How to calculate avogadro's number

Updated February 21, 2017

The determination of Avogadro's number is a common experiment in high-school and college-level chemistry courses. Avogadro's number, 6.022 E23, is the number of atoms in a mole. Note that the exponential notation 6.022 E23 means 6.022 times 10 to the power of 23. This is often written as 6.022 x 10^23. The most common procedure for its determination involves the electrolysis of copper by passing an electric current between two copper plates. In the course of the reaction, the copper atoms in the plate attached to the negative terminal of the power source---the anode---lose electrons to form Cu(2+) ions. As the copper atoms lose electrons, they dissolve into the liquid electrolyte. The copper plate attached to the positive terminal---the cathode---simultaneously "plates" Cu(2+) ions from the electrolyte onto the electrode by adding electrons to convert the ions back to copper metal. The copper anode therefore gradually loses mass as the reaction proceeds and the cathode gains a mass of copper equal to the mass lost at the anode. If the experimenter monitors the electrical current delivered to the cell and the time over which it is delivered, then this information, along with the mass of the copper anode before and after electrolysis, allows the calculation of Avogadro's number.

Collect the necessary experimental data. In the case of the popular copper electrolysis experiment, this includes the mass, in grams, of the copper electrode before and after the electrolysis, the average current, in amps, used during the experiment, and the time, in seconds, that the current was applied.

Calculate the total electrical charge transferred by multiplying the average current, in amps, by the time, in seconds. Because 1 coulomb = 1 amp second, the answer is in units of coulombs. For example, an average current of 0.109 amps applied for 60 minutes, or 3600 seconds, would be

(0.109 amps) * (3600 seconds) = 392 coulombs.

Calculate the number of electrons transferred by dividing by the charge of a single electron: 1.602 E-19 coulombs/electron.

(392 coulombs) / (1.602 E-19 coulombs/electron) = 2.45 E21 electrons

Calculate the number of copper atoms transferred by dividing the result from step 3 by two. This results from copper assuming a charge of +2 during electrolysis, which means that two electrons transfer for every one copper atom.

(2.45 E21 electrons) / (2 electrons/atom) = 1.23 E21 copper atoms.

Determine the moles of copper electrolyzed during the process by subtracting the weight of the copper electrode after electrolysis from its starting weight and dividing by its atomic mass.

For example, if a 35.975-g copper electrode weighed 35.846g at the end of the experiment, then 35.975g - 35.846g = 0.129g. And given that the atomic weight of copper is 63.55 grams per mole, then

(0.129g) / (63.55g/mol) = 0.00203 moles of copper.

Calculate Avogadro's number, N, by dividing the number of copper atoms transferred, determined in step 4, by the moles of copper lost from the electrode, determined in step 5.

Continuing the previous example,

(1.23 E21 atoms) / (0.00203 moles) = 6.06 E23 atoms/mole, which is very close to the accepted value of 6.022 E23.

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