12-ST-3 Treatment of Complex Ionic Equilibria
A. Acid HA or Base BOH
We first illustrate the method for a monobasic acid HA before proceeding to more complex situations. The material balance equation (12-102) is now written in the form
/tot = / H A + / M A = (HA) + ^ a , using Eq. (12-99) to eliminate ( A-) . Rearrangement gives
F h a = [JW(H+)i + ι ' ( 1 2"1 2 6 )
where FHA — (HA)//iot and is the fraction of the total acid-substance which is present as undissociated acid HA. Alternatively, we may eliminate (HA) to obtain
1 + [(H+)/tf»]
FA- ι _L rru+\/r ι · (12-127)
Equations (12-126) and (12-127) are usually displayed as a plot of log F versus pU.
Such a plot is called a logarithmic diagram. That for acetic acid is shown in Fig. 12-15. Notice that if the pH is much less than pK&, Eq. (12-127) reduces to
\ogFA-=pH-pK&
and so the plot of log FA- versus pH becomes a straight line of slope + 1 and intercept —pK& in the region of high acidity. Similarly, if pH ^> ρΚΛ, then the plot of log FH A versus pH becomes a straight line of slope — 1 and intercept pK& . The logarithmic diagram for a weak electrolyte resembles a phase diagram.
It provides a map of the pH domain of each species so that one can tell at a glance the general makeup of a solution at any given pH. The diagram is used
quantita-SPECIAL TOPICS, SECTION 3 487
F 0.1
0.01
F I G . 12-15. Logarithmic diagram for acetic acid at 25° C.
tively as follows. The charge balance equation
(M+) + (H+) = (A-) + (OH-) [Eq. (12-101)]
can be put in the form
(M+) + (H+) = FA-/tot + (OH-). (12-128) One knows /H A and /M A and hence /tot and (M+), and Eq. (12-128) is solved by successive approximations. A first guess at ( H+) allows FA- to be read off the logarithmic diagram, and substitution into the equation will indicate whether the value is too high or too low. This guides a second choice of ( H+) , and so on, until a self-consistent answer is reached.
Example. W e can calculate the pH o f a solution which is 0.002 / in H A c a n d 0.001 / in N a A c ; /t o t is then 0.003 and Eq. (12-128) b e c o m e s
0.001 + (H+) = FA- ( 0 . 0 0 3 ) + (OH")
FA- = 0.333 + (H+) - ( Q H - ) 0.003
W e can guess immediately a pH of 4.45, at which FA- = i. The test of the equation is then
? 3.54 χ 1 0 -5
0.333 == 0.333 + — — = 0.345.
0.003
FA- is slightly t o o small, and we next try a pH of 4.46, FA- = 0.345. The test is n o w
? 3.45 x 10"5
0.345 = 0.333 + = 0.345.
0.003
The desired p H is then close to 4.46.
One may also calculate a titration curve. In Eq. (12-128), ftot is n o w the initial formality of the acid, and ( M+) gives the concentration of added strong base. One may n o w insert successive choices for ( H+) and calculate ( M+) for each. The fraction of neutralization FN is just
F <M + ) /tot
Several points on the titration curve for 0 . 0 0 2 / H A c are summarized thus. Equation (12-128) becomes ( M+) + ( H+) = 0 . 0 0 2 /A_ + (OH"), or FN = fA- - {[(H+) - (OH~)]/0.002}; some sample calculations are given in Table 12-10. The calculation illustrates several items. The first two values for FN are negative, meaning that excess strong acid must be present. The third line gives the actual starting point of the titration; the relatively rapid change in FN between pH 4 and 6 characterizes the buffer region, and the asymptotic approach to FN = 1 marks the endpoint.
The last entry s h o w s that 5.3% excess base has been added. T h e curve is plotted in Fig. 12-13.
The logarithmic diagram approach offers little advantage in speed over the straight attack in the case of a simple acid. Being graphical, it is also less precise, but this is not a matter of great importance since the overriding uncertainty will be in the value for Ky, that is, in the size of the activity coefficient correction.
The treatment of a simple weak base BOH is analogous to that just given:
F b o h = [tfb/(OH-)] + 1 ' F B + = 1 + [(OH-)/tfb] ' ( 1 2'1 2 9 )
The logarithmic diagram is still a plot of logF versus /?H, and the associated charge balance equation is
FB+ ftot + (H+) = ( Χ " ) + (OH-), ( 1 2 - 1 3 0 ) where /tot = /BOH + /BX > where X is a nonhydrolyzing anion. The plots for
ammonium hydroxide are included in Fig. 12-18.
Logarithmic diagrams may be used for any mixture of weak electrolytes. Thus, for a mixture which contains both a weak acid and a weak base, the charge balance equation becomes
(M+) + FB+ /(BOH+BX) + (H+) = ( X - ) + FA- / ( H A+M A) + (OH") ( 1 2 - 1 3 1 )
and the correct pH for a given mixture is found by trial-and-error solution. As an example, a solution which is 0 . 0 0 2/ i n HAc, 0 . 0 0 1/ i n NaAc, 0 . 0 0 3/ i n N H4O H ,
T A B L E 12-10.
(H+) (OH") / A - [(H+) - (OH-)]/0.002
2 0.01 — 1.7 χ 1 0 -3 5 - 5
3 0.001 — 1.7 x>10~2 0.5 - 0 . 4 8 3
3.75 1.78 χ ΙΟ"4 — 0.089 0.089 0
4 1 χ ΙΟ"4 — 0.149 0.05 0.099
4.76 1.75 Χ ΙΟ"5 — 0.500 0.009 0.491
6 1 X 10"e 1.05 χ ΙΟ"8 0.9461 — 0.9461
8 1 χ 1 0 -8 1.05 χ 1 0 -8 1 - (6 χ 1 0 -4) — 0.9994 10 1 χ ΙΟ"1 0 1.05 x ΙΟ"4 1.000 - 0 . 0 5 3 1.053
SPECIAL TOPICS, SECTION 3 489
β. Successive Dissociations of a Weak Acid
In the case of a dibasic acid H2A the equilibrium constants are
_ (H+XHA-) (H+)(A*-)
Ki - — ΤΪΓΎ(H2A) Λ— A N D K 2 = / U A -(HA-) ' X > (12-132) and substitution into the material balance statement /tot = (H2A) + (HA") + ( A2 -) gives
^H2A = 1
A 1 + [ΑΓχ/ίΗ+Μ + [ΚχΚ^(Ά+γ\ 9 _ 1
H A" - [(H+VAxJ + 1 + ^ ( Η + ) ] 9 FA 2_ = 1
(12-133) (12-134) (12-135)
A2
~ KH+)»/A:A]
+ KH+)//y + ι ·The logarithmic diagram for H2C 03 is shown in Fig. 12-16. Its use follows the
F o.i
o.oi
pH
FIG. 12-16. Logarithmic diagram for HaC Oa at 25°C.
and 0.005 / in NH4C1 would have a pH such that the equation
0.001 + 0.008FN H 4+ + (H+) = 0.005 + 0.003FA c_ + (OH~)
is obeyed. In this case, (H+) and ( O H-) will be negligible compared to the other terms, and so
W = 0.5 + 0.375FA C .
A few successive choices of pH should serve to locate the value such that FN H+ and FA c_ as read oif the logarithmic diagrams satisfy the equation.
same scheme as before, the charge balance equation now being
(M+) + (H+) = FH A_ /tot + 2 FA 2_ /tot + (OH-). (12-136) Figure 12-17 shows the titration curve for 0.1 Μ H2C 03 calculated by the same procedure as before. That is, each assumed pH provides a value for ( M+) through Eq. (12-136) and hence for the degree of neutralization.
The treatment for a tribasic acid H3A yields the equation
* H3A = j 1
+ [«i/(H+)] + [KMH+Y] + [K^KJiH+f] ' (12-137) and so on. The logarithmic diagram for phosphoric acid is given in Fig. 12-18.
Phosphate buffers are much used and the figure allows the calculation of the pH of any mixture of phosphoric acid and its various salts. The dashed curves are for ammonium hydroxide, so the combined plots can be used for mixtures that include ammonium salts as well as phosphates.
F I G . 12-17. Titration curve for H2C OA.
0 0.2 0.4 0.6 0. 1.0 1.2
0.01
0 2 4 6 8 10 12 14
F I G . 12-18. Logarithmic diagrams for H3P 04 (full lines) and N H4O H (dashed lines).
EXERCISES 491
C . Complex Ions
The logarithmic diagram approach is not limited to weak acids and bases but may be applied to any set of successive dissociations. For example, C o2 + forms a succession of ammine complexes:
H20 + C o ( N H3)e 2 + = C o ( N H3)5( H20 )2 + + N H3, pK6 = - 0 . 7 4 ,
H20 + C o ( N H3)5( H20 )2 + = C o ( N H3)4( H20 )2 + + N H3, pKh = 0.06,
and so on. The values of pKx, pK2, pK3 , and pK± are 1.99, 1.51, 0.93, and 0.64, respectively. Note that the reactions have been written as interchanges of water for ammonia in the coordination sphere, in recognition of our belief that C o2 + is octahedrally coordinated.
Application of the standard procedure leads to
F c o ( N H 3 > J + = 1 + [K6/(NH3)] + [K5KJ(NH3Y] + [Κ4Κ,ΚβΚΝΗ3γ] + •••'
and similarly for the other species. The logarithmic diagram now consists of plots of the l o g F ' s against /?(NH3), that is, against — log(NH3). Application of the charge balance equation then allows the calculation of the composition of any mixture of ammonia and a cobalt salt.
G E N E R A L R E F E R E N C E S
HARNED, H . S . , AND OWEN, Β. B. (1950). "The Physical Chemistry o f Electrolyte Solutions."
Van Nostrand-Reinhold, Princeton, N e w Jersey.
BOCKRIS, J. O ' M . , AND CONWAY, Β. E. (eds.) (1954). "Modern Aspects of Electro-Chemistry."
Butterworths, L o n d o n and Washington, D . C .
LEWIS, G . N . , AND RANDALL, M . (1961). "Thermodynamics," 2nd ed. (revised by K . S . Pitzer and L. Brewer). McGraw-Hill, N e w Y o r k .
ROBINSON, R. Α . , AND STOKES, R. H . (1959). "Electrolyte Solutions." Academic Press, N e w York.
MACINNES, D . A . (1939). "The Principles o f Electrochemistry." V a n Nostrand-Reinhold, Princeton, N e w Jersey.
C I T E D R E F E R E N C E S
GIEBEL, W . , AND SAECHTLING, H . (1973). A Combination of Micro-Disc Electrophoresis with Antigen-Antibody Crossed Electrophoresis. Identification and Quantitative Determination of Individual Serumproteins. Hoppe-Seyler'sZ. Physiol. Chem. 354, 6 7 3 - 6 8 1 .
PALIT, S. R. (1975). Chemistry 4 8 , 1 6 .
EXERCISES
Neglect interionic attraction effects in t h e following Exercises and Problems unless specifically directed otherwise. T a k e a s exact numbers given t o o n e significant figure.
12-1 T h e measured resistance of a 0.02 Μ solution of N a C l is 793 o h m in a cell whose path length can be taken t o be 10 c m . Calculate (a) the specific conductivity of the solution, (b) its conductance, (c) the effective area of the electrodes, and (d) the cell constant.
Ans. (a) 2.53 χ 10"3 o h m "1 c m "1, (b) 1.26 χ 10"3 o h m "1, ( c ) 5 . 0 c m2, (d) 2 . 0 1 c m "1.
12-2 The resistance of electrolyte solution A is 45 o h m in a given cell and that of electrolyte solution Β is 100 o h m in the same cell. Equal volumes of solutions A and Β are then mixed. Calculate the resistance of this mixture, again in the same cell.
Ans. 62.1 o h m . 12-3 Calculate the resistance of a 0.03 Μ solution of N a2S 04 in a cell of cell constant 1.50 c m- 1. Ans. 192 o h m . 12-4 The specific conductivity of a saturated solution of AgCl in pure water at 25°C is 1.79 χ 1 0- 6 o h m- 1 c m- 1 while that of the water used is 6.0 χ 1 0- 8 o h m- 1 c m- 1. F r o m Table 12-2, calculate Λ for Ag+, CI" and thence the solubility of AgCl.
Ans. 138.26 c m2 o h m "1 e q u i v1, 1.26 x 1 0 "δ M . 12-5 Calculate Λ for (a) N a4F e ( C N )e, (b) C u ( N 03)2, and (c) the double salt ( N a ) ( N H4) S 04,
using the data of Table 12-2.
Ans. (a) 161.1, (b) 125.3, (c) 141.5 ( c m2 o h m "1 e q u i v "1) . 12-6 T h e solubility product for barium oxalate is 2.00 x 1 0 "7 at 25°C. Calculate the specific
conductivity of the saturated solution.
Ans. 1.23 χ 1 0- 4 o h m- 1 c m- 1. 12-7 The dissociation constant for N H4O H is 1.80 χ 10"5 at 25°C. Calculate ΛΛ ρ ρ and the
specific conductivity of a 0.02 Μ solution.
Ans. 8.0 c m2 o h m- 1 e q u i v *1, 1.60 x 1 0 "4 o h m "1 c m *1. 12-8 Calculate the specific conductivity of 0.05 Μ sodium chloride at 25°C, allowing for
interionic attraction effects.
Ans. 5.33 χ 10"3 o h m "1 c m "1. 12-9 The equivalent conductivity of a cation M+ is determined at 25°C by means of a moving boundary experiment. A 0.005 Μ solution of MCI is used, and after 30 min of passing a current of 0.2 m A the cation boundary has moved 0.208 c m ; the area of the column of solution is 1.50 c m2. Calculate λΜ+ . ( ΛΜ 0 1 = 132 c m2 o h m "1 e q u i v "1. )
Ans. 55.2 c m2 o h m ~1 e q u i v "1. 12-10 Calculate the electrochemical mobility and the effective radius of (a) an ion M+ whose equivalent conductivity is 55.0 c m2 o h m- 1 e q u i v- 1, and (b) F e ( C N ) }-, whose λ value is in an aqueous K N Oa solution. Calculate (a) the solubility product, (b) the mean molarity of the saturated solution, (c) the solubility in the K N Os solution, (d) the mean activity coefficient for the electrolyte P b2 +, IOs" in the K N Oa solution.
PROBLEMS 493
12-14 Calculate γ± for 0.02 m acetic acid at 25°C using Table 12-7.
Ans. 0.976.
12-15 A s s u m i n g the ionic strength principle, estimate y± for 0.0333 m C u ( N 08)2 using the data of Table 12-8 (and assuming that the principle is obeyed by each ion separately).
Ans. 0.52.
12-16 Calculate γκ + and y s o4~ (separately) at 25°C in 0.05 m K2S 04 using the D e b y e - H u c k e l theory and compare the resulting γ± with the value in Table 12-8.
Ans. 0 . 6 3 5 , 0 . 1 6 3 , 0 . 4 0 4 . 12-17 What is the D e b y e - H u c k e l value for y± of 0.5 m N a C l at 50°C?
Ans. 0.42.
12-18 The solubility product of Ag2CrC>4 is 2.0 χ 10~7 at 25°C; calculate the solubility of this salt in 0.1 m silver nitrate, recognizing nonideality.
Ans. 1.85 x 1 0 "4m . 12-19 Obtain the degree of dissociation of 0.1 m chloroacetic acid in 0.05 m HC1 at 25°C.
Ans. 0.0256.
12-20 What would the pH of the solution in Exercise 12-19 be if 0.06 mole liter"1 of N a O H were added to it?
Ans. 1.91.
Some exercises in S I units.
12-21 T h e equivalent conductivity of N a2S 04 is 1.299 χ 1 0 "2 m2 e q u i v1 o h m- 1. Calculate the resistance o f a 0.005 Μ solution in a cell w h o s e cell constant is 150 m "1.
Ans. 1.155 x 1 08 o h m . 12-22 Calculate the specific conductivity o f a saturated solution o f A g C l . A s s u m e the water
used has a specific conductivity o f 7 0 χ 1 0 "8 o h m "1 m "1.
Ans. 2.42 χ 1 0 " * o h m "1 m "1. 12-23 Calculate the i o n atmosphere radius for a 0.02 m solution o f a 1-1 electrolyte.
Ans. 2.155 n m .
P R O B L E M S
12-1 The following data apply to aqueous solutions of sodium propionate at 25°C:
Concentration ( Μ x 10s) 2.1779 4.1805 7.8705 14.272 25.973 Λ ( c m2 o h m "1 e q u i v1) 82.53 81.27 79.72 77.88 76.64 Find the limiting equivalent conductivity o f (a) sodium propionate, (b) propionic acid.
12-2 A conductivity cell has a resistance of 3736 o h m when filled with 0.028 m H2S solution and of 59.0 o h m when filled with 0.0100 m KC1. The measurements are m a d e at 18°C, at which temperature the equivalent conductivity for H S_ is 62 c m2 o h m- 1 e q u i v- 1.
494
CHAPTER 12: SOLUTIONS OF ELECTROLYTESCalculate K& for H2S (relevant data are available in the text, but should be corrected to 18°C with the use of Walden's rule).
12-3 The specific conductivity of a saturated solution of silver iodate at 80°C is 1.25 χ 1 0- 5 o h m- 1 c m- 1; that of the water used is 1.4 χ 1 0- β o h m- 1 c m- 1 and the equivalent c o n ductivity of silver iodate is 89 c m2 o h m- 1 e q u i v- 1. Calculate the solubility product for silver iodate.
12-4 The specific conductivities at 25°C were measured for the following solutions:
Solution Specific conductivity ( o h m- 1 c m- 1)
12-6 One hundred cubic centimeters of 0.10 Ν sodium acetate solution is titrated with 0.1 Ν HC1 solution. Calculate the specific conductivity of the resulting solution when 90, 99, 101, and 110 c m3 of the HC1 solution has been added. Bear in mind that acetic acid is only slightly ionized in the presence of HC1 and N a A c ; in these calculations neglect the variation of equivalent conductivity with concentration and use the value for infinite dilution. Your answers need be correct to only 1 %. M a k e a semiquantitative plot of your calculated specific conductivities (as ordinate) versus the volume of HC1 solution added.
12-7 If pure water has a conductivity of 4.5 χ 1 0- 8 o h m- 1 c m- 1 at 20°C, calculate the specific
12-9 For an incompletely dissociated electrolyte the Onsager equation is A = <x[A0 -(A+ BA0)(*C)1'2) = ocA',
where A = S2AJ^DTy29 Β = 8.2 χ WI(DTfi\ D is the dielectric constant, and η is the viscosity. The equivalent conductivity of dichloroacetic acid in 0.03 Μ solution is 273 o h m- 1 c m- 1. For dichloroacetic acid, A0 = 388.5. Calculate the degree of dissociation α from the Onsager equation. [Hint: use a procedure of successive approximations, starting with α = A/A0 .] Assume 25°C.
12-10 In a transport experiment in 0.02 Μ NaCl solution at 25°C, using the moving boundary method, Longsworth found the boundary between N a C l and C d C l2 solutions to
PROBLEMS 495 m o v e 6.0 c m in 2070 sec with a current of 0.00160 A . Tube cross section was 0.12 c m2. Calculate t+ .
12-11 Longsworth determined the transference number of sodium ion by the following moving boundary experiment. The data refer to the movement of a rising boundary between solutions of sodium and cadmium chlorides; the lower electrode was a cadmium anode and the upper a silver/silver chloride cathode. The temperature was 25°C, the current was maintained constant at 16.00 χ 10~4 A , the cross section of the tube was 0.1115 c m2, and the concentration of the sodium chloride 0.02 mole l i t e r- 1. The table gives some corresponding readings of the time / and the distance of traverse of the bound
ary jr.
/ ( s e c ) 172 344 2757 3104 3454 Λ: (cm) 0.5 1.0 8.0 9.0 10.0 Calculate the transference number of sodium ion. [Note: For the most accurate value of x/t divide the difference between the average of the last three distances and that of the first two by the difference between the average of the last three values of / and that of the first two.]
12-12 Ion-exchange particles exhibit the D o n n a n effect. Here, the p o r o u s particle corresponds to the left side o f Fig. 12-12 in the case o f a n anion exchanger. That is, N+ denotes the positively charged exchange sites that are attached t o the ion-exchange polymer matrix.
S u p p o s e that the concentration of exchange sites is 2.5 Μ for a certain i o n exchanger.
Calculate the interior concentration o f N a+ and o f Cl~ w h e n the exchanger is immersed in 0.01 Μ N a C l solution.
12-13 Calculate the concentration of H2S , H S ~ , S2~, and H+ in a 0.200 Μ N a H S solution (to an accuracy of about 1 %). [Note: The solution to this problem can be much simplified by making judicious approximations at each stage.]
12-14 Calculate the concentrations of acetate ion, benzoate ion, and H+ in a solution made up of 0.0100 mole of acetic acid and 0.0100 mole of benzoic acid dissolved in water and then diluted to 1 liter.
12-15 A total of 0.01 mole of N a C l and 0.01 mole of solid A g2C r 04 are shaken with a liter of water. Calculate the equilibrium constant for the reaction
A g2C r 04 + 2C1- = 2AgCl + C r 04~
-Calculate also the concentrations of each ion at equilibrium and the number of moles of any solids present. The K*v values are 1.8 χ 1 0 "1 0 for AgCl and 1.2 χ 1 0 ~1 2 for A g2C r 04.
12-16 Derive Eq. (12-90) from Eq. (12-84).
12-17 The following are mixed until equilibrium is achieved: 0.02 mole of AgCl, 0.02 m o l e of A g C N , 0.01 mole of N a C N , and 1 liter of water. Calculate within 1 or 2 % relative accuracy the final concentration of each species in solution and the amounts of each solid present given the following data: final pH is 7.00; #8 p for AgCl is 1.8 χ 1 0- 1 0; KBp for A g C N is 7 χ 1 0 "1 δ; K& for H C N is 1 χ 1 0 ~1 0; Κ = ( A g ( C N )2- ) / ( A g+) ( C N " )2 is 2.6 χ 1 01 8.
12-18 Solid N a O H is added to 1 liter of a 0.1 / solution of H2S until the pH rises to 12. Taking Κι and K2 as 10~9 and 1 0 "1 4, respectively, (a) calculate the initial pU and (b) calculate the number of moles of N a O H added and the concentration of all species present in this final solution.
12-19 Leucylglycine is an amino acid which dissociates into both hydrogen and hydroxide ions.
SPECIAL T O P I C S P R O B L E M S
12-1 Calculate the limiting value for the diffusion coefficient of aqueous NaCl at 25°C.
12-2 The equivalent conductivity for 0.01 m KC1 is 146 c m2 o h m "1 equiv"1 at 25°C. Calculate the diffusion coefficient for 0.01 m KC1 using Eq. (12-125).
12-3 A solution containing 0.14941 w t % KC1 is electrolyzed in a Hittorf cell at 25°C with A t 2 5 ° C the constant for the dissociation into anions and hydrogen ions is 1.51 χ 1 0- 8. The apparent dissociation constant for the dissociation into cations and hydroxyl ions is 3.02 χ 1 0- 1 1. Calculate the pH at which the degree of dissociation into hydrogen ions and hydroxyl ions is the same.
12-20 H o w many millimoles of H A should be added to 100 c m3 of a 0.01 Μ solution of base B O H in order to give a solution with a pU of 8.90? pK& for H A is 4.76, pKn for B O H is 5.40. H o w many cubic centimeters of 0.01 Μ H A would one have to add to 100 c m3 of 0.01 Μ B O H to obtain this p H ?
12-21 One hundred cubic centimeters of 0.1 / H2S 04 is mixed with 100 c m8 of 0 . 0 2 5 / N a O H . Calculate the pH of the resulting solution. The second dissociation constant of sulfuric acid is 0.015 and the first corresponds to a strong acid.
12-22 Barney et al. obtained data on the solubility of cobaltous oxalate (CoOx) as a function of added potassium oxalate concentration. The solubility is at first depressed due to the c o m m o n ion effect, then increased, due to the complex formation:
C o2 + + 2 0 x2" = C o ( O x )2~ .
The minimum in solubility occurs at S = 9.2 χ 10~5 and ( K2O x ) = 4.5 χ 1 0- 4; the solubility of C o O x in pure water is 1.44 χ 10~4. Derive the equation whereby Κ can be calculated from the solubility minimum, and calculate K.
12-23 The solubility of lead chloride is 0.005 mole liter"1 at 25°C. Calculate the activity product (that is, make correction for activity coefficients). Calculate also the solubility of PbCl2 in 0.02 m sodium nitrate solution.
12-24 Chlorine dissolved in water reacts according to the equation Cl2(aq) + HzO = H+ + CI" + HCIO.
Since all the forms present are essentially nonconducting with the exception of the HC1, the concentration of this last may be determined by measuring the conductance of the solution. If the total dissolved chlorine is known, then the equilibrium constant for the reaction may be determined. Given the following data, calculate this equilibrium constant:
The specific conductivity of 0.01 M C 12 solution is 0.00351 o h m- 1 c m- 1. The equivalent conductivities of 0.01 M H O and 0.005 ΜHC1 solutions are 412 and 415.6, respectively.
Using Eq. (12-12) and the data given, calculate the hydrolysis constant (do not use conductivity values other than the ones given).
12-25 At 25°C, pK for the dissociation of A g ( N H3)2+ into its components is 7.22. For AgCl, AgBr, and A g l , pKBP is 9.77, 12.48, and 16.07, respectively. Calculate how many milli
grams of these salts are dissolved by 1 liter of 1 . 0 / w N H3. Neglect A g ( N H3)+, N H4+ , and OH".
SPECIAL TOPICS PROBLEMS 497 silver/silver chloride electrodes. After the electrolysis, which deposits 0.16024 g of silver in a silver nitrate coulometer, one of the end cells is analyzed and found to contain 120.99 g of solution of 0.19404 w t % KC1. Calculate the transference number for K+.
12-4 A 0.01 m solution of HC1 is electrolyzed in a Hittorf cell with a P t / H2 anode and a silver/
silver chloride cathode. Each compartment contains 50 c m3 of solution. A current of 2 m A is passed through the cell for 1 hr. Calculate the final concentrations of the various species present in the anode and cathode compartments.
12-5 A famous early experiment by Washburn attempted to find the amount of water of hydra
tion carried by ions. The procedure was to carry out an electrolysis in a Hittorf cell with solutions containing a sugar. The sugar, being neutral, was assumed not to m o v e during the electrolysis (an assumption later found not to be quite correct). In one ex
periment a solution contained 4.939 wt % of LiCl and 4.73 % of a sugar and an amount of electricity corresponding to 0.0464 & was passed through the cell with a silver/silver chloride cathode and a silver anode. After the electrolysis the cathode solution weighed 81.47 g and contained 5 . 5 6 5 % of LiCl and 4 . 6 1 9 % of sugar, while the anode solution weighed 104.4 g and contained 4.440 % of LiCl and 4.806 % of sugar. Find nc as a function of wa , the number of water molecules bound per cation and per anion, respectively.
12-6 By means of a logarithmic diagram, find the pH of a solution 0.1 Μ in ammonia and 0.1 Μ in K H C 03.
12-7 The acid dissociation constants for monochloroacetic acid ( H M ) and acetic acid ( H A C ) are 1.55 χ 1 0- 3 and 1.8 χ 1 0- 5, respectively.
(a) Make a semilogarithmic plot of the fractions of H M , M-, H A c , and A c- versus pH.
(b) Using this plot, calculate the p H of a solution 0.01 m in H M (total concentration of acid) and 0.02 m in H A c (again total concentration of acid).
(c) Calculate the pH if 0.01 mole of solid N a O H is added to a liter of the solution in (b).
(d) Calculate the pH if 0.02 m o l e of solid N a O H is added to a liter of the solution in (b).
12-8 The acids H A and H B have pKA values of 4.5 and 7.5; pKy, is 14.0. Find by means of a logarithmic diagram the pH for solutions that have been mixed s o as to contain: (a) 10 m M o f H A ; (b) 10 m M o f H A , 5 m M o f H B ; (c) 10 m M o f N a A , 5 m M o f H B ;
12-11 Ethylenediaminetetraacetic acid is a tetrabasic acid H4Y . The successive pKys are 2.00, 2.67, 6.16, and 10.26. It forms a stable complex with C o ion, C o2 + + Y4" = C o Y2~ .
For this complex formation Κ = 1 01 6; B a2 + forms a similar complex with Κ = 107. Both C o Y2 - and B a Y2 - are the anions of strong acids, that is, one does not get H2C o Y and so on in acid solution (although the solids are known). Calculate and plot the loga
rithmic diagram for the various forms of ethylenediaminetetraacetic acid for the pR range from 0 to 7, and the similar diagram for the distribution of cobalt and barium between C o2 + and B a2 + and C o Y2 - and B a Y2~ as a function of pC, where C is the con
centration of Y4~ . Calculate the percentage of complexing of C o2 + and B a2 + in solutions of (a) 0.01 / C o ( N 03)2, 0.01 / B a ( N 03)2, 0.1 / N a2H2Y ; (b) the same as (a) but also 0.1 / in N a O H . A l s o give the /?H's of these solutions.
12-12 Derive Eq. (12-98). Calculate the osmotic pressure at 25°C if C = 0.01 m and ( N+) = 0.1m, neglecting activity coefficient effects.