Studies of Electrolytes in Dioxane Water Mixed Solvent
Subject: Chemistry | Topics:

All praise goes to almighty Allah, without His endless mercy I could not reach so close to my destination, for the time being. Simultaneously I am remembering my prophet Hazrat Mohammad (SM), the supreme guide to knowledge and wisdom for mankind.

I have the pleasure to express my deepest gratitude and indebtedness to my reverend supervisor, Dr. Mahbub Kabir, professor, Department of chemistry, Jahangirnagar University, Savar, Dhaka, for his indispensable guidance, encouragement and suggestions throughout the period of my research.

I am particularly grateful to our honorable teacher Prof. Dr. Ilias Mollah, Chairman, Department of chemistry, Jahangirnagar University, Savar, Dhaka, for his kind co-operation fruitful discussions and spontaneous help out.

I am also grateful and indebted to Dr. Menarul Islam, Assistant Professor, Department of chemistry, Jahangirnagar University, Savar, Dhaka, for his indispensable guidance, encouragement and suggestions throughout the period of my research.

I also take this opportunity to express my gratefulness to all of my honorable teachers of the Department of chemistry, Jahangirnagar University, for their help and co-operation.

I would like to pay my respect and gratefulness to Md. Abdul Kuddus and Subir chowdhury, PhD researcher in physical laboratory for their utmost help to me during my thesis work.

I offer my grateful to Md. Mohibullah Khan Sowrav, Md. Rasedul Islam Ripon and Abul Kalam Azad for their utmost help to me during my thesis work.

I want to give thanks to all of my friends for their co-operation and help during the course of my lab work.

I offer my heartfelt thanks to my brothers for their constant inspiration. Finally I express my deepest gratitude and sincere thanks to my parents for keeping me in their good wishes forever.

 2.1   REAGENTS  AND  CHEMICALS 

A list of the chemicals is given below:

  1.  Ferrous Sulphate    (Ana. R.)  :  B. D. H. England
  2. Copper Sulphate (Ana. R.)       :  Ridel –dettean
  3. Cadmium Sulphate (Ana. R.)   : B. D. H. England
  4. Potassium chloride (R.)           : B. D. H. England
  5. Dioxane  ( R.)                           : Ridel –dettean

Iron, cadmium and copper sulphates of analytical reagent grade were recrystallized twice from conductivity water at a temperature between 10 and 20  and then dried at room temperature. Reagent grade 1,4-dioxane  was fractionally distilled after being dried to remove traces of water. Potassium chloride used for the cell calibration was reagent grade and was recrystallized three times from conductivity water. It was then dried in vacuum at 200   for more than one week.

Dioxane-water mixtures were carefully prepared by using conductivity water (specific conductivity < 2  10-6 Scm-1 at 25  ). Solutions of different concentrations were carefully prepared by using dioxane – water mixture.

 2.2    CONDUCTIVITY   WATER 

Water used in conductance was deionized water purified by passing it through a double Barnsted ion- exchange column (organic materials exchange and mixed cation – anion exchange). The conductance of this water was monitored by measuring the conductance during the collection. The value was < 1  10-6 Scm2 at room temperature.

2.3   MEASUREMENT OF DENSITY, VISCOSITY AND DIELECTRIC CONSTANT 

The density of pure liquid and mixtures of liquids were measured by weighing a definite volume of the liquid in a density bottle. The viscosity of dioxane – water mixtures were measured experimentally by using Oswald viscometer. The dielectric constant of the solvent mixtures was interpolated from the published data.36 The viscosity and dielectric constants of dioxane – water mixtures are summarized in    table 1.

2.3.1 MEASUREMENT OF DENSITY

The relative density is the ratio of the weight of a given volume of the substance to the weight of an equal volume of water at the same temperature and the density of the substance at temperature T   is equal to the relative density multiplied by the density of water at that temperature. Densities of liquids were measured by weighing a definite volume of the liquid in a density bottle. The densities of liquids   and different solutions were calculated by the equation.

            dT   =    DT

where

          w´ = the weight of liquid or solution, w   = the weight of water and

          = the density of water at T

2.3.2    MEASUREMENT OF   VISCOSITY 

According to the poiseuelle’s equation the ratio of the viscosity coefficients of the two liquid is given by

Where, t1 and t2 are time of outflow of water and liquid respectively.

Since the pressure p1 and p2 are proportional to the densities of the two liquids d1 and  d2 then

  = Consequently, once d1, d2 and  and  are known, determination of t1 and  t2  permits  the calculation of , the viscosity coefficient of the liquid  under consideration.

2.4   PREPARATION OF METAL SULPHATES   SOLUTIONS  

Solution of metal salts were prepared  measuring  required  amount  of  the compound  in an analytical  balance  and dissolving the solvent  to give  the appropriate  value  at  25 . Then solutions of different concentrations were carefully prepared by dilution of the stock solutions of metal sulphates at 25 , with increasing temperature, concentrations were changed. Solutions of different concentrations at different temperature were calculated by the equation

Where  and  are the concentrations of solution at temperature 25  and T   respectively. d1  and  d are  the  densities  of  solution  at  temperature 25  and  T   respectively.

2.5   CONDUCTIVITY   MEASUREMENTS  

The electrical conductivity of the solutions was measured at 50/60 Hz by the conductance linear – bridge method. A conductivity  cell  which  is designated  for  solutions of  low conductivity  was used  throughout  this study.  The conductivity cell was calibrated using 0.1 and 0.01 decimal solutions of purified fused potassium chloride. The cell constant was determined to be 0.610 cm-1 using a standard potassium chloride   solution and exhibited no tendency to change with the two standard solutions. The solution in cell was magnetically stirred at a rate of 1.2 revolutions per second.  The experimental error of the conductivity measurement was less than 1%. All the measurements were carried out in an electrically grounded thermostat bath containing distilled water. Temperature was controlled and measured with sensitively of 0.05 .

2.6 TABLES  FOR  THE  PHYSICAL  PROPERTIES  OF  DIOXANE – WATER MIXTURESAND  EQUIVALENT  CONDUCTIVITY OF  DIFFERENT  SOLUTIONS  

The physical properties  of  dioxane – water  mixtures are summarized  in  Table  1  and  the equivalent  conductance at different concentrations of  ferrous  sulphate,  copper  sulphate and cadmium sulphate  solutions  at  different temperatures  are listed  in Table  2.1  to  2.12.

Table – 1:  Physical properties of dioxane – water mixture.

              5% Dioxane              10% Dioxane              15% Dioxane           20% Dioxane

T   D     η       mNsm-2      D   ηmNsm-2         D    ηmNsm-2     D    ηmNsm-2                          
2574.380.966469.851.072265.331.178060.801.2720
3072.650.869468.200.951163.751.045159.301.1300
3570.680.782666.350.853262.030.928157.701.0110
4069.050.703864.800.770560.550.838156.300.9110

Table-2.1:  Equivalent conductance (Λ) of FeSO4   in 5% (w/w) dioxane – water mixture at different temperature.

Concentrationmol  dm            ΛScm2 equ-1             ΛScm2 equ-1             ΛScm2 equ-1            ΛScm2 equ-1

250C

30

35

40

2.00  10-4

116.50

130.18

140.32

151.54

4.00 10-4

109.08

124.73

134.25

144.75

6.00  10-4

105.25

117.10

126.05

138.10

8.00  10-4

100.10

112.25

122.20

133.08

12.00  10-4

96.05

108.00

117.00

128.25

 Table-2.2:  Equivalent conductance (Λ) of FeSO4   in 10% (w/w) dioxane – water mixture at different temperature.

Concentrationmol  dm-3            ΛScm2 equ-1         ΛScm2 equ-1            ΛScm2 equ-1            ΛScm2 equ-1

25

30

35

40

2.00  10-4

104.50

118.05

127.25

138.25

4.00 10-4

98.05

111.70

120.50

130.75

6.00  10-4

93.29

104.85

112.50

121.60

8.00  10-4

90.00

100.19

107.00

115.30

12.00  10-4

84.50

94.00

98.00

106.10

 Table -2.3:  Equivalent conductance  (  Λ )  of  FeSO4   in  15%  (w/w)  dioxane – water  mixture at different  temperature.

Concentrationmol dm-3          ΛScm2 equ-1           ΛScm2 equ-1           ΛScm2 equ-1            ΛScm2 equ-1

25

30

35

40

2.00  10-4

91.51

101.08

110.85

124.05

4.00 10-4

84.10

92.73

102.15

113.60

6.00  10-4

79.24

87.30

96.10

107.08

8.00  10-4

75.09

83.00

91.23

101.75

12.00  10-4

71.25

79.15

87.40

96.10

Table -2.4:  Equivalent conductance (Λ) of FeSO4 in 20% (w/w) dioxane – water mixture at different temperature.

Concentration

mol  dm-3           Λ

Scm2 equ-1        Λ

Scm2 equ-1          Λ

Scm2 equ-1          Λ

Scm2 equ-1

25

30

35

40

 

 

2.00  10-4

80.15

90.25

100.23

110.75

 

 

 

4.00 10-4

72.52

81.54

90.75

99.50

 

 

 

6.00  10-4

66.50

75.50

84.10

92.00

 

 

 

8.00  10-4

63.75

73.25

81.50

89.10

 

 

 

12.00  10-4

61.24

70.50

78.00

86.05

                                                      Table –2.5:  Equivalent conductance (Λ) of CuSO4   in 5% (w/w) dioxane – water mixture at different temperature.

Concentration

mol  dm-3

Λ

Scm2 equ-1           Λ

Scm2 equ-1           Λ

Scm2 equ-1           Λ

Scm2 equ-1      25     30        35     402.00  10-4 113.95127.98141.87155.99

4.00 10-4

107.20

124.18

137.21

151.15

6.00  10-4

103.53

118.01

131.05

142.35

8.00  10-4

101.75

113.10

125.75

137.05

12.00  10-4

98.50

109.50

122.08

131.92

 Table-2.6:  Equivalent conductance (Λ) of CuSO4 in 10% (w/w) dioxane – water mixture at different temperature.

Concentration

mol dm-3

Λ

Scm2 equ-1          Λ

Scm2 equ-1           Λ

Scm2 equ-1           Λ

Scm2 equ-1     25     30        35     402.00  10-4

101.95

113.98

126.10

138.10

 

 

4.00 10-4

96.50

109.90

120.08

132.85

 

 

 

6.00  10-4

91.25

105.05

114.60

124.98

 

 

 

8.00  10-4

88.30

101.00

109.80

118.10

 

 

 

12.00  10-4

84.50

96.00

103.00

112.90

 water mixture at different temperature.

Concentration

mol dm-3

Λ

Scm2 equ-1         Λ

Scm2 equ-1            Λ

Scm2 equ-1         Λ

Scm2 equ-1

25

30

35

40

2.00  10-4

89.96

99.98

112.15

122.75

 

 

4.00 10-4

83.50

95.87

107.00

116.98

 

 

 

6.00  10-4

78.25

90.00

98.75

108.25

 

 

 

8.00  10-4

74.10

83.15

93.10

102.85

 

 

 

12.00  10-4

70.30

78.50

87.00

95.00

 

 

 Table-2.8:  Equivalent conductance (Λ) of CuSO4   in 20% (w/w) dioxane – water mixture at different temperature.

Concentration

mol  dm-3        Λ

Scm2 equ-1           Λ

Scm2 equ-1          Λ

Scm2 equ-1            Λ

Scm2 equ-1

25

30

35

40

2.00  10-4

79.15

88.10

99.50

107.90

 

 

4.00 10-4

71.25

82.90

93.00

102.10

 

 

 

6.00  10-4

67.20

74.70

83.25

93.30

 

 

 

8.00  10-4

64.10

67.12

78.50

85.50

 

 

 

12.00  10-4

59.00

62.80

72.00

77.10

 Table-2.9:  Equivalent conductance (Λ) of CdSO4   in 5% (w/w) dioxane – water mixture at different temperature.

Concentration

mol dm-3

 

Λ

Scm2 equ-1         Λ

Scm2 equ-1          Λ

Scm2 equ-1        Λ

Scm2 equ-1

 

25

30

35

40

2.00  10-4

118.25

131.70

141.00

152.50

 

 

4.00 10-4

 

110.50

125.50

135.25

145.75

 

 

 

6.00  10-4

 

106.00

119.20

127.00

139.25

 

 

 

8.00  10-4

 

102.06

113.00

122.20

134.50

 

 

 

12.00  10-4

 

97.15

109.00

118.00

129.30

 Table-2.10:  Equivalent conductance (Λ) of CdSO4   in 10% (w/w) dioxane –water mixture at different temperature.

Concentration

mol dm-3

 

 

Λ

Scm2 equ-1           Λ

Scm2 equ-1          Λ

Scm2 equ-1             Λ

Scm2 equ-1

25

30

35

40

 

 

2.00  10-4

106.50

119.75

128.00

139.25

 

 

 

4.00 10-4

99..00

112.50

121.20

132.10

 

 

 

6.00  10-4

94.10

106.25

116.50

126.00

 

 

 

8.00  10-4

91.00

101.30

110.15

120.20

 

 

 

12.00  10-4

86.30

96.00

106.00

116.50

 Table-2.11:  Equivalent conductance (Λ) of CdSO4 in 15% (w/w) dioxane – water mixture at different temperature.

Concentration

mol dm-3

Λ

Scm2 equ-1          Λ

Scm2 equ-1          Λ

Scm2 equ-1         Λ

Scm2 equ-1

25

30

35

40

2.00  10-4

93.50

103.00

111.50

124.75

 

 

4.00 10-4

86.00

94.75

103.10

115.60

 

 

 

6.00  10-4

81.20

89.30

97.30

109.00

 

 

 

8.00  10-4

77.00

85.00

92.00

103.75

 

 

 

12.00  10-4

73.25

82.15

88.40

98.00

 Table-2.12:  Equivalent conductance (Λ) of CdSO4   in 20% (w/w) dioxane – water mixture at different temperature.

Concentration

mol  dm-3

Λ

Scm2 equ-1          Λ

Scm2 equ-1          Λ

Scm2 equ-1         Λ

Scm2 equ-1

25

30

35

40

2.00  10-4

82.10

92.25

102.30

112.75

 

 

4.00 10-4

74.50

83.50

92.75

101.50

 

 

 

6.00  10-4

68.50

77.50

85.10

93.70

 

 

 

8.00  10-4

65.15

74.25

82.50

90.15

 

 

 

12.00  10-4

60.25

71.50

79.00

87.05

 3.1  DATA  TREATMENT 

For  the treatment  of  the data the Fuoss-Onsagar  equation in  the form  for  an associated  symmetrical  electrolyte was used .

          Λ = Λ0 S(cγ) 1/2  + Ecγ log(cγ)  + Jcγ KA (cγ) f±2 Λ                 (3.1)

Where Λ0 is the limiting equivalent conductivity, c is the molar concentration, γ is the degree of dissociation, S is the Onsager limiting slope, E and J are theoretical coefficients, and f± is the mean ionic activity coefficient.

For   the actual analysis of the association, the Fuoss“ y – x ” method  was used.

Introducing   some new variables defined by Fuoss by the equation:

           Λ׳ = Λ + S (cγ)1/2 – Ecγ log (cγ)                                                  (3.2)

          Δ Λ = Λ׳ – Λ0                                                                                (3.3)

          y = Δ Λ / c γ                                                                                  (3.4)

 and     x =  f±2 Λ                                                                                      (3.5)

The equation (3.1) is transformed into a simple form

         y = J – KA x                                                                                    (3.6)

Equation (3.6)  implies  that  if  the variables  x  and  y  are known, the  values  of  J  and KA can be determined  by a plot of  y against  x ( the  y–x  plot).The coefficient, J is  a  function  of  ion size parameter  and is used  for  the evaluation  of  ‘a’  the  closest  distance  of  approach  between  the  oppositely  charged  ions .

In  order  to  compute  y,  values  of  γ  and  Λ0  are needed.  The terms in  E  and  J  are of opposite  sign, if  they  are  both neglected  the  conductance  equation  reduces to

         Λ = γ (Λ0 Sc1/2 γ 1/2)

This  is the modified  form  of  the  Oswald  dilution  law  used  formerly  for  analysis  of  conductance  data.37,38

 The  starting  approximation  for  γ  is  obtained  by  the  classical  Onsager  equation :

           = Λ / [Λ0   S (c. Λ / Λ0   )1/2]                                             (3.7)

Λ0  is  estimated  from the intercept  on  y  axis  of the   plot  of  Λ  vs  √c.  S  is  Onsager  limiting slope  of  the  above  plot  and  the  observed  ‘S’  value  is used .  Λ0 is used to compute E, Λ, Λ’ and x.

 For  the initial calculation  of  x, the  mean  activity  coefficient  f±2  is estimated  by  the following equation.39

log f±2   =                                (3.8)

 Here Ka .2 for dilute solution.40

Trial values  of  Λ0 are  used  in  ΔΛ and  y  until correct one is found, the “correct”40 one  is  taken  as the  value  which  linearize  the ‘y-x’ plot. Too small  trial  value  gives  a curve  which is  concord upwards, while  too large a  Λ0  value  leads  to  a   ‘y-x’  plots which is concave downwards. From the ‘y-x’ plot we get Λ0,KA, a through J.

A  series of  calculations  are  done  for  a set  of  Λ0   values  using  equation  (3.7)   and  (3.2)  to calculate  a fitting   parameter for the  y-x line  for each Λ0  originally  using  1  or  2  Λ0 unit  until  increments.  Then  Λ0  is selected  which  gives  the  best fit  and the whole calculation is repeated  with  smaller increment  of  Λ0 This  process is continued until  the increment  are  only 0.01 Λ0   units.  Then for higher approximation, γi ( i= 2 , 3 .  .  . )  is calculated by the equation

           γi = Λ/ ( Λ0 – S ( cγi-1 )1/2 + Ecγi-1 log cγi-1   +  J cγi-1)                      ( 3.9 )

where, on the right hand side, the  first approximation for γ from  (3.7)  and the values just obtained for Λ0 and  J are used. The calculation is repeated using equation (3.9) until γ (in) = γ (out) i.e., γn-1 = γn. This values of γ is used to calculated Λ’ i. e., Λ0  from equation  (3.2). For any small difference in Λ0 values between the two, a second time Λ0 fixation is carried out using equation (3.9) and (3.2).

For the calculation of x at second time, the mean activity coefficient, f± is estimated by means of the Debye-Huckel equation.

               –log f±2 =                                                   (3.10)

where z (z = |z+| = |z|  for a symmetrical electrolyte) is charge number;                 I,the ionic strength, and A and B, the theoretical coefficients.

where

              A =

and           B =

In the calculation of f± by above equation, the initial ‘a’ is obtained from the initial J  is used.

Then a final “y-x” plot is made. From this we get final Λ0,KA and aJ through J.

Calculation   of aJ from J

In the equation for J from the relation J = Ϭ1 Λ0 + Ϭ2, different trial values of   ‘a’ is used. The values of ‘a’ which fits the J equation is desired aJ value. The equation  (3.1)  is  a three- parameter equation in  Λ0,  the equivalent  at  infinite dilution; J the coefficient  of the linear term,  and  KA, the  association constant.  The symbols  in equation  (3.1) are the same as used  by Fuoss  in his monograph38,41 adopted properly  to 2:2  electrolytes by the introduction  of valences  z.

The various coefficients   then   read   for homologues electrolytes

 where   | z+ |  =  | z| = | z | = z.

             S = α Λ0  + β  =   z3 Λ0  +    z2

             E = E1 Λ– E2 =   z6 Λ0 

         J = Ϭ1 Λ0 + Ϭ2

            = {1012 z6 [ h(b)  + 0.9074 + ln ( )]} Λ0  +

                  z5 +  z3a

                   – z2 (1.0170 + ln  )

 Where

          h(b) = (2b2 +2b – 1) /  b3

        b =

           K =

       log f±2 =

 The calculation of the various coefficients is   shown below:

We know

            k = √ (

where  k  is the  gas  constant  per  molecule i.e., R / N ,  T  the  absolute  temperature, and  ni  the  number  of  any given  kind of    ions  per  cubic  centimeter  of  solution.

The  concentration  of  ions  c  in  gram ionic  weight  per liter  from  the  density .

            c =  1000

          Then

       k = √ ( )

Here, z+   =   z = z   for homologues electrolytes.

         =  √ ( )

      = √ ( ) z √ c

Here, e = electronic charge = 4.80298  10-10e.s.u.

           K = Boltzmann constant

               = 1.38054    10-16 erg.deg-1

          k = √ (   z √ C

     or, k  =   z √ c

           b  =    =   z2

                                   =   z2

        E1 = 2.3026 (k2 a2 b2 / 24 c)   =

        E2 = 2.3026 (k a b β / 16 c 1/2)

             = 2.3026

                ð E2 =

Ϭ1 =  ( k2 a2 b2 /12 c )  [ h ( b )  + 0.9074  + ln (    )

      =      Z6 [ h  ( b )  +  0.9074 +  ln (  ) ]

        Ϭ2 = α β + (11 β Ka / 12 c 1/2) – (ka b β / 8 c 1/2) [1.0170 + ln (  )]

     =  z5 +  z3a

     – z2 (1.0170 + ln )

 Calculation of Ϭ and Ϭ2 

Ϭ1 and Ϭ2   for dioxane – water mixtures at different temperatures.

For 5 % (w/ w) dioxane – water mixture.

When     T = 298 0 K

        Ϭ1 = 229394405.6 a + 7.6080 10 14 a2 – 1.2616 1021 a3 + 34.5832 ln a

                     + 654.8611

          Ϭ = 1.4205 1010 a – 584.0591 ln a – 10667.5706

When     T = 303 0K

      Ϭ1 = 232579377.8 a + 7.6606 1014 a2 – 1.2616 1021 a3 + 35.3059 ln a

                + 691.5675

          Ϭ = 1.5899 1010 a – 658.2373 ln a –12024.6696

When   T = 308 0 K

           Ϭ1 = 237811681.6 a + 7.7463  1014 a2 – 1.2616  1021 a3 + 36.5040 ln a

                   +691.5675

           Ϭ = 1.7860  1010 a – 747.6947 ln a – 13663.0334

When T = 313 0 K

           Ϭ1 = 241274629.6 a + 7.8025   1014 a2 – 1.2616   1021 a3 + 37.3042 ln a

                   + 706.8628

           Ϭ2 = 2.0040 1010 a – 843.5160 ln a – 15417.0781

 

For 10 % (w/w) dioxane – water mixture.

When T = 298 0 K

          Ϭ1 = 260113174.5 a + 8.1014 1014 a2 – 1.2616 1021 a3 + 41.7575 ln a

                    + 792.0302

           Ϭ2 = 1.3634  1010 a –596.9219 ln a – 10921.2563

When T = 303 0K

           Ϭ1 = 263920844.5 a + 8.1605 1014 a2 – 1.2616   1021 a3 + 42.6771 ln a

                   + 809.6399

           Ϭ2 = 1.5482  1010 a – 682.7763 ln a – 12494.5262

When T = 308 0K

           Ϭ1 = 269863663.1 a + 8.2519  1014 a2 – 1.2616   1021 a3 + 44.1273 ln a

                   + 837.3855

           Ϭ2 = 1.7445  1010 a – 778.2596 ln a – 14246.1641

When T  = 313 0K

           Ϭ1 = 273961169.5 a + 8.3143  1014 a2 – 1.2616 1021 a3 + 45.1361 ln a

                   + 856.6996

           Ϭ2 = 1.9471  1010 a – 874.8776 ln a – 16018.0675

 For 15 % (w/w) dioxane – water mixture.

When T = 298 0K

           Ϭ1 = 297351308.5 a + 8.6547  1014 a2 – 1.2616   1021 a3 + 51.0382 ln a

                   + 969.7688

           Ϭ2 = 1.3268  1010 a – 621.0914 ln a – 11384.2358

When T = 303 0K

           Ϭ1 = 302052241.8 a + 8.7301  1014 a2 – 1.2616  1021 a3 + 52.2533 ln a

                   + 993.0615

           Ϭ2 = 1.5073  1010 a – 711.1400 ln a – 13037.5636

When T = 308 0K

           Ϭ1 = 308761188.1 a + 8.8265  1014 a2 – 1.2616  1021 a3 + 54.0038 ln a

                   + 1026.6268

           Ϭ2 = 1.7160  1010 a – 818.5757 ln a – 15011.7124

When T = 313 0 K

           Ϭ1 = 313769502.1 a + 8.8978 1014 a2 – 1.2616   1021 a3 + 55.3231 ln a

                   + 1051.9299

           Ϭ2 = 1.9157 1010 a – 921.1828 ln a – 16897.1105

 For 20 % (w/w) dioxane – water mixture.

When T = 298 0K

           Ϭ1 = 343311231.6 a + 9.3073  1014 a2 – 1.2616  1021 a3 + 63.3173 ln a

                   + 1205.3577

           Ϭ2 = 1.3202 1010 a – 664.0975 ln a – 12196.3738

When T = 303 0 K

           Ϭ1 = 349086500.6 a + 9.3852    1014 a2 – 1.2616   1021 a3 + 64.9217 ln a

                   + 1236.1713

           Ϭ2 = 1.4986  1010 a – 760.1259 ln a – 13963.1386

When T = 308 0K

           Ϭ1 = 356840910.9 a + 9.4874 1014 a2 – 1.2616  1021 a3 + 67.0969 ln a

                   + 1277.9571

           Ϭ2 = 1.6935  1010 a – 868.4692 ln a – 15958.1212

 When T = 313 0K

           Ϭ1 = 362929469.5 a + 9.5631  1014 a2 – 1.2616   1021 a3 + 68.8215 ln a

                   + 1311.0948

           Ϭ2 = 1.8954  1010 a – 980.2454 ln a – 18016.1541

 3.2    SPECIMEN   CALCULATION

Specimen  calculation  of  ion – association  constant  of  ferrous  sulphate  in  5%      (w/ w)  dioxane – water  mixture at temperature  298 0K   is  shown  below :

The starting approximation for     is obtained by the classical   Onsager equation.

                  = Λ / [ Λ0 – S (c. Λ / Λ0)1/2]

Where Λ0 is estimated from the Λ vs. c1/2 plot in Fig. 1 is 128.8.  The Onsager limiting slope ‘S’ obtained from of   Λ vs. c1/2 plot is 899.50.

This trial value Λ0 is used to compute E,  and Λʹ.  These  values  are  used  to  calculate  y  and  x  by  using  equation   ( 3.4 ),  ( 3.7 ) and  ( 3.5 ).

Then the series of calculations are made for   a set of Λ0values. For calculation of , Λ׳ and    the  following  values  are  needed.

       T = 298 0K, D = 74.38, η = 0.009664 poise,

       S = 899.50 and E1, E2

       E1 =    Z6 =  26  =  39.82

     E2 =   Z5 =   25 = 672.43

   And,      E = E1 Λ0 – E2

Using the value Λ0 = 128.8, E = 4455.82

       = 116.50 / [128.8 – 899.50 (2.00  10-4    1/2]

        = 0.998271

     Λ׳ = Λ + S (cγ)1/2 – Ecγ log (cγ)

          = 132.50

and the  difference  between  Λ׳ – Λ0  =  3.69

if Λ0 =  132.0  is used,   then    = 0.9704  and   Λ׳  =  132.241168.

  and  Λ׳ – Λ0 =  0.24

To  fix  Λ0,  the  difference  between ( Λ׳ – Λ0)  become  less  than  0.01.

For this we put Λ0= 132.21. Then  = 0.9686, Λ׳ = 132.219586  and  ( Λ׳ – Λ0 )  = 0.009  which  is less than  0.01

Thus Λ0= 132.21 is fixed.

Using  this  Λ0 = 132.21 ,  , Λ׳, y  and  x   are  calculated  for  each  c  and  Λ.

 Calculation of  y

       y =

        =

        = 49.48

Calculation of   x 

         x =    Λ

–log   =

             = 0.789

     x =    Λ = 91.90

Thus  the  value  of  y  and  x  are  calculated  in this  manner  for  each  concentration  and  equivalent  conductance.

Then the initial y vs. x  plot  is made  according  to  the  equation  y  =  J – KA x  and  the  slope  and  intercept  give  KA  and  J  respectively.

In this case, the initial value of KA and J is 251 and 22979 respectively.

From  the  value of  J  the  values  of  aJ  are  obtained  as  follows:

           J = Ϭ1 Λ0 + Ϭ2

Where

          Ϭ1 = (k2 a2 b2 /12 c) [h (b) + 0.9074 + ln ( )

      =      Z6 [h (b) + 0.9074 + ln (  )]

 Ϭ2 = α β + (11 β Ka /12 c 1/2) – (ka b β / 8 c 1/2 ) [1.0170 +  ln ( ) ]

       =   z5 +  z3a

      – z2 (1.0170 + ln  )

 For 5% (w / w) dioxane – water mixture at 298 0K.

         Ϭ1 = (229394405.6 a + 7.608005233  1014 a2– 1.26120645  1021 a3

                + 34.58317374 lna + 654.8660589)

        Ϭ2 = 1.420509192 1010 a – 584.059164 lna – 10667.570558.

 If Λ0 = 132.21, then

      J = 4.451010 a + 1.0058 1017 a2– 1.67  1023 a3 + 3988.18 lna +75912.27

In this equation, different trial values of ‘a’ is used.  The  values of  ‘a’  which  fits  the  J  equation  is the  desired  ‘aJ’  value.

J = 22979 is obtained from the slope of   y vs.  x plot.

When

        a = 16.50  10-8 cm,   J = 22958

        a = 16.55  10-8 cm,     J = 23002

        a = 16.52  10-8 cm,    J = 22975

        a = 16.53  10-8 cm,      J = 22979

Thus the initial value of ‘aJ’ desired as 16.53  10-8 cm or 16.53 Å.

Then for higher approximation, γi  ( i= 2 , 3 .  .  . )  is calculated by the equation

           γi = Λ/ ( Λ0 – S ( cγi-1 )1/2 + Ecγi-1 log cγi-1   +  J cγi-1)

where, on the right hand side, the  first approximation for γ from  (3.7)  and the values just obtained for Λ0 and  J are used. The calculation is repeated using equation (3.9) until γ (in) = γ (out) i.e., γn-1 = γn. At second time, Λ0 is fixed in same way.

If Λ0 = 132.17 is used in the calculation of  γ in the above equation, then the constant γ׳ = 0.9643 and Λʹ׳ = 132.176245 for Λ =116.50 and c = 2.0 10-4. Then (Λʹ׳–Λ0) = 0.006 i.e., less than 0.01. Thus final Λ0 = 132.17 is obtained.

Using Λ0 = 132.17, J = 22979, Λ= 116.50 and γ1 = 0.9686, we get from the above equation:

               = 0.9643

                = 0.9643 using

Here,  =   = γ (constant).

Using this constant γ׳ (0.9643), Λʹ׳ = 132.176245 and y = 32.38 is obtained. Similarly different values of ‘y’are obtained for different Λ and c.

For the calculation of x at second time the equation of the mean activity coefficient is used.

               =  –

         = {1/2 (2.0  10-4  22 + 2.0  10-4  22 )}

                 = 0.02966439

            a = aJ (initial value) = 16.53 10-8 cm.

            A =  =  = 0.552430962

            B =   =   = 33778893.3

               = –

             = 0.8830799

                  = 0.7798

                       x =    Λ = 0.7798  116.50

                                         = 90.85

Thus different x values are calculated for different Λ and c. Thus final “y – x” plot is made. From this plot final KA and J are obtained.

The final aJ is obtained from final J. Using final Λ0 = 132.17 and

            J = Ϭ1 Λ0 + Ϭ2

              = 4.45  1010 a + 1.005    1017 a2 – 1.67  1023 a3+3986.8 lna + 75885.42

 Final J = 24263

Different trial values of ‘a’ is used in this equation.

when

             a = 17.55  10-8 cm, J = 23870

            a = 17.95  10-8 cm, J = 24219

            a = 17.98  10-8 cm, J = 24263

Thus, the final aJ = 17.98 Ǻ is obtained.

Now for FeSO4  in  5%  (w/w)  dioxane – water  mixture  the  values   are  as  follows:

     Λ0 = 132.17,    KA = 268, J = 24263   and aJ = 17.98 Å.

The initial  y – x  plot for  5%  (w/ w)  dioxane – water  mixture  at  298 0K  is  shown  in  Fig. 4.1. The final  y – x  plots for  5%  (w/ w)  dioxane – water  mixture  at  298 0K  is  shown  in  Fig. 4.2  and other  plots  are  shown  in Fig. 5  to 15.

The  calculated  values  of   γ, γ,׳ Λ’, Λ’׳,  y , x , KA ,  J  and  aJ  are  shown  in  appendix  Tables 10.1 to 12.16.

 Calculation of   aK from KA

ak  are  calculated  from  the  slope  of  the  plots  of   log KA  vs. 1/ D according to  the  equation

            KA =    exp

From the log KA vs.1/ D (Fig.17) for FeSO4   in  5 %  (w/ w)  dioxane-water  mixture  at  298 0K .

        Slope =   = 113.00

       Or,   =      = 113.00

     Or,     =   19.85 10-8 cm

                  =   19.85 A˚

 CALCULATION OF   THERMODYNAMIC PARAMETER

Calculation of ΔH0

From the plot of log KA vs. 1/ T (Fig.21)  for  FeSO4  in  5%  ( w/w )  dioxane – water  mixture.

        Slope =    = – 945.90

      ΔH    =   – 8.316  2.303  (– 945.90) Joule mol-1

                   = 18115.64 Joule mol-1

                  =   18.12 k Joule mol-1

 Calculation of ΔG0

From equation (1.51),

            ΔG0 = – 2.303 RT log KA

Here, T = 2980K, log KA = 2.40

               ΔG0 = – 8.316  2.303  298  2.40

                      = – 13697.33 Joule mol-1

                      = – 13.69   k J mol-1

 Calculation of ΔS0

From equation (1.54), ΔS0 =

                                                 =

                              ΔS0298 = 106.75 J K-1 mol-1

Calculation of   ΔGt0 

ΔGt =   ΔGt0( mixed  solvent) –  ΔGt0 ( water )

ΔG0 2980K for FeSO4   in water = – 13.05 kJ mol-1 42

ΔG0 2980K for CuSO4   in water = – 13.24 kJ mol-1 42

ΔG0 2980K for CdSO4   in water = – 13.43 kJ mol-1 42

 ΔG02980K( 5% dioxane )   for  FeSO4  = -13.69  kJ  mol-1

ΔGt0 = –13.69 + 13.05 kJ mol-1

          = – 0.64 kJ mol-1

          = – 640  J mol-1

ΔG0t ( el )  =  4.184 166  (  – 0.0127)   (  + )

For FeSO4   in 5 %  dioxane-water  mixture

ΔG0t ( el )  =  4.184 166  (  – 0.0127)   (  +  ) kJ  mol-1

                = 0.914 kJ mol-1

               =   914 J mol-1

Where   r1 = ionic radii of Fe2+ = 0.75 Ǻ    and

            r2 = ionic radii of SO42- = 2.30 Ǻ

 ΔG0t ( ch )  =  ΔGt0 –  ΔG0t ( el )

                = – 640 – 914 = – 1554 J mol-1

 Calculation of Hydrodynamic Radii

The hydrodynamic radius for a cation and anion is given by

          R+ =

        R =

To  calculate    and  ,  the  value  of    = 79.80 in water  at  250C has  been  taken.43,44 The Λ0 values of  FeSO4, CuSO4  and  CdSO4   in  water are 138.36, 135.43 and 141.65 respectively at 250C43,44  The anion transport  number  of  infinite  dilution  was  calculated  by  the  equation.

                    t0 =     and    t0+  =  (1 – t0).

 For FeSO4 in 5 wt. % dioxane- water mixture at 250C.

 t0 =     =    =  0.58

  and    t0+  =  ( 1- 0.58 ) =  0.42

Assuming  t0+  to  remain  constant  with  solvent  composition   R+  and  R   could  be  calculated  at  different  solvent  compositions.

                 = 0.42    132.17 = 55.51

   = 132.17 – 55.51 = 76.66

              R+ =   = 3.06 Ǻ

          R =    = 2.21 Ǻ

 4. RESULTS   AND   DISCUSSION

The equivalent conductance (Λ) of ferrous sulphate, copper sulphate and cadmium sulphate solutions at different temperatures varying solvent compositions are listed in Table 2.1 to 2.12. Plots of Λ vs. √ C are shown in Fig. 1 to 3. The limiting Onsagar slope (S) was found from the slope of the resulting straight lines.  Extrapolation of Λ at √C = 0  gave  values  of  limiting  equivalent conductance (Λ0) which  were  used  in  the  Fuoss-Onsagar  equation as a preliminary  data.

 4.1  ION-ASSOCIATION   CONSTANTS

The ion – association constant (KA), for the following reaction

          M2+ + SO42- ↔ M2+. SO42-   (M = Fe, Cu, Cd)

were  calculated  from  conductivity  data  according  to the  Fuoss-Onsagar  conductance equation.40,41 The revised Fuoss-Onsgar equation for the equivalent conductance of the  associated  homologues  electrolyte  is given by

             Λ = Λ0 – S(cγ) 1/2  + Ecγ log(cγ)  + Jcγ – KA (cγ) f±2 Λ

where     KA = (1 – γ) / c γ2

The  values  of  Λ0, KA, J and aJ at  different  temperatures  and solvent  composition  are  summarized  in  table  3.1 to 3.3. Fig. 16 shows that the values of Λ0 decreased with decrease dielectric constant (D) of the medium. The ion-association constants (KA) values were found to increase with increase of organic portion of the solvent mixture. The KA values of  CuSO4 found to at each temperature  and at each solvent  composition are larger  than  those of  FeSO4  and   the  KA  values  of  FeSO4  larger  than  those  of  CdSO4. The trend of the all KA values are shown below

SUMMERY

The conductance  of  three  homologous  electrolytes  namely  FeSO4, CuSO4 and CdSO4 is  measured  in  dioxane-water  mixtures  at  varying  composition at different  temperatures. The ion-association constant (KA) of the three electrolytes are found to increase with increase of organic portion in the solvent mixture and follow order at certain temperature.

                            CuSO4 > FeSO4 > CdSO4

The values of KA are found to increase with decreasing cation size. This result suggests that ion-association is cation size dependant. The KA values also increase with increase of temperature.

The changes of standard Gibbs free energy of ion – association are negative which shows that   the association occurs thermodynamically spontaneously. The changes of standard entropies of ion – association are positive and decrease with increase of temperature. This phenomenon can be explained as the result of reduction of electric field of the associating ion. The positive values of standard enthalpy change reveals that the association is an endothermic process.

The change of standard Gibbs free energy  of  transfer (ΔGt0) from water to mixed solvent are  always  negative  which suggests that the ion pair are in  a lower energy-state  in  aqua-organic  solvents than in water.The ΔG0t (ch) values for all the three electrolytes are formed negative which indicates spontaneous solvation and specific ion–solvent interaction. The values of ΔG0t ( el ) are   positive  for  all  the  three electrolytes and  magnitude  decreases  with  increase  of  dielectric  constant  of  the  solvent  mixture.  The  lower  the  values  of  ΔG0t ( el )  the  greater  is  the  electrostatic  interaction  between  ion  and  total  charges  on  the  solvent  molecules.

The walden products of all electrolytes in different solvent mixture are not constant which indicates that the stoke’s  model  of  continuous  solvent  structure  is  not  valid  for  the  system. The walden products (Λ0η) for the three electrolytes follow the order

                             CdSO4 > FeSO4 > CuSO4

      The walden products of CuSO4 only show positive temperature coefficient almost every solvent composition except 10% of dioxane-water mixture. This result shows that CuSO4 has the greatest    structure making character than FeSO4 and CdSO4.

The values of aK  are closer to the distance of closest approach, aJ and the values  of  aK  as  well  as  aJ for all the three electrolytes much larger than the sum of their lattice radii which indicates that  the solvent molecules enter  into  the  structure  of  the  ion – pairs  giving  rise  to solvation   and formation of solvent separated ion pairs. The  enhanced  electric  effect  due  to  the  double  charges on each  ion  and   the  small  size of Cu2+ gives  rise  to  considerable  polarization  to  a  number .

 Capture

ABSTRACT

 Ion-association constant (KA), distance of closest approach (aJ) and  thermodynamic parameters for several electrolytes  namely ferrous  sulphate, copper  sulphate  and  cadmium  sulphate  were  calculated  from their conductance data in  dioxane- water  mixtures  of  varying compositions  at  temperature of 250C, 300C, 350C and 400C. The values of ion-association constants are increased with increase of dioxane content and it also increased with increase of temperature. The standard Gibbs free energy, entropy and enthalpy for the reaction M2+ + SO42- = M2+ SO42- were calculated from the temperature dependence of   the ion-association constant. The standard free energy of transfer (G0t) from water to dioxane–water mixtures was calculated. The  electrostatic  and  non-electrostatic  contributions  to  the  transfer  free  energy  change, the  free  energy  of   transfer  of  individual ions  in  different  solvent  mixtures  have  been  calculated. The solvated ionic radii   have also been calculated. The distance closest of approach (aJ) of each solvated ion has been calculated. The walden products of the electrolytes in different solvent compositions were evaluated

 

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