Physics 204, Spring 2011

Batteries

A battery is an arrangement of chemical reactants that allows, and in fact requires, electrons to pass through an external wire as the reaction proceeds. Reactions occur at two places that are spatially separated, but joined by the wire. In the absence of the wire, each reaction would lead to separation of charge that would quickly bring the process to a halt. With the wire to convey electrons the whole arrangement can remain electrically neutral as the reactions proceed. The spatially separated reactions that individually would separate charge are called “half-reactions”.

We will build a Daniell cell, the battery that powered the telegraph system in the 19^th century. The half-reactions are

The reduction potential in the first reaction is 0.34 V, meaning the copper ion lowers its energy in plating out by 0.34 eV per electron. The reduction potential in the second reaction is -0.76 V, meaning the zinc ion raises its energy by 0.76 eV per electron. In the Daniell cell, however, this half reaction goes in reverse: zinc metal goes into solution as zinc ions, lowering the energy by 0.76 eV per electron. In all, then, these two reactions lower the energy of the system by 1.10 eV for each participating electron. The system can thus do this much work on each electron that goes through the wire, and this energy is available for us to use.

The spatial separation is achieved by having copper ions only available to plate out at one of the electrodes, and zinc metal only available to go into solution at the other one. The copper electrode is bathed in a copper sulfate solution, and the zinc electrode is bathed in a zinc sulfate solution. As zinc ions dissolve, and as copper ions plate out, the zinc sulfate solution would become positively charged and the copper sulfate solution would become negatively charged. If there were not some way for charged ions to move to maintain electrical neutrality in the solution, this charge separation would halt the reactions. In the textbook’s description of the Daniell cell, the ion pathway is a “salt bridge”, a porous connection that doesn’t allow actual mixing of the two solutions. In our Daniell cells – and it is remarkable that this works! – the two solutions will be separated only by a meniscus, not even a permeable barrier, with the denser, supersaturated copper sulfate solution on the bottom. Be careful not to mix the solutions by jostling them. How would that degrade the operation of the battery? Of course the solutions will mix to some extent, so you will see the effect.

Making the battery: Pour in just enough copper sulfate solution (dark blue) to cover the copper metal at the bottom of the beaker, about 225 ml. If you splash some on the zinc electrode (the crow’s foot mounted near the top of the beaker) you will find it leaves a dark film on the zinc. What is this? Brush off the film, which you will find is not bonded to the zinc but is just loosely sitting on it.

Now, with as little mixing as possible, and very slowly, pour down the side of the beaker enough zinc sulfate solution to cover the zinc. The object is to form a liquid cell with two layers, copper sulfate solution on the bottom, and zinc sulfate solution on the top.

Galvanometer: To see if your battery can really generate current, connect it to a galvanometer. This is nothing but a coil of wire with a little magnet pivoted delicately inside it. If the coil carries current, it becomes an electromagnet, i.e., there is a magnetic field inside, and the suspended magnet aligns with the field, just like a compass needle. Try reversing the battery leads to see if the deflection of the galvanometer is now the other direction.

Voltage: Your battery will probably create a potential difference of only about 0.7 volt, because of the mixing of the solutions, and not the theoretically possible 1.10 volts. Use the multimeter to watch the voltage as a function of time and conditions. What happens when you clean the electrodes with the brush? (Try not to mix the solutions!)

Potentiometer: Connect the battery to the two ends of a nichrome wire and, using one end of the wire as a reference potential, measure the potential as a function of position along the wire. Is it a linear function? A quick estimate of voltage vs position is good enough – just record a few values rapidly, as the battery characteristics will probably be changing in time.

Resistivity: By Ohm’s law, the potential you measured is IR, where I is the current and R is the resistance. Carefully configure the multimeter as an ammeter and measure the current through the nichrome wire. Use the data above, together with the cross-sectional area of the wire to find the resistivity of nichrome.