116......34 slides 18

Calculating Activity Coefficients

Calculate the activity coefficients of Ca2+ and F- in 0.050 M NaClO4

M 050.0)1(050.0)1(050.02

1 22

49.02Ca

81.0-F

(Ca2+= 0.600 nm, F- = 0.350 nm)

)(3.31

51.0log

2

z


920116......34 slides 19

Activity of the ion in a solution depends on its hydrated radius not the size of the bare ion.



α → g


Z → g α → g

920116......34 slides 21

Activity Coefficients

approaches 1 in very dilute solution at which approaches 0.

The effect of on is greater for larger z and small .

FCa2

)(3.31

51.0log

2

z

Note that if m >0.1 M it is necessary to

experimentally determine g, otherwise use referenceTable as an approximation

Z,α→ g


920116......34 slides 22

Activity coefficients for differently charged ions with a constant hydrated radius of 500pm.

1. As ionic strength increases, the activity coefficient decreases.

2. As the charge of the ion increases, the departure of its activity coefficient from unity increases. Activity corrections are much more important for an ion with a charge of 3 than one with the charge 1.


Z→ g

→

0 1




920116......34 slides 25

Activity and Equilibrium

• The correct form of the equilibrium expression is…

ba

dc

aa

aaK

BA

DC

aA + bB cC + dD

XX ]X[ abbaa

ddcc

BA

DC

]B[]A[

]D[]C[

ba

dc

]B[]A[

]D[]C[

ba

dc

BA

DC

ba

dc

BA

DC

K spK '


920116......34 slides 26

Solubility of a salt

calculate [Ca2+] in saturated CaF2 solid.

Ksp = 3.9×10-11


Ksp = 3.9×10-11 = [Ca][F]2

3.9×10-11 = X·(2X)2=4X3

x = 2.14×10-4M

CaF2(s) Ca2+ + 2F-

920116......34 slides 27

Solubility in presence of common ion

calculate [Ca2+] in 0.050 M NaF saturated with CaF2 solid.

Initial conc. (M) 0 0.050

Eq conc. (M) x 2x+0.050

Change x 2x

Ksp = 3.9×10-11


Without activity coefficient considerations:

Ksp = 3.9×10-11 = [Ca][F]2 3.9×10-11 = x·(0.050)2

x = 1.6×10-8M

CaF2(s) Ca2+ + 2F-

<< 2.14×10-4M

920116......34 slides 28

Solubility and Activity

With activity coefficient considerations:

2222 .]F[]Ca[ 22

FCaspFCasp KK


2.2

FCa

spsp

KK

920116......34 slides 29


Calculate the activity coefficients of Ca2+ and F- in 0.050 M NaClO4

M 050.0)1(050.0)1(050.02

1 22

49.02Ca

81.0-F

(Ca2+= 0.600 nm, F- = 0.350 nm)

)(3.31

51.0log

2

z


920116......34 slides 30

Solubility and Activity

Assume that 2x << 0.050 and due to Ca2+ is negligible.

3.9×10-11 = x(0.49)(0.050)2(0.81)2 x = 4.9×10-8 M


22

22

)81.0(]2050.0[)49.0(][

][][ 2

xxK

FCaK

sp

FCa

2sp

3 timesx = 1.6×10-8M


[Ca2+] or solubility of CaF2 solid in 0.050 M NaF


Solubility and ActivitySolubility of PbI2 in 0.1M KNO3

= [0.1(1m +)2 + 0.1(1-)2]/2 = 0.1 (ignore Pb2+,I-)

ƒPb = 0.35 ƒI = 0.76

Ksp = (aPb)1(aI)2 = ([Pb2+]Pb )1([I-]I )2

Ksp = ([Pb2+] [I-]2) (Pb I2

) = K sp (Pb I2

)

K sp = Ksp / (Pb I )

K sp = 7.1 x 10-9 /((0.35)(0.76)2) = 3.5 x 10-8

(s)(2s)2 = K sp s = (K sp /4)1/3 s =2.1 x 10-3

M

s = (Ksp/4)1/3 then s =1.2 x 10-3M920116......34 slides 31http:\\asadipour.kmu.ac.ir

Without activity coefficient considerations:

With activity coefficient considerations:Solubility approx.43%


920116......34 slides 33

Acids, Bases, and Activity

Calculate the pH of water containing 0.10 M KCl at 25°C.(H+ = 0.900 nm and OH- = 0.350 nm)

76.083.0 -OHH

OHH

]OH[]H[. OHHKW1.0×10-14 = x(0.83) x(0.76)

pH=-log aH+

aH+= g.[H+] pH = -log (0.83×1.26×10-7) = 6.98

x = 1.26×10-7 M with activityx = 1.00×10-7 M without activity


920116......34 slides 34


Calculate the activity coefficients of Ca2+ in 0.080 M NaClO4.

M 080.0)1(050.0)1(050.02

1 22

g

0.1 0.4

0.08

0.05 0.48

X

)40.048.0(

08.01.0

05.01.0

40.0032.0http:\\asadipour.kmu.ac.ir

???

TEXT

X

)40.048.0(

05.01.0

08.01.0

reverse

0.432

920116......34 slides 35

At high ionic strengths:

Activity coefficients of most ions increase

Concentrated salt solutions are not the same as dilute aqueous solutions

H+ in NaClO4 solution of varying ionic strengths


In concentrated salt solutions g is dependent to type of ion

and interpretation is difficult.

In diluted salt solutions g is independent to type of ion

We try not to work with solutions >0.01 MIf µ→0 g =1activity ≈ concentration


Documents

920116......34 slides 1 Activity & Activity Coefficients http:\\asadipour.kmu.ac.ir