10 Effects Of Electrolyte on Chemical Equilibria Chaper

10 Effects Of Electrolyte on Chemical Equilibria

Chaper 10 Effect of electrolytes on chemical equilibria 10 A The effect of electrolytes on chemical equilibria 10 A-1 The effect of ionic charges on equilibria 10 A-2 The effect of ionic strength(ex 10 -1, 10 -2) 10 A-3 The salt effect 10 B Activity coefficients 10 B-1 Properties of activity coefficients 10 B-2 The Debye –Hückel equation 10 B-3 Equilibria calculations using activity coefficients 10 B-4 Omitting Activity coefficients in equilibrium calculations

10 A EFFECTS OF ELECTROLYTES ON CHEMICAL EQUILIBRIA If an electrolyte is added to this solution, the color of the triiodide ion becomes less intense. A relationship that approaches a constant value as some variable (here, the electrolyte concentration) approaches zero is called a limiting law; the constant numerical value observed at this limit is referred to as a limiting value. Limiting value is the accepted thermodynamic value.

concentrationbased ion product is designated K’w thermodynamic ion -product constant for water, Kw

10 A-1 How Do Ionic Charges Affect Equilibria? 1. the magnitude of the electrolyte effect is highly dependent on the charges of the participants in an equilibrium. 2. 2. neutral species essentially independent of electrolyte concentration 3. 3. with ionic participants, the magnitude of the electrolyte effect increases with charge. In a 0. 02 M solution of potassium nitrate, the solubility of barium sulfate, is larger than it is in pure water by a factor of 2. Barium iodate by a factor of only 1. 25 and that of silver chloride by 1. 2.

10 A-2 What Is the Effect of Ionic Strength on Equilibria? • Systematic studies have shown that the effect of added electrolyte on equilibria is independent of the chemical nature of the electrolyte but depends on a property of the solution called the ionic strength. • Ionic strength = μ =

Example 10 -1 Calculate the ionic strength of (a) a 0. l M solution of KNO 3 and (b) a 0. 1 M solution of Na 2 SO 4. (a) For the KNO 3 solution, [K+] and [NO 3 -] are 0. 1 M and • μ= = 0. 1 M (b) For the 0. 1 M Na 2 SO 4 solution, [Na+] = 0. 2 and [SO 42 - ] = 0. 1. Therefore, • μ = = 0. 3 M

• Example 10 -2 What is the ionic strength of a solution that is 0. 05 M in KNO 3 and 0. 1 M in. Na 2 SO 4? • μ = • • =0. 35 M

For solutions with ionic strengths of 0. 1 M or less, the electrolyte effect is independent of the kind of ions and dependent only on the ionic strength. Note that this independence with respect to electrolyte species disappears at high ionic strengths.

10 A-3 The Salt Effect 1. The electrolyte effect results from the electrostatic attractive and repulsive forces that exist between the ions of an electrolyte and the ions involved in the solution. 2. These forces cause each ion from the dissociated reactant to be surrounded by a sheath of solution that contains a slight excess of electrolyte ions of opposite charge. 3. When a barium sulfate precipitate is equilibrated with a sodium chloride solution, each dissolved barium ion is surrounded by an ionic atmosphere that, because of electrostatic attraction and repulsion, carries a small net negative charge on the average due to repulsion of sodium ions and an attraction of chloride ions.

10 B ACTIVITY COEFFICIENTS Chemists use the term activity to account for the effects of electrolytes on chemical equilibria. The activity, or effective concentration, of species X depends on the ionic strength of the medium, γx is a dimensionless quantity called the activity coefficient p. 27/ K’sp is the concentration solubility product constant and Ksp is thermodynamic equilibrium constant. The activity coefficients γx and γy vary with ionic strength in such a way as to keep ksp numerically constant and independent of ionic strength (in contrast to the concentration constant K’sp)

10 B-1 Properties of Activity Coefficients Activity coefficients have the following properties: 1. The activity coefficient of a species is a measure of the effectiveness with which that species influences an equilibrium in which it is a participant. At moderate ionic strengths, γx ＜ 1; as the solution approaches infinite dilution, however, γx → 1 and thus ax → [X] and K’sp → Ksp. At high ionic strengths ( μ ＞ 0. 1 M), activity coefficients often increase and may even become greater than unity. 2. In solutions that are not too concentrated, the activity coefficient for a given species is independent of the nature of the electrolyte and dependent only on the ionic strength. 3. For a given ionic activity coefficient of an ion departs farther from unity as the charge carried by the species increases. This effect is shown in Figure 10 -3. 4. The activity coefficient of an uncharged molecule is approximately unity, regardless of ionic strength

5. At any given ionic strength, the activity coefficients of ions of the same charge are approximately equal. The small variations that do exist can be correlated with the effective diameter of the hydrated ions. 6. The activity coefficient of a given ion describes its effective behavior in all equilibria in which it participates. For example, at a given ionic strength, a single activity coefficient for cyanide ion describes the influence of that species on any of the following equilibria:

Increasing influential effect with increasing charge

10 B-2 The Debye - Equation (10 -5) where • γx = activity coefficient of the species X • Zx = charge on the species X • μ = ionic strength of the solution • αx = effective diameter of the hydrated ion X in nanometers

Example 10 -3 (a) use equation 10 -5 to calculate the activity coefficient for Hg 2+ in a solution that has an ionic strength of 0. 085 M. Use 0. 5 nm for the effective diameter of the ion. ( b) Compare the value obtained in (a) with the activity coefficient obtained by linear interpolation of the data in table 10 -2 for coefficients of the ion strengths of 0. 1 M and 0. 05 M. =0. 4016 Table 10 -2 indicates 0. 46 when μ = 0. 050. Thus, for μ = 0. 085, = 0. 38 when μ = 0. 100 and

Table 9 -1 give satisfactory activity coefficients for ionic strengths up to about 0. 1

10 B-3 Equilibrium Calculations with Activity Coefficients • Equilibrium calculations with activities yield values that are better in agreement with experimental results than those obtained with molar concentrations. • Unless otherwise specified, equilibrium constants found in tables are generally based on activities and are thus thermodynamic equilibrium constants.

Example 10 -4 solubi 1 ity = [Ba 2+] [IO 3 - ] = 2 × 0. 033 + 2[Ba 2+] 0. 066 [Ba 2+](0. 066)2 = 6. 8 × 10 -9 (9 -6) [Ba 2+] = solubility = 1. 56 × 10 -6 M If we neglect activities, the solubility is [Ba 2+](0. 066)2 = 1. . 57 × 10 -9 [Ba 2+] = solubility = 3. 60 × 10 -7 M relative error = × 100 % = -77 % [Ba 2+][IO 3 -]2 = 6. 8 × 10 -9

Example 10 -5 Also, from rule 3 (page 209), we can write Note that assuming activity coefficients are unity gives [H 3 O+] = 9. 2 × l 0 -3.

10 B-4 Omitting Activity Coefficients in Equilibrium Calculations • The reader should be alert to the conditions under which the substitution of concentration for activity is likely to lead to the largest error. Significant discrepancies occur when the ionic strength is large (0. 01 or larger) or when the ions involved have multiple charges (Table 9 -1). With dilute solutions (ionic strength ＜ 0. 01 ) of nonelectrolytes or of singly charged ions, the use of concentrations in a mass-law calculation often provides reasonably accurate results. • It is also important to note that the decrease in solubility resulting from the presence of an ion common to the precipitate is in part counteracted by the larger electrolyte concentration associated with the presence of the salt containing the common ion.

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