Tài liệu Chapter 8A: Activities doc

The Effect of Electrolytes on Chemical Equilibrium The concentrations and charge strength of “spectator” or non-reacting electrolytes The tendency to form precipitates will be decreas

Chapter 8A:

Activities

The Effect of Electrolytes on Chemical Equilibrium

The concentrations and charge strength of

“spectator” or non-reacting electrolytes

The tendency to form precipitates will be

decreased with increasing ionic strength

1) interactions (but not necessarily reactions)

of the reactant species with other charged

species

2) interactions of the charged product species with the spectator ions.

Examples:

> AgCl (s) <==> Ag* + CI-

K,,, increases with increasing ionic strength, so AgCl becomes more soluble

> H,O + HCO, <===> H,O* + HCO.-

K,, Increases with increasing ionic strength, so the solution becomes more acidic.

Effect of Ionic Strength

> lonic strength is a measure of the concentration and charge of the ions in solution It is defined by the

w= 40.2 X 1? + 0.1 x 2) = 0.3 M

KNO, AI a rae te mos

| mole | mole | mole 0.05 M 0.05 M 0.05 M

| mole 2 mole | mole

0.1 M 0.2 M 0.1 M

Ionic Strength (u)= = (AIZ 3 +[B]Z2 +[C]Z./£ + )

- (Ke +[NO 312.4, +[Na"]Z\, + [80 7125.2

= ! 0.05 x1° + 0.05 x1? + 0.2x1° +0.1x2°)=0.35M

2

Effect of Ionic Strength

» Dependent on

1) concentrations 2) charges

» Independent on

The chemical properties of the ions

Therefore, the effect of ionic strength on a reaction (e.g.,

solubility or dissociation constant) is not dependent on the types of spectator ions, but on the concentration and

charges of spectator ions.

Any Questions?

Activity Coefficients

> Definition

A factor to describe quantitatively the effective

concentration of participants in an equilibrium at any given ionic strength

> Equation

a, = [X] +,

= a, = Is the activity or observed concentration

= y, =the activity coefficient

Activity Coefficient at Indicated

lonic Strength

Rb*, Cs*; Ti", Ag” NH; 250 0,264 0.924 0.898 0.80 0,75

Mg?*, Bec?* 800 0.872 (0.755 (0.60 0.52 0.45

Ca?*, Cu2~, Zn?†, Sn?*, MnŠ*, Ee?†*, Ni?! , Co?*, Phthalate?” 600 0.870 0.749 0.675 0.48 0.40

AB*t, Fe4+, Cr3†, La3*, Ce31* 900 0.738 0.54 0.44 ().24 O.18 PO}-, Fe(CN)3- 400 0.725 0.50 0.40 0.16 0.095 Th݆, Zr‡*, Ce**, Sn‡† 1100 0.588 0.35 0.255 0,10 0.065

Fe(CN)} 500 0.57 0.31 0.20 0,048 0,021

LLL

*From J Kielland, J Am Chem, Soe., 1937, 59, 1675 By courtesy of the American Chemical Society.

Mean Activity coefficients

Example 8-3: What is mean activity

coefficients (y, ) of MgCl, at 0.005 M ionic

0.005

lonic Strength Activity Coefficient at Indicated

0.80 O78 0.76 0.76 0,75 0.45 0.40 0.38 0.3? 0.36 O18 0.095 0.065 0.02]

lon ex pm 0.001 0.01 0.05

Li*, C,H„COO 600 0.965 0.929 0.907 0.84

Nat, Oy, HSO;, HCOs, H,PO;, Hs AsOz, OAc™ 400-450 0.964 0.928 0.902 0.82

OH~, E-,§CN-, HS~-, ClIOr, CIOZ, BrOz IOz„ MnO;z 350 0.964 0.926 0,900 0.81

Mg?*, Be? 800 0.872 @75D 0469 0.52

Ca**, Cu*~, Zn**, Sn?>, Mn2*, Fe**, Ni*!, Co2*, Phthalate? 600 0.870 0.749 0.675 0.48

Sr2+, Ba2+, Cd*+, Hp**, S?- 500 0.868 0.744 0.67 0.46

Pb?*, CO3~, SO‡~, C;O3- 450 0.868 0.742 0.665 0.46

Hg‡* SO‡~, §,0%>, CrOz”, HPOZ 400 0.867 0.740 0.660 0.44

Alt, Fe4+, Cr?*, La3*, Ce3* 900 0.738 0.54 0.44 0.24

Properties of Activity Coefficients

A Rule I: (Figure 8-1)

¢ As ionic strength increases, its activities coefficient (y) decreases

¢ At moderate ionic strengths, y < 1

¢ As the solution approaches infinite dilution, y ~ 1

and hence a ~ [X] and K ~ K’

¢ At high ionic strengths (u > 0.1 M), the activity

coefficients often increase and may even become larger

than unity

B Rule II: (Table 8-1)

In solutions that are not too concentrated (u < 0.1 M), the activity coefficient for a given species 1s

independent of the types of electrolyte and dependent

only upon the ionic strength.

Properties of Activity coefficients

C Rule III

an ion departs farther from unity as the charge of the

species increase (Fig 3)

> The activity coefficient of an uncharged molecule is

approximately unity, regardless of ionic strength

D Rule IV

At a given ionic strength, the activity coefficients

of ions of the same charge are approximately the same There are exceptions (Table 8-1)

Any Questions?

y, =acitivity coefficient of species X

⁄ = charge on the species X

uu =1onic strength of the solution (M)

o = effective diameter of the hydrated ion X in picometers (10”“ m)

>Table 8-1

Activity Coefficient at Indicated

lonic Strength

Rb*, Cs*; Ti", Ag” NH; 250 0,264 0.924 0.898 0.80 0,75

Mg?*, Bec?* 800 0.872 (0.755 (0.60 0.52 0.45

Ca?*, Cu2~, Zn?†, Sn?*, MnŠ*, Ee?†*, Ni?! , Co?*, Phthalate?” 600 0.870 0.749 0.675 0.48 0.40

Pb2*, COF™, SOF, C3097 450 O.868 0.742 0.665 0.46 0.3?

AB*t, Fe4+, Cr3†, La3*, Ce31* 900 0.738 0.54 0.44 ().24 O.18 PO}-, Fe(CN)3- 400 0.725 0.50 0.40 0.16 0.095 Th݆, Zr‡*, Ce**, Sn‡† 1100 0.588 0.35 0.255 0,10 0.065 Fe(CN)j 500 0.57 0.31 0.20 0.048 0,021

LLL

*From J Kielland, J Am Chem, Soe., 1937, 59, 1675 By courtesy of the American Chemical Society.

Hydronium ion concentrations in solutions of

weak acids (See Chapter 7}

HA + H,O <===> H,O' + A- K

2H,O <===>H,O* + OH: K

Ww

a

since K, usually >> K,,, we normally can neglect

the water hydronium ion contribution (but not

always, particularly if the c,,, is very low)

[A] = [H,O*], and recalling that

Cu, = [H,0*] + [HA] or

[HAI = cua - [H;O"]

Equilibrium expression for the acid dissociation:

Simplified Equilibrium Expression

Assume C,,, >> [H,O0*]) :

when c,,,/K, = 104, the error is 0.5%

when c,,,/K, = 10°, the error is 1.6%

when c,,,/K, = 102, the error increases to 5%.

Equilibrium Calculation Using Activity Coefficients

aA + bB <====>cC + dD

K — tin (Kˆ: Concentration equilibrium constant)

x —acan _ [Cl vel lyn

ana, [AT YA[BP yp

(ix: Thermodynamic equilibrium constant)

x —ICFIDM ver _ gr VeYb

[APIB) yaYe — YTAYn

Chemical Equilibrium:

The ratio of the molar concentrations of reactants

and products is a constant at certain temperature

H,O + HCOOH <====> H,O* + HCOO-

[H,O*][HCOO']

Tho" Thcoo: Tho" Thcoo:

EXAMPLE 8-5 NaCl <=> Na* + Cl-

Use activities to calculate the hydronium ion concentration in a 0.120 M

solution of HNO, that is also 0.050 M in NaCl

uw = 4(0.0500 X 1? + 0.0500 % 1) = 0.0500

ae : + = =

dissociation constant from the thermodynamic constant of 5.1 * 107* (Ap-

pendix 3):

+ -

[H.O*|[NOz] Ky* Yano, 5-1 X 10-4 x 1.0 : [H;0° |[NO}]7, 6: Vno-

` (HNO) 2 — TH,O* YNO; NENG RECUR : 7980505: t0du DI [HNO, lYuno, —

Note that neglecting the activity coefficient gives [H,O*] = 7.8 X 10” N{

Li*, C,H„COO 600 (I.965 0.929 0.907 0.84

Nat, IOz, HSOF, HCOy, H,PO;, H>AsOz, OAc™ 400-450 «0.964 0.928 0.902 ().82

OH~, E-, SCN~-, HS~-, ClOr, CIO£, BrOz IOZ, MnO; 350 0.964 0.926 0,900 0 81

K',CI-,Br- 1-CN- NOz,NOz, HCöO- 300 0.964 0.925 0.899 0.80

Rb*, Cs*, Ti', Ag', NHJ 250 0.964 0.924 (0.898 0.80

Me?*, Be** 800 0.872 0.755 0.69 0.52

Ca**, Cu*~, Zn**, Sn?>, Mn2*, Fe**, Ni*!, Co2*, Phthalate? 600 0.870 0.749 0.675 0.48

Sr2+, Ba2+, Cd*+, Hp**, S?- 500 0.868 0.744 0.67 0.46

Pb2*, CO3“, SO‡~, CO4“ 450 O.868 0.742 0.665 0.46

AI°*, Fc1+, Cr3†+, Lat~, Ce?* 900 0.738 0.54 (0.44 0.24

0.37

0.36 O.L8 0.095 0.065 0.021

Solubility Product Constants

y, =mean activity coefficient =(y* y,, )**

K S Ủ Concentration Solubility Product Constant

K : Thermodynamic Solubility Product constant

Example 8-4: Find the relative error introduced by neglecting activities

in calculating the solubility of BaUlO;), in a 0.033 M solution of Mg(IO;), The thermodynamic solubility product for Ba(IO3), is 1.57x10°

Ba(IO,), ———> Ba** + 2IO,;

K', CI, Br-, 17, CN~, NOz, NOz;, HCQO- 300 0.964 0.925 (0.899 0,80 0.76

Rb*, Cs*, Tl’, Ag', NHJ 250 0.964 0.924 (0.898 0.80 0,75

Ca?* Cu2~, Zn?†, Sn2*, MnÊ~*, Fe?†, NI?! , Co2*, Phthalate2' 600 0.870 0.749 0.675 0.48 0.40

Sr?† |Ba21Í Cd?*, Hgˆ†, S2~ 500 0.808 0.744 0.67 0.46 0.38

ABT, Fe4+, Cr3+, Lat*, Ce* 900 0.738 0.54 0.44 ().24 OLS PO}, Fe(CN)a~ 400 0.725 0.50 0.40 0.16 0.095

using activity (true value)

Homework

¢ 8-A, B, C, E, F, G, 2, 4, 11, 12, 18, 20, 24, 26

Before working on Homework,

Practice with all examples that we discussed in the class and examples in the textbook!!