Electrochemistry: Lead Acid Battery

Computer-Interfaced Experiments - Voltage Measurement

Electrochemistry
Lead Acid Battery (Model)

Objectives: Charging and Discharging of the Battery, Determination of the Capacity and the Battery Efficiency

Peter Keusch

Datalogging and data analysis using the Program "Measuring and Evaluating"
and the Analog-Digital-Converter CASSY-E - LEYBOLD DIDACTIC

German version

Chemicals:
sulfuric acid 20%

Apparatus:
glass trough 100 mm × 50 mm × 120 mm
two lead plates 76 mm × 40 mm × 1 mm
a pair of electrode mounting plates (with sockets)
DC voltage source
ammeter
voltmeter
slide rheostat 100 W
switcher
path cords

Hazards and safety precautions:

Sulfuric acid 20 % is harmful if swallowed. Corrosive.

Safety glasses and protective gloves required.

Theoretical background

Preparation of the experiment:

A glass trough filled with 20% sulfuric acid is fitted with two lead plates (thoroughly cleaned using steel wool). The plates are arranged in such a way that the distance between them is approx. 3 cm. The surface of the electrodes immersed in the acid is approx. 40 cm ².

The cell is charged by connecting it to a power source with a slide rheostat and an ammeter in the circuit. A direct current of 0.5 to 1 A is passed through the cell. The 'gassing' of the lead accumulator (decomposition of water) indicates the end of the charging process. The DC voltage source is switched off. The lead plate connected to the positive terminal of the voltage source is brown in color (PbO₂) while the plate used as cathode is grey in color (Pb) (Fig. 1). The current is allowed to pass an equivalent long time in reverse direction through the electrolyte. The coloring of the lead plates is inverted.

Fig. 1: Charging of the battery
Fig. 2: Discharging of the battery

Charging:
The positive terminal of the voltage source is connected via the slide rheostat and the ammeter to the "PbO₂"-electrode. The Pb-electrode is connected to the negative terminal of the voltage source. The circuit is switched on and the slide rheostat adjusted such that a constant current of 50 mA flows through the circuit. When a uniform gassing occurs at the two electrodes, the voltage source is switched off.

Discharging:
The "PbO₂"-electrode is connected to the Pb-electrode via an ammeter (the terminals are changed), a slide rheostat, and a switch. The switch is turned on and the slide rheostat is adjusted such that a constant current of 50 mA flows through the circuit in the opposite direction to that during the charge process (Fig. 2).

'Forming process': The battery is put through a series of charging and draining cycles. After the above procedure has been repeated 6 times, the battery has reached a maximum capacity. The battery is operational for the following experiments.

Experimental procedure:

The voltmeter is replaced by the CASSY INTERFACE.

The cell is connected to the input B of the INTERFACE.

Matching of the program 'Multimeter':
In the program 'Measuring and Evaluating' the subprogram 'Multimeter' is activated and under the menu item <F3> 'Select measur. quantities'®'Reselect channel B' the quantity 'Voltage DC' is selected.
CASSY indicates a voltage of 2.2 V.

Charging of the battery:
The cell is charged at a constant current of 100 mA. The change in voltage is recorded at a 2 second interval.

Fig. 3: Real time graph voltage changes during the charge process

Fig. 3 shows that the voltage increases slowly (within approximately 150 seconds) during the course of charge. Afterwards the voltage rises within a couple of seconds to 2.6 V. After 300 seconds the appropriate value is about 2.8 V.

Discharging of the battery:
At first, the cell is discharged at a discharge current of 100 mA. Afterwards the re-charged battery is discharged at 200 mA and 300 mA, respectively.

A direct comparison of the measurements (Fig. 4) is allowed in an overlay mode that may be activated by switching to <F8> 'Disc operations'®'Multigraph on'. The desired series of measurements are selected individually, in order to represent them together in the main menu under <F6>'Evaluate in graph'. Condition for a successful overlay is a identical labelling of the axes.

discharging

Fig. 4: Multigraph screen voltage changes during the discharge of the cell
discharge currents: 100 mA (1) 200 mA (2) 300 mA (3)

At the beginning of the discharge, the voltage declines slightly. Afterwards the voltage remains constant for some time, until it suddenly decreases within a couple of seconds. At a voltage of 1.6 V the battery is to be regarded as discharged. The discharge time is found in the data table.

	I ₀ [ mA ]	t (discharge) [ s ]
Run 1	100	174
Run 2	200	98
Run 3	300	56

Tab. 1: Discharge time t (discharge)

Data analysis:

In order to determine the electrical energy E _el supplied by the cell during the discharge process, the integral from t = 0 to t (discharge) must be calculated:

E _el (discharge) = I ₀ (discharge) · ò U (cell) dt

ò U (cell) dt is represented by the appropriate area below the appropriate graph.

After the switching to <F9> one enters the number of the graph. By means of the key combinations <Strg> <®> and <Strg><¬> in the plot of I versus t is highlighted the region of the curve between the start of the measurement and the point where the battery is practically 'dead'. By pressing the function key <F5> and by entering the graph number the appropriate area is colored. The 'integral' for the marked area is displayed by pressing <Alt><F5 > and by the input of the appropriate graph number (Fig. 5).

Fig. 5: Multigraph screen determination of òU(cell)dt
Discharge current: 100 mA (1) 200 mA (2) 300 mA (3)

	I ₀ [ A ]	area V · s	E _el [ J ]
Run 1	0.1	329.6	32.96
Run 2	0.2	181.3	36.23
Run 3	0.3	99.3	29.79

Tab. 2: Electrical energy E _el (discharge)

For discharging the cell, defined initial currents I ₀ are adjusted by the variable rheostat. Thus initial voltages U ₀ are generated that correspond to the currents I ₀. The values
for U ₀ are found in the data table.

	I ₀ [ mA ]	U ₀ [ V ]
Run 1	100	1.945
Run 2	200	1.917
Run 3	300	1.832

Tab. 3: Initial currents and initial voltages when discharging

The time-dependent currents I (t) during the discharge process can be calculated with the following equation

I (t) = U · I ₀ / U ₀

Determination of the Battery capacity

Matching of the program 'Multimeter':
The program 'Measuring and Evaluating' permits not only an overlay of individual series of measurements, but also a conversion of the measured values. In the subprogram 'Multimeter' a formula editor is provided, in which the measured values can be integrated into a formula. Thus the capacity of the lead accumulator can be determined. Using the instruction <F4>'Automatic/Param./Select formula' a submenu opens, permitting the entering of a formula. For the 'Physical symbol' I is enterted. mA stands for 'Physical unit' . The 'No. decimal places' is set to 3 and the beginning of the formula I(n,t,U) = is completed by entering e.g. U · 100 / 1.945 (run 1).

After switching to <F7> 'Select representation', the x-axis is labelled with t and the y-axis with I. The y2-axis is switched off.

A direct comparison of the series of measurements processed is allowed again using the overlay mode (see above).

Battery capacity is determined by the amount of electrical energy the battery can deliver over a certain period of time and is normally measured in Ampere hours (Ah).

As a result of integration of the current I (t) over the discharge time the battery capacity Q can be determined.

Q = ò I dt

Q is represented by the appropriate area below the appropriate graph in Fig 6.

Fig. 6: Multigraph screen plot of I (t) versus t, determination of the battery capacity Q = ò I dt

	I ₀ [ mA ]	Q [ mA · s ]
Run 1	100	17110
Run 2	200	18910
Run 3	300	16259

Tab. 4: Battery capacity Q

Battery charge/discharge efficiency

Fig. 7: Determination of the area below the charge curve

The area below the charge curve is 759.4 V · s. The charge current is 100 mA. Thus the electrical energy E _el (charge) results in 75.94 J.

Battery charge / discharge efficiency = E _el (discharge) / E _el (charge)

	Discharge current I ₀ [ A ]	E _el (discharge) [ J ]	E _el (charge) [ J ]	Battery efficiency
Run 1	0.1	32.96	75.94	0.43
Run 2	0.2	36.23	75.94	0.48
Run 3	0.3	29.79	75.94	0.39

Tab. 5: Battery charge / discharge efficiency

References:
Computergestützte Experimente Elektrochemistry: Edison Cell (Iron-Nickel-Battery) - Model
Messungen zum Laden und Entladen eines Modell-Bleiakkumulators (Download)
Sealed Lead Acid Battery Application

Index of CASSY Experiments