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Effects of Ion Concentration on Equipotential Lines and Electric Field

Bucsit, Cyril David; Barrios Kyla; Manuel, John Rommel; Quintero, Ramon Paolo College of Engineering, University of the Philippines,

Diliman, Quezon City 1101, Philippines

Abstract An electric field’s magnitude may be obtained by using equipotential lines. In the experiment the effects of ionic concentration of a solution on the electric field produced by a charged object immersed in it were determined. Two electrodes were immersed in 0.16 M and 0.58 M NaCl solutions, and the voltages at various points were determined. It was found out that due to ion movement, the voltage between the two electrodes decreased, resulting to a decrease in the electric field’s magnitude. Although discrepancies in the procedure and data were present, the main objective of the experiment was still met

1. Introduction

An electric field is an electric property associated with each point in space whenever a charge is present at any form [1]. One of the ways to describe an electric field is its quantification, given by Equation 1,

���� � � ����� ��������

where ���� is the electric field and �������is the electric force exerted on a charge with charge ��. Measuring the magnitude of an electric field by experimental means is a very tedious process, since it involves

placing a test charge, say q, in a specific location and determine the electric force experienced by test charge q in that point. Nonetheless, a much simpler way to measure the magnitude of an electric field is by using equipotential lines. An equipotential line is an imaginary line around a charged object wherein the electric potential at each point of that line is the same. The magnitude of the electric field can be calculated using the equation below, [2]

������ � ����� � where ������ is the electric field magnitude, �� is the potential difference between two equipotential lines and �� is the perpendicular distance between the said equipotential lines.

An ionic solid, such as sodium chloride (NaCl), will be dissociated into its corresponding ions (Na+ and Cl-) when placed in water; and the resulting solution will be able to conduct electricity. The ability of a solution to conduct electric current is called electrolytic conductivity [3], given by

� � � ��

Where � is the electrolytic conductivity of the solution while � is its resistivity. However, the effects of a solution’s ion concentration on the magnitude of the electric field generated by

electrodes immersed in the solution are not known. The experiment aims to establish a relationship between the electrolytic conductivity, which is manifested by the ion concentration, and the magnitude of the electric field produced by two electrodes submerged in the solution, using equipotential lines.

2. Methodology The experimental setup consisted of an electrolytic tank, a disc and rod electrode, a sensing probe, a voltmeter,

and a power supply. Then, 0.58 M and 1.16 M NaCl solutions were prepared by dissolving 12.5 g and 25.0 g of iodized salt ( 7 99% NaCl), respectively, in 372 mL of tap water ( ¾ of the electrolytic tank). The rod and cylindrical electrodes were connected to the power supply, while the handheld probe was connected to the voltmeter. The setup is shown in Figure 1. The electrolytic tank was then filled with the 0.58 M NaCl solution.

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Figure 1. Setup for tracing equipotential surfaces. The iron stand is not

a part of the actual setup; rather, the probe was held by hand.

After the inspection of the setup, the disc and rod electrodes are placed at coordinates (0,5) and (0,-5), respectively. The power supply was plugged in, and then the probe was manually transferred from one grid box to another, measuring the electric potential for each grid box. After completing the data, they were examined for approximate similarities, which were then traced, forming the equipotential lines. The perpendicular distance from each equipotential line was then measured. Using Equation (2), the magnitude of the electric field, in V/cm, was calculated.

3. Results and Discussion

Using the potential values at each point, a V vs. (x,y) surface plot can be generated, as shown in Figure 2. The three surface plots correspond to three different ion concentrations.

Figure 2. V vs. (x,y) plots for electrodes immersed in: A. tap water, B. 0.58 M NaCl solution, C. 1.60 M NaCl solution

Based from Figure 2, the electric potential near the disc is higher than the potential near the rod, so the flow of charges is from the disc electrode to the rod electrode, since the natural tendency of charges is to flow from an area of higher potential to an area of lower potential. It can be concluded that the anode is the disc while the cathode is the rod. It can be seen in Figure 2 that as the ion concentration of the water used increases, the potential difference between the two electrodes decreases. This is primarily due to the movement of the ions in the solution. The Cl- ions travel to the disc electrode (anode) while the Na+ ions travel to the rod electrode (cathode), lowering the potential

A B

C

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difference between the two electrodes. As current passes through the electrodes, the Cl- ions are converted to Cl2 (chlorine gas), while the water molecules near the cathode are broken down into H2 (hydrogen gas). This explains the formation of a yellowish gas at the disc electrode and the formation of bubbles (H2) at the rod electrode. [3]

Also, the potential values for each point varies inversely with the ion concentration of the solution. When the ion concentration of the solution is high, its conductivity is also high. Based from Equation (3), the solution will have a low resistivity and low resistance. Assuming constant current, by Ohm’s Law (V = IR), the voltage reading will be low, as observed. The equipotential lines of the electrodes immersed in 0.58 M NaCl and 1.60 M NaCl solutions are shown in Figure 3.

Figure 2. left: Equipotential lines for the setup with 0.58 M NaCl; right: Equipotential

Lines for the setup with 1.60 M NaCl A lot of inconsistencies can be seen in the patterns of the equipotential lines. This is also due to the presence of the freely moving ions in the solution. Being charge carriers, the ions disperse through the entire system, making the equipotential lines less evident. Using Equation (2), the following values of electric field magnitude are obtained.

Table 1. Electric field magnitudes for tap water, 0.58 M and 1.60 M NaCl solutions

Tap water [4] 0.58 M NaCl solution 1.60 M NaCl solution x ∆l ������ x ∆l ������ x ∆l ������

0 0.90 cm 0.51 V/cm 0 0.25 cm 0.40 V/cm 0 4.30 cm 0.023 V/cm 2 0.90 cm 0.51 V/cm 2 0.27 cm 0.37 V/cm 2 4.20 cm 0.024 V/cm 4 1.00 cm 0.46 V/cm 4 0.30 cm 0.33 V/cm 4 3.30 cm 0.030 V/cm 6 1.80 cm 0.26 V/cm 6 0.43 cm 0.24 Vcm 6 3.00 cm 0.033 Vcm As compared to the obtained values when tap water was used, the potential values of the 0.58 M NaCl solution

are lower; the values of the 1.60 M solution is much lower. As stated earlier, when the ion concentration increases, the voltage reading decreases. Consequently, the value of the electric field magnitude will also decrease. Also, as the potential difference decreases, less work is done to move from one equipotential line to another.

Since no measurement is done in this experiment, the primary source of error would be parallax error. Most of the values of electric potential obtained are not precise. The handheld probe must have detected electric potential not

0.25 cm 0.43 cm

4.3 cm

4.2 cm

3.3 cm

3.0 cm 0.27 cm 0.30 cm

∆V = 0.1 V ∆V = 0.1 V

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at the corners of the grid boxes, but somewhere else. Failure to calibrate or improper calibration may have also been a source of error. These led to the erroneous measurement of the required parameters, affecting the outcome of the experiment to a significant degree.

4. Conclusion

When an ionic solid is placed in water, it is dissociated into its corresponding ions, which are free to move. As the concentration of the ions in the solution increases, the conductivity increases. Consequently, the resistance of the solution decreases, making its voltage low. Also, migration of the ions towards the electrodes decreases potential difference between them. As a result, the electric field magnitude decreases as well. Therefore, electric field magnitude and electrolytic conductivity are inversely related to each other.

This experiment has applications generally at everything which utilizes electric fields. This is most helpful in the analysis of various water samples. This procedure can be applied in analyzing the relative concentration of ions in the water samples. For the sample to be distilled (deionized), the voltage reading must be relatively high as compared to tap water. Otherwise, the water sample is not deionized and might contain potential health hazards. To prevent the repetition of errors which occurred in this experiment, future experimenters are advised to develop a way to accurately place the probe at the corner of the grid cube, optimizing accuracy and minimizing deviation from the expected results. Also, more time must be allotted for the experimental procedure to ensure that no part of the experiment will be compromised.

References 1. Young, H., University Physics, 12th ed., Addison-Wesley Publishing Co. USA (2007). 2. Physics Laboratory Manual, National Institute of Physics, University of the Philippines Diliman (2007). 3. Chang, R., Chemistry: The Essential Concepts, McGraw-Hill Co. (2008) 4. Petrucci, R.H., et al., General Chemistry: Principles and Modern Applications, Pearson Education Inc. (2011)