Determination Of The Conductance Of Strong And Weak Electrolyte

Experiment 5: Determination Of The Conductance Of Strong And Weak Electrolytes

Objective 1.

To measure the conductance of potassium chloride, hydrochloric acid, sodium chloride and sodium acetate.

2.

To determine the dissociation constant of acetic acid.

Introduction Pure water does not conduct electricity, but any solvated ionic species would contribute to conduction of electricity. An ionically conducting solution is called an electrolyte solution and the compound, which produces the ions as it dissolves, is called an electrolyte. A strong electrolyte is a compound that will completely dissociate into ions in water. Correspondingly, a weak electrolyte dissolves only partially. The conductivity of an electrolyte solution depends on concentration of the ionic species and behaves differently for strong and weak electrolytes.

The conductance (L) is generally used for dealing with electrolytes and it is defined as the reciprocal of the resistance of the solution L (Ω-1) =

1 R

Equation 1:

Once R is known, the conductivity or specific conductance (X) may be obtained from X (Ω-1 cm-1) =

_d AR

Equation 2:

where A and d are the area and separation between the electrodes of the cell. The cell constant k of the conductivity cell is defined as k= d A

Equation 3: and therefore Equation 4:

X=kL

Thus, the molar conductivity Λ of an electrolyte solution is defined as Λ (Ω-1 cm2 mol-1) =

where

C

is

X C

the

= kL C molar

Equation 5:

concentration.

For weak electrolytes, the increase of molar conductivity with increasing dilution is ascribed to increased dissociation of the electrolyte molecules to free ions. The degree of dissociation (α) at a given concentration C is given by α= Λ Λ0

Equation 6:

where Λ0 is the molar conductivity in the limit of zero concentration.

For strong electrolytes, the molar conductivity is higher than those of weak electrolytes at high concentrations. As the electrolytes become dilute, the molar conductivities also increase but is less steep than for weak electrolytes. For strong electrolytes in dilute solution, the variation of molar conductivity with dilution can be expressed as Equation 7:

Λ = Λ0 – (A + B Λ0) C1/2

where A and B are constants.

For weak electrolytes, the values of Λ0 can be deduced from the limiting molar conductivities of strong electrolytes using Kohlrausch’s law. Alternatively, Λ0 and the dissociation constant of a weak electrolyte may be obtained from the Ostwald dilution

law 1 Λ

= _1 Λ0

+ CΛ kaΛ02

Equation 8:

Apparatus Conductivity meter, dilution flasks (100mL), pipette, burette and measuring cylinder.

Materials 0.2000 M potassium chloride solution, 0.1000 M acetic acid, 0.1000 M hydrochloric acid, 0.1000 M sodium chloride solution and 0.1000 M sodium acetate solution.

Experimental Procedures 1. Determination of cell constant 

The conductance (L) of 0.2000 M potassium chloride solution was measured.



The specific conductance (X) of this solution is 2.768 x 10-3 Ω-1 cm-1.

 The cell constant (k) was determined by using equation 6.

2. Measurement of conductance 

From the solution of acetic acid provided, successive dilution with conductivity water solution of 0.0500, 0.0250, 0.0125, 0.00625, 0.00312, 0.00156 and 0.00078 M were prepared.

 The conductance of these solutions was measured.  The procedure was repeated with hydrochloric acid, sodium chloride and sodium acetate.

 The conductance of water used was measured.

Results and Calculation Calculation of cell constant (k) Conductance of 0.2000 M KCl

= 1 / 49.59 = 0.0202 Ω-1

By using equation 6, Cell constant, k = X / L = (2.768 x 10-3 Ω-1 cm-1) / 0.0202 Ω-1 = 0.1373 cm-1

Table 1: Resistance (Ω) of four electrolytes -3

C (mol dm ) 0.1000 0.0500 0.0250 0.0125 0.00625 0.00312 0.00156 0.00078

CH3COOH 2883 3669 6440 8605 12395 18280 25100 44970

Resistance, R (Ω) HCl 31.91 63.79 122.70 243 472.44 940.88 1823.4 3569.8

NaCl 96.04 193.3 366.0 717.1 1438 2825 5451 10400

CH3COONa 166 297.9 600.5 1178 2577 4485 8975 17210

NaCl 0.0104 5.173 x 10-3 2.732 x 10-3 1.395 x 10-3 6.954 x 10-4 3.540 x 10-4 1.835 x 10-4 9.615 x 10-5

CH3COONa 6.024 x 10-3 3.357 x 10-3 1.665 x 10-3 8.489 x 10-4 4.207 x 10-4 2.230 x 10-4 1.114 x 10-4 5.811 x 10-5

Table 2: Conductance, L (Ω-1) of four electrolytes -3

C (mol dm ) 0.1000 0.0500 0.0250 0.0125 0.00625 0.00312 0.00156 0.00078

Conductance, L (Ω-1) CH3COOH HCl -4 3.469 x 10 0.0313 2.726 x 10-4 0.0157 -4 1.553 x 10 8.150 x 10-3 -4 1.162 x 10 4.115 x 10-3 8.068 x 10-5 2.117 x 10-3 5.470 x 10-5 1.063 x 10-3 -5 3.984 x 10 5.484 x 10-4 2.224 x 10-5 2.801 x 10-4

Table 3: Specific conductance, X (Ω-1 cm-1) of four electrolytes

-3

C (mol dm ) 0.1000 0.0500 0.0250 0.0125 0.00625 0.00312 0.00156 0.00078

Specific Conductance, X (Ω-1 cm-1) CH3COOH HCl NaCl -5 -3 4.762 x 10 4.302 x 10 1.430 x 10-3 -5 -3 3.742 x 10 2.152 x 10 7.103 x 10-4 2.132 x 10-5 1.119 x 10-3 3.751 x 10-4 -5 -4 1.596 x 10 5.650 x 10 1.915 x 10-4 1.108 x 10-5 2.906 x 10-4 9.548 x 10-5 7.511 x 10-6 1.459 x 10-4 4.860 x 10-5 -6 -5 5.470 x 10 7.530 x 10 2.519 x 10-5 3.053 x 10-6 3.846 x 10-5 1.320 x 10-5

CH3COONa 8.271 x 10-4 4.609 x 10-4 2.286 x 10-4 1.166 x 10-4 5.776 x 10-5 3.061 x 10-5 1.530 x 10-5 8.020 x 10-6

Table 4: Molar conductivity, Λ (Ω-1 cm2 mol-1) of four electrolytes C (mol cm-3) -4

1.0 x 10 5.0 x 10-5 2.5 x 10-5 1.25 x 10-5 6.25 x 10-6 3.12 x 10-6 1.56 x 10-6 0.78 x 10-6

C1/2 (mol cm-3)1/2 0.01 7.071 x 10-3 5.000 x 10-3 3.536 x 10-3 2.500 x 10-3 1.766 x 10-3 1.249 x 10-3 8.832 x 10-4

Molar conductivity, Λ (Ω-1 cm2 mol-1) CH3COOH HCl NaCl CH3COONa 0.4762 43.0210 14.3000 8.2711 0.7484 43.0475 14.2059 9.2179 0.8528 44.7596 15.0055 9.1457 1.2768 45.2039 15.3173 9.3243 1.7728 46.4990 15.2768 9.2419 2.4074 46.7717 15.5775 9.8119 3.5064 48.2680 16.1462 9.8064 3.9141 49.3098 16.9255 10.2819

Table 5: 1 / Λ and C Λ values for acetic acid 1 / Λ (Ω cm-2 mol) 2.100 1.336 1.173 0.783 0.564 0.415 0.285 0.255

C Λ (mol cm-3) (Ω-1 cm2 mol-1) 4.762 x 10-5 3.742 x 10-5 2.132 x 10-5 1.596 x 10-5 1.108 x 10-5 0.751 x 10-5 0.547 x 10-5 0.305 x 10-5

Calculation of Λ0 for CH3COOH using Kohlrausch’s law From Figure 1,

Λ0 (HCl)

= 53.0 Ω-1 cm2 mol-1

Λ0 (NaCl)

= 24.5 Ω-1 cm2 mol-1

Λ0 (CH3COONa)

= 11.5 Ω-1 cm2 mol-1

By using Kohlrausch’s law, Λ0 (CH3COOH)

= Λ0 (CH3COONa) +Λ0 (HCl) – Λ0 (NaCl) = (11.5 + 53.0 – 11.5) Ω-1 cm2 mol-1 = 40.0 Ω-1 cm2 mol-1

Calculation of degree of dissociation (α) of CH3COOH at the concentrations of 0.0500, 0.0125 and 0.00156 M At 0.05000 M, Λ = 0.7484,

α = Λ / Λ0 = 0.7484 / 40.0 = 0.0187

At 0.01250 M, Λ = 1.2768,

α = Λ / Λ0 = 1.2768 / 40.0 = 0.0319

At 0.00156 M, Λ = 3.5064,

α = Λ / Λ0 = 3.5064 / 40.0 = 0.0877

Calculation of dissociation constant ka of CH3COOH α2C 1-α = (0.0187)2 (0.05 mol dm-3) 1 – 0.0187 = 1.782 x 10-5 M

ka =

Calculation of ka and Λ0 from Figure 2 Gradient of graph, __1 = _(2.14 – 0.30) Ω cm-2 mol _ 2 kaΛ 0 (4.75 – 0.60) x 10-5 Ω-1 cm-1

= 44337.35 mol cm-3 = 4.4337 x 107 mol dm-3 kaΛ 0 = 1 / (4.4337 x 107 mol dm-3) 2

= 2.2554 x 10-8 mol-1 dm3 The intercept at CΛ = 0, 1 = 0.04Ω cm-2 mol Λ0 Λ0 = 1 / (0.04 Ω cm-2 mol) = 25.0 Ω-1 cm2 mol-1 = 25.0 Ω-1 (0.1dm)2 mol-1 = 0.25 Ω-1 dm2 mol-1

Equilibrium constant, ka = kaΛ20 /Λ20 = 2.2554 x 10-8 mol-1 dm3 / (0.25 Ω-1 dm2 mol-1)2 = 3.609 x 10-7 Ω2 mol dm-1 According to Atkins’ Physical Chemistry (8th edition) page 1007 Table 7.4, the theoretical value of dissociation constant of acetic acid (ka) is 1.4 x 10-5 M. From calculation, the experimental value of ka is 1.782 x 10-5 M. Percentage error of ka = 1.782 x 10-5 M – 1.4 x 10-5 M 1.4 x 10-5 M

x 100%

= 27.29 % According to lab manual Component A page 19, the theoretical value of molar conductivity in the limit of zero concentration of acetic acid, Λ0 = Λ+ + Λ= 34.96 + 4.09 = 39.05 mS m2 mol-1 From calculation, the experimental value of Λ0 is 40.0 Ω-1 cm2 mol-1(from Kohlrausch’s law). Percentage error ofΛ0 = (40.0 – 39.05) Ω-1 cm2 mol-1 39.05 Ω-1 cm2 mol-1

x 100%

= 2.43 % Discussion The

molar

conductivity

is

found

to

vary

according

to

the

concentration. One reason for this variation is that the number of ions in the solution might not be proportional to the concentration of the electrolyte. For instance, the concentration of ions in a solution of a weak acid depends on the concentration of the acid in a complicated way, and doubling the concentration of the acid added does not double the number of ions. Secondly, because ions interact strongly with one another, the conductivity of a solution is not exactly proportional to the number of ions present.

The concentration dependence of molar conductivities indicates that there are two classes of electrolyte. The characteristic of a strong electrolyte is that its molar conductivity depends only slightly on the molar concentration. The characteristic of a weak electrolyte is that its molar conductivity is normal at concentrations close to zero, but falls sharply to low values as the concentration increases.

The solution conducts electricity through motion of the ions under the effect of an electric field. At high concentrations, each ion is surrounded by other ions, both positive and negative. The field affecting any particular ion changes slightly because of these surrounding ions. At infinite dilution, the distance between nearest neighbor ions is large, and only the effect of the applied electric field is felt by individual ions. This is the reason for extrapolating the data to infinite dilution.

The conductivity of any particular ion will also be affected by the ease with which the ion can more through the water. Hence different ions should contribute differently to the total measured conductivity. The ease with which any ion moves through the solution depends on considerations such as the total charge and the size of the ion; large ions offer greater resistance to motion through the water than small ions.

Conclusion The conductance (L) of potassium chloride, hydrochloric acid, sodium chloride and sodium acetate range from 9.615 x 10-5 Ω-1 to 0.0104 Ω-1. The experimental value of dissociation constant of acetic acid (ka) is 1.782 x 10-5 M. The experimental value of molar conductivity of acetic acid (Λ0) is 40.0 Ω-1 cm2 mol-1

Precaution 1.

Always rinse the electrode with deionized water before use.

2.

Blot the inside of the electrode cell dry before the next measurement to avoid water droplets diluting or contaminating the sample to be tested.

3.

Before taking readings, always shake the electrode briefly to release possible air bubbles trapped in the electrode.

4.

Ensure that the electrode surfaces in the elongated cell are completely submerged in the liquid.

5.

Always stir to ensure that the solution is homogenous during the measurement.

References 1.

http://www.csun.edu/~jeloranta/CHEM355L/experiment4.pdf

2.

http://www-ec.njit.edu/~grow/conductivity.htm

3.

http://wwwchem.uwimona.edu.jm:1104/lab_manuals/c10expt19.html

4.

Atkins’ Physical Chemistry , Peter Atkins and Julio de Paula, (8th edition), Oxford New York