By definition, Avogadro's number is the number of atoms in exactly 12 g of carbon 12C. Avogadro's nu — Physical Chemistry — Kinetics Chemistry Question
An electrochemical method for determination of Avogadro's number
By definition, Avogadro's number is the number of atoms in exactly 12 g of carbon 12C. Avogadro's number recommended by CODATA (Committee on Data for Science and Technology) in 2002 is 6.0221415(10)×1023 mol–1, where the number in parenthesis represents one standard deviation in the last two digits.
Avogadro's number can be determined electrolytically. Current and time are measured in order to obtain the number of electrons passing through the electrochemical cell from Q = I t (charge = current × time). Copper electrodes were used for electrolysis of H2SO4 solution (c = 0.5 mol dm–3). During electrolysis, copper is lost from the anode as the copper atoms are converted to copper ions. The copper ions pass through the solution. At the surface of the cathode, hydrogen gas is liberated through reduction of hydrogen ions in the acidic solution.
Experimental results are as follows:
decrease in anode mass: 0.3554 g
constant current: 0.601 A
time of electrolysis: 1802 s
Note that 1 A = 1 C s–1 or 1 A s = 1 C and the charge of one electron is 1.602×10–19 C.
Write the reactions at both the anode and cathode.
Model Answer
Anode: Cu(s) → Cu2+(aq) + 2 e– ; cathode : 2 H+(aq) + 2 e– → H2(g)
Calculate the total charge that passed through the circuit.
Model Answer
Total charge = (0.601 A × 1 C s–1 ) / 1 A × 1802 s = 1083 C
Calculate the number of electrons involved in the electrolysis.
Model Answer
Number of electrons = (1083 C × 1 electron) / 1.602×1019 C = 6.760×1021
Calculate the mass of a copper atom.
Model Answer
Number of copper atoms = 6.760×1021 / 2 = 3.380×1021
Mass of a copper atom = 0.3554 g / 3.380×1021 = 1.051×10–22 g
Determine Avogadro's number. Molar mass of copper is 63.546 g mol–1.
Model Answer
Avogadro’s number = 63.546 g / 1.051×10–22 g = 6.046×1023
It is also possible in principle to collect the hydrogen gas evolved and use its mass to determine Avogadro's number. Calculate the mass. What is the percent error in this measurement of Avogadro's number?
Model Answer
Error (in %): (6.046×1023 – 6.022×1023) / 6.022×1023 = 0.4 %
It is also possible in principle to collect the hydrogen gas evolved and use its mass to determine Avogadro's number. Calculate the mass of evolved hydrogen gas. Is this determination of Avogadro's number from the mass of evolved hydrogen practical?
Model Answer
Mass of H2 evolved = 1 g × 6.760×1021 / 6.02×1023 = 0.011 g
Collecting and weighing such a small amount of any gas is not practical considering buoyancy correction.