Using the electrolysis of water to measure the charge on the electron

A simple apparatus for performing the electrolysis of water, to create hydrogen and oxygen gases, is used to accurately determine the charge on an electron.

Ingredients: Hoffman electrolysis apparatus, sodium sulfate, DC voltage source with ammeter

Procedure: A complete recipe follows.

1. Prepare a 0.5 M solution of sodium sulfate.

2. Add solution to Hoffman apparatus, leaving room for displacement of solution into the central reservoir.

3. Attach wires to voltage source and tune voltage to achieve 0.25 A current.

4. At the moment that the current begins to flow, begin to measure time.

5. As time passes, gases are collected at each electrode. Stop after 15.0 minutes.

6. Carefully measure the volumes of gas produced at the anode and cathode.

7. Use data collected to compute the charge on an electron.

Understanding: G. Johnstone Stoney began his study of the electron and its properties long before the now more famous experiments of J. J. Thomson and Robert Millikan. Stoney's method for the determination of the electron charge is one that is quite powerful and can be used today to determine the charge on a single electron with little more than water, wires, a battery, and Avogadro's number.

Stoney's method is beautifully simple. He knew that if he inserted two electrodes into a bowl of water, each under an inverted glass, by applying a voltage across the wire he could cause the water to separate into the elemental gases

2 H2O(l) → 2 H2(g) + O2(g)

Moreover, he could collect the pure hydrogen gas, H2, at one electrode, and pure oxygen gas, O2, at the other electrode. By measuring the amount of gas collected, and knowing Avogadro's number, he could determine the number of molecules of water that had been dissociated.

What role did the wire play? Why was voltage applied? It turns out that under one glass, there was the reaction

4 H+(aq) + 4 e- → 2 H2(g)

while under the other glass, there was the reaction

2 H2O(l) → 4 H+(aq) + 4 e- + O2(g)

If we add these two half reactions together, we recover the overall reaction

2 H2O(l) → 2 H2(g) + O2(g)

That is a special sort of electrochemistry that we will study in detail later. For now, we just need to know that the two half reactions can occur in different places as long as those two places are connected by a wire so that the electrons, products in one reaction, can be transported to the other reaction, where they are reactants.

Computing the charge on an electron

Stoney knew that if he produced 2 grams of hydrogen gas, he had created one mole of hydrogen gas, which was Avogadro's number of hydrogen molecules. To create one hydrogen molecule, two electrons had to flow through the wire. Therefore, he knew that

total # electrons = ne = 2 x number of H2 molecules produced = 2 x N0 x nH2

where nH2 is the number of moles of hydrogen gas produced and N0 = 6.022 127 x 1023 mol-1 is Avogadro's number of hydrogen molecules in a mole of hydrogen gas. He could compute the moles of hydrogen gas produced using the ideal gas law

nH2 = PVH2 / RT

Stoney also knew that if he could measure the current, I, that flowed, and how long the current flowed in time, t, he could determine the total amount of charge of the electrons that flowed through the wire

total charge passed = I x t = ne e

Knowing the current, the time it ran, and the volume of hydrogen gas produced in that time, he could determine the absolute magnitude of the charge on the electron

e = I x t / ne

Now that is truly remarkable. Stoney performed nothing more than a bench top experiment using water, wire, a battery, an ammeter, a measuring cup, to determine the volume of the gas by the volume of the water that was displaced, and a watch. The result was nothing less than a direct measurement of one of the most fundamentally important physical constants - the charge on the electron! Try to devise an experiment of similar simplicity to measure the speed of light, c, or Planck's constant, h, or Boltzmann's constant, kB. Good luck!

You can do this experiment yourself and find the charge on the electron to be 1.6 x 10-19 C which is the currently accepted value. It isn't easy to get a more accurate measurement using this method, but two significant figures is not bad at all! Stoney did this experiment and arrived at a value for the charge on the electron of 1.0 x 10-19 C. Not so great. As a result, when we think of the charge of the electron today, we think of Thomson and Millikan.

What went wrong for Stoney? It turns out that his method is just fine, but the value of Avogadro's number, essential for converting his moles of hydrogen gas into numbers of individual electrons, was poorly known at the time. The value that Stoney used was N0 = 1.0 x 1024 mol-1 and that led to his precise but inaccurate determination of e.

Computing the charge on a single electron

Question: The Hoffman apparatus is prepared and run at a temperature of 21.9C and atmospheric pressure of 30.11 inches (of Hg). When 22V is applied to the cell, a current of 0.25 A is created which is allowed to run for 15.0 minutes. During that time, a volume of 28.7 mL of gas is collected at one electrode, and a volume of 14.4 mL of gas is collected at the other electrode.

Using the data collected and the method devised by Stoney, compute the charge on a single electron.

You can check your answers here.

Correcting the calculation by accounting for the vapor pressure of water

Question: In the Hoffman apparatus, the gases collected above the two electrodes consist of hydrogen or oxygen gas, and also water vapor. Take the vapor pressure of pure water at 21.9C to be 19.8 mmHg.

Correct your estimate for the charge on the electron, by accounting for the presence of water vapor in the collected gases. Does the correction improve our result, relative to the accepted experimentally measured value of 1.60217646 x 10-19 C?

You can check your answers here.