Electrical Cells and Batteries

Introduction

In it's most simple form a battery can be regarded as a pump that provides the energy to move charge around a circuit.

In order to provide a potential difference, or electro-motive force (EMF) a store of energy is required. One such method is a battery or cell. The common usages of the term battery is any device that converts chemical energy into electrical energy. However, strictly speaking, the term battery is used when several electrical cells are connected together to provide a source of a potential difference in a circuit. If it is just a single chemical source then it is called a cell.

History

In 1791, Galvani noticed that a circuit created with two different metals, when touched on the ends of the leg of a dead frog, would cause it twitch. The two metals were creating an electric current within the frog's leg, causing the muscles to contract. Early batteries were an improvement of this method transfering chemical energy into electrical energy.

The first battery was invented in 1793 by Alessandro Volta. Just as the two different metals touching the wet skin of a frog's leg, caused an electrical current to flow, early batteries increased the voltage that could be produced by stacking a pile of discs made from silver and zinc sandwiched between paper soaked in a salt water solution as shown in Figure 2. In honour of Volta, we use the Volt as the unit of potential difference and EMF.

Battery Operation

Why does this produce electricity? The flow of current can be understood as the flow of ions from the more reactice metal to the less reactive metal. The ions moving from one electrode to the other creates an electrical charge which is neutralised by the flow of electrons across the wire.

Before considering the reaction of two metals, consider what happens when we place a single metal electrode in an electrolyte. Some of the metal atoms in the electrolyte go into solution as ions while the remaining electrons create a negative charge on the metal. The separation of ions and electrons leads to a separation of charge. However, this build up of charge cannot continue indefinitely because as the negative charge builds up in the metal it becomes increasingly difficult for positive metal ions to go into solution. A similar build up in positive charge in the electrolyte also prevents the build up of charge. This degree of charge build up depends on the metal and represents the work required to separate electrons from the ions. This is known as the electroneutrality principle

Similarly, if a copper strip is placed in an aquaous Copper(II)Sulfate solution the copper will also lose ions. These reactions are often written as Cu | Cu⁺² this is the half-cell reaction.

The tendancy for Zinc to lose ions is greater than that of Copper. When the two cells are joined together (using a copper wire to connect the electrodes and porous barrier that allows the ions to pass known as a salt-bridge connect the elecrolytes, the build up of electrons on the zinc will flow to through the wire onto the copper.

The copper ions in the electrolyte gain electrons and become copper atoms.

Thus the reaction can be written,

Zn | Zn²⁺ | | Cu²⁺ | Cu

To continue the reaction, the charge must be removed. This can be acheived by coupling a second reaction which uses the electrons in the metal to convert the ions in the electrolyte into a metal. For a more specific example, consider a zinc electrode in an electrolyte of Copper(II)Sulphate solution.

The loss of electrons by the Zinc is known as oxidation. Zn(s) → Zn²⁺ + 2e^-.(1)

A wire connecting the Zinc electrode to a Copper electrode, allows the electrons to flow to the Copper electrode. Copper ions in the copper sulphate solution take up the electrons and become atoms of copper on the copper electrode. The gaining of electrons by ions is known as reduction

Cu⁺² + 2e^- → Cu(s).(2)

The net reactions is then,

Zn(s) + Cu²⁺ → Cu(s) + Zn²⁺

When the two electrodes are joined by a wire the charge stored can flow and the electrons combine. The simplest kinds of battery have two conductors made of different materials which are partially emersed in a solution which allow the electrons and ions to flow freely known as an electrolyte.

At the copper electrode (cathode), the acid dissolves the copper metal producing hydrogen gas, H⁺. The reaction will continue until the supply of zinc is used up. The electrons, with their negative charge, are attracted to the copper electrode which causes a current to flow. One of the problems with this cell is that the current stops flowing after a short time because the hydrogen bubles block the current.

Cells using aqueous (containing water) electrolytes are limited in voltage to less than 2 Volts because the oxygen and hydrogen in water dissociate in the presence of voltages above this voltage. Lithium batteries (see below) which use non-aqueous electrolytes do not have this problem and are available in voltages between 2.7 and 3.7 Volts. However the use of non-aqueous electrolytes results in those cells having a relatively high internal impedance.

Activity Series

In the activity series, a metal will give up electrons to any other metal which is below it on the activity series. Elements which gain electrons are called negative irons. Elements which lose electrons are called positive ions. Any more active metal will give up electrons to a less active metal. This will serve to protect the less active metal from corrosion. For example, steel ships often have bars of zinc attached to the sides of the ship. As the steel is corroded by the oxygen of water and air, the zinc will give up electrons to the steel and protect it from corrosion.

Batteries in Circuits

Just like any other electrical component, individual cells can be placed in series or parallel. In series their voltage sum to create a battery with a higher voltage but the current remain the same as in a single cell. In parallel, the batteries have the same voltage but the current is summed to create a battery with a higher current.

Batteries and Internal Resistance

A real battery has internal resistance, r, which lowers the voltage when the cell is connect to a load. If you try to send too much current through a battery, the internal resistance will convert the battery’s own chemical potential energy into thermal energy. The battery will get warm and electrons will leave the negative electrode with relatively little energy.

The EMF of the battery is given by E and represents the voltage when the battery is open circuit. If the battery had no internal resistance, the current flowing in the circuit would be given by Ohm's law, I =E/R where R is the resistance of the load.

The internal resistance adds to the total resistance of the circuit. If we call the new total resistance of the cell and load, R_eq = r + R

Then current is then I= E/R_eq = E/(r + R).(3)

Since R_eq is larger than R the current flowing in the circuit is reduced. Therefore, if we are making a cell we want the internal resistance to be a small as possible.

What is the voltage across the resistor R? Clearly it is not the same as the EMF because of the internal resistance. We know that the EMF, E = Ir + IR. We also know that the voltage across the resistor R is IR. Rearranging these two equations we find the voltage in terms of E, r and R.

V = E - Ir (4).

This equation also shows that if we draw a lot of current from the circuit we see the voltage reduces. A good example of this is a car starting with its lights switched on. When the ignitioin key is turned, the electric starter-motor uses a lot of current before it starts to turn. The current for this is supplied by the car battery, which also powers the lights. The voltage available for the lights is reduced at this moment and the lights dim as the car starts. They quickly become bright again once the engine is turning over because less current is required by the starter motor. (When the car has started no current is drawn by the starter motor because it disengages from the engine.)

Metal	Metal Ion	Reactivity
Lithium	Li+	Most Reactive
Potassium	K+
Calcium	Ca2+
Sodium	K+
Magnesium	Mg2+
Aluminum	Al3+
Manganese	Mn2+
Zinc	Zn2+
Chromium	Cr2+, Cr3+
Iron	Fe2+, Fe3+
Lead	Pb2+
Copper	Cu2+
Mercury	Hg2+
Silver	Ag2+
Gold	Au+,Au3+	Least Reactive
Platinum	Pt2+

Power and Efficiency

The power output of the battery is given by P_E = I²R(5)

But from equation (3), I = E/R_eq = E/(r + R), therefore, P = E²R/(r + R)²(6)

Similarly, the power given off as heat by the battery to due to internal resistance is P_r = I²r = E²r/(r+R)²(7)

The efficiency, η of the circuit is the ratio of the power actually produced by the battery with its internal resistance to the power supplied by the source, P₀. P₀ = I E

The power generated is given by I V_R, where V_R is the voltage across the resistor R.

η = P_E/P₀ = IV_R/IE = R/(r + R)

The smaller the internal resistance, the closer the efficiency, η will be to its maximum value of 1.

If we plot the power tranferred to a load resistance R against the increasing R along with the efficiency we find that the maximum power is transferred by the battery when R = r. This is a very important result and find applications in many electrical devices is known as Jacobi's theorem

To check this is true we can also differentiate the expression for the power P against R and set it equal to zero to find the maximum value of R.

dP/dR = -dE²/dR (r + R)^-2 + d(R+r)^-2/dR (E²R) = 0

E²/(r + R)² - 2 E²R/(r + R)³ = 0

(r + R)³ - 2R(r + R)² = 0

(r + R) - 2R = 0

r - R = 0 or r = R

While the power transferred may be at a maximum, the efficiency at this percent is only 50%. The higher the load resistance, the greater the efficiency. In practise the exact loading of the circuit is dependent on the application, a good voltmeter has an extremely high-resistance so that the power transmitted is as small as possible.

Types of Battery

Over the years, progress in battery technology has been rather slow but the need for small more powerful batteries in the many small electrical items we carry around with us has driven research into higher power, longer lasting batteries.

Zinc Carbon

This is commonly known as the Leclanché Cell and despite being the oldest type of battery it is still the most commonly used as it is very low-cost. Traditional Zinc Carbon batteries cannot be reused when their chemical energy has been released

Alkaline Cells

Alkaline chemistry is used in common Duracell and Energizer batteries, the electrodes are zinc and manganese-oxide, with an alkaline electrolyte. Alkaline batteries can be re-used upto 100 times with the correct type of battery charger. A normal battery charger must not be used to charge these batteries.

The active materials used are the same as in the Leclanché cell – zinc and manganese dioxide. However the electrolyte is potassium hydroxide, which is very conductive, resulting in low internal impedance for the cell. This time the zinc anode does not form the container; it is in the form of a powder instead, giving a large surface area.

Silver Zinc

Lightweight but expensive. Used in aeronautical applications.

Rechargable or Secondary Cells

Rechargeable batteries are rechargeable because the chemical reaction that leads to the flow of current is reversible by passing a current through the battery. The animation shows a battery undergoing charging and discharging. When the battery is charged the current can flow through a resistive load.

Lead-Acid

Lead acide batteries are used to provide large amounts of current for a relatively short time. They consist of plates of lead and lead oxide in a solution of sulphuric acid. Lead combines with SO₄ (sulphate) to create PbSO4 (Lead Sulphate), plus one electron. Lead dioxide, hydrogen ions and SO₄ ions, plus electrons from the lead plate, create PbSO₄ and water on the lead dioxide plate. As the battery discharges, both plates build up PbSO₄ and water builds up in the acid. The characteristic voltage is about 2 volts per cell, so by combining six cells you get a 12-volt battery.

half-reaction V	vs SHE
Pb + SO42- → PbSO4 + 2e-	.356
PbO2 + SO42- + 4H+ + 2e- → PbSO4 + 2H2O	1.685

Nickle Cadmium (Ni-Cad)

Nickle-Cadmium cells are the most common type of re-chargable battery. They have a high-energy density and a EMF of 1.2 V. They can be recharged more times than other types of rechargable batteries but unless they are fully discharged before recharging suffer from a memory effect which reduces their capacity to store charge.

Nickle-Metal Hydride (Ni-Mh)

Lithium Ion (Li-Ion)

Lithium is the most electronegative metal in the electrochemical series. It also has a low density so it is an atractive material for the anode of batteries. However, lithium is also very reactive with aqueous electrolytes producing hydrogen gas. Because of this it took many years to develop a stable electrolyte. Lithium batteries must be sealed from moisture and air due to the reactivity of lithium. Non-rechargable lithium batteries have been available since the 1980s with rechargable lithium batteries becoming widely available around 1995. Lithium-ion batteries can be recharged between 500 - 1000 cycles. The half-reactions are:

The following reactions take place upon discharge:

Anode: xLi⁺ + Mn₂O₄ → Li_xMn₂O₄

Cathode: Li_xC₆ → xLi⁺ + 6C + xe^-

Overall: Li_xMn₂O₄ + 6C → Li_xC₆ + Mn₂O₄

Lithium Polymer (Li-poly)

Lithium polymer batteries use a solid polymer electrolyte.