# The Conductance Of Solutions Biology Essay

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In this experiment, we shall be concerned with electrical conduction through aqueous solutions. Water itself is not a good conductor of electricity, but presence of ionic species in form of solution increases its conductance. The conductance of such a solution depends on the nature of the ions present and the concentration of the same ions. Also, conductance behavior as a function of concentration is different for weak and strong electrolytes. Atkins and Paula note that both weak and strong electrolytes must be studied at a number of different dilution concentrations, and from the data obtained, the ionization constant can be determined through calculations (2009).

## Theory

All electrolytic solutions obey Ohm's law as do the metallic conductors. Therefore, the current I passing through a certain body is proportional to the existing potential difference E; E/I = R. R is the resistance of that body in ohms. Thus, conductance, L, is defined by the reciprocal of resistance.

L = 1/R (1)

The units are ohms-1. The conductance of a given uniform body with a cross sectional area is proportional to the cross section area and inversely proportional to its length. This has been shown using the equation below:

L = LA/l or L =1/R*l/A = k/R. (2)

Where L represents the specific conductance in ohm-1 cm-1. Thus, the reciprocal of resistivity gives specific conductance. To determine the specific conductance of a solution in a cell with arbitrary dimensions and design, you first determine the cell constant k by measuring the resistance of that solution which has known specific conductance. For calibration purposes, 0.02N potassium chloride can be used whereby; L is equal to 0.002768 ohm-1 cm-1 at room temperature. Once the cell constant has been obtained, then specific conductances can be obtained through calculations using the experimental resistances obtained.

Specific conductance L depends on the mobilities and the concentration of the ions present in the solution for a single electrolyte giving ions A+ and B+, and assuming that they have an alpha ionization at a solute concentration c in equivalents per liter, and then you get the following equation:

L = αcF/1000(UA+ + UB-) (3)

Where U's are the true ionic mobilities and F is the faraday constant. Thus, its convenient to define a new quantity, the equivalent conductance É… by

É… =1000L/c (4)

Comparing equations 3 and 4, we find that

É… = Αf (UA+ + UB-) (5)

This conductance is sometimes described as actual conductance of that volume of solution which contains one equivalent weight of solute when placed between parallel electrodes 1 cm apart with a uniform electric field within them. The ionized fraction is unity at all concentrations for a strong electrolyte. Thus, É… is a roughly constant which varies to some extent depending on the changes in mobilities with concentration but approaching a finite value É…0 at infinite dilution. This can be shown by the following equation:

É… = É…0 (1 - B √c) (6)

Using this relation, É…0 for strong electrolytes can be determined experimentally by measuring conductance as a function of concentration of the solutions. At infinite dilutions, ions act independently hence, making it possible to express É…0 as the sum limiting conductances of the separate ions.

É…0 = ÊŽ0+ + ÊŽ0- (7)

É… varies greatly for weakly ionized substance with concentration because the degree of ionization varies greatly withconcentration. The equivalent of conductance must approach a finite value at infinite dilution É…0, which corresponds to the sum of the limiting ionic conductances. Practically, it is not possible to determine the limiting value by simply extrapolating the the É… values obtained with the weak electrolyte itself. However, one can deduce É…0 values from a strong electrolyte using equation (7). For very weak electrolytes, the ionic concentration is minute and the effect of ion attraction on mobility of the same is slight. Thus, we can make an assumption that the mobilities are independent of the concentration and from this, we obtain the following expression:

α ≈ É…/ É…0 (8)

its possible to get the actual degree of ionization of a weak electrolyte at concentration c, if one measures É… of a weak electrolyte at that concentration cand calculates É…0 from the conductivity data for strong electolytes as described above.

Therefore, the equilibrium constant for a weak electrolyte can be calculated if one knows the concentration c of that weak electrolyte, HAc, its degree of ionization α, the concentration of H+ and Ac - ions and unionised HAc. This gives the following expression:

K c = {(H+)(Ac-)/(HAc) = c α2/(1 - α) (9)

Thus, equilibrium Kc can be determined given appropriate data.

## Materials and Reagents

Volumetric flasks, analytical balance, pipettes, 0.02 M potassium chloride, 0.02 M potassium acetate, hydrochloric acid, Erlenmeyer flasks, phenolphthalein indicator, various pipettes, and standardized 0.1 M NaOH.

## Procedure

Several solutions were made and diluted with double DI water. 200 ml of the following solutions were made using a volumetric flask and an analytical balance: 0.02 M potassium chloride and 0.02 M potassium acetate. Using the above solutions provided together with acetic acid and hydrochloric acid, 100 ml of each of the following solutions was made: 25 to 100, 20 to 100, 10 to 100, and 5 to 100 for a total of 16 diluted solutions. Each was marked with a sharpie and tightly capped. The pipettes were rinsed before dispensing the solutions. In order to determine the actual molarities, there was need for titration to be done. Erlenmeyer flasks, phenolphthalein indicator, various pipettes, and standardized 0.1 M NaOH were provided.

The water bath was heated to 25&deg;C and the solutions thermostated a few times before being tested. Conductivity cells and meters were obtained and I familiarized with its operation. Then they were used to measure the conductance, G, of each of the solution studied. In addition, the conductance of the double DI water was determined. The cells were then rinsed at least twice with the solutions to be tested and then filled so that the black electrode plates were submerged. The readings were taken after they stabilized. The solution was discarded and the same repeated with the next most concentrated. Care was taken when switching on by rinsing the electrodes severally with the new solution.

## Results

Weight of potassium acetate used: 0.4907g

Weight of potassium chloride used: 0.3728g

Table 1: Results of various concentrations of KCl, HCl and KAc and their conductivity values in milliseimans (mS)

Solution #

Conductivity (G) in mS

Specific Conductance (L)

Equivalent conductance

KCl 5

1.379

0.095

254.828

KCl 10

2.77

0.191

512.339

KCl 20

5.39

0.371

995.172

KCl 25

6.76

0.466

1250.000

KCl stock

24.9

1.716

4603.003

HCl 5

4.63

0.319

855.687

HCl 10

9.21

0.635

1703.326

HCl 20

17.96

1.238

3320.815

HCl 25

23.1

1.592

4270.386

Acetic 5

0.814

0.0561

114.326

Acetic 10

1.156

0.0797

162.421

Acetic 20

1.656

0.114

232.321

Acetic 25

1.847

0.1273

259.425

KAc 5

1.072

0.0739

150.601

KAc 10

2.12

0.146

297.534

KAc 20

4.18

0.288

586.917

KAc 25

5.19

0.358

729.570

KAc stock

0.0186

0.00128

2.609

## Correction for K value

K (Sm-1) = 14.984c - 9.84c3/2 + 5.861c2logc + 22.89c2 - 26.42c5/2

## Calculation of the cell constant

Cell constant (k) = L * R where L is the specific conductance and R is the Resistance

0.002768 * 24.9 = 0.06892

## Calculation of specific conductance of each solution

Cell constant can be noted as G*, so specific conductance = G*(K)*G

I.e. 0.06892 * 1.379 = 0.095

As shown above, using this relation, É…0 for strong electrolytes can be determined experimentally by measuring conductance as a function of concentration of the solutions. Also, given that the cell constant and the specific conductance of each solution are known, the degree of ionization of the weak electrolyte can be calculated if the concentration of the same is known. Also, given the conductivity of the various concentrations of the solutions made during the experiment, equivalent conductance of each concentration was determined as shown in the above table. É… varies greatly for weakly ionized substance with concentration because the degree of ionization varies greatly withconcentration. Wright argues that the equivalent of conductance must approach a finite value at infinite dilution É…0, which corresponds to the sum of the limiting ionic conductances (2007). Practically, it is not possible to determine the limiting value by simply extrapolating the the É… values obtained with the weak electrolyte itself.

## Work Cited

Atkins, P. W., and Julio Paula. Elements of physical chemistry. 5th ed. Oxford: Oxford University Press, 2009.

Garland, Carl W., Joseph W. Nibler, and David P. Shoemaker. Experiments in physical chemistry. 8th ed. Boston: McGraw-Hill Higher Education, 2009.

Wright, Margaret Robson. An introduction to aqueous electrolyte solutions. Chichester, England: John Wiley, 2007.