What is the number of kilowatt-hours of electricity required to produce 5.50 kg of metallic sodium?

Question

The town of Natrium, West Virginia, derives its name from the sodium produced in the electrolysis of molten sodium chloride (NaCl) mined from ancient salt deposits. The number of kilowatt-hours of electricity required to produce 5.50 kg of metallic sodium from the electrolysis of molten NaCl(s) is ________ when the applied emf is 5.00 V.

Answer 1

5.50 kg of Na = 5.50 x 1000 g /22.99 g/mole = 239.2 moles. This would require the Faraday constant of approximately 96500 Coulombs/mole x 239.2 moles Na = 2.31 x 10^7 coulombs of electricity.

As volts is joules / coulomb, 5 volts = 5 joules /C x 2.31 x 10^7 coulombs = 1.16 x 10^8 joules to produce 5.50 kg of Na.

1 Kw-hr = 1000 j / sec x 3600 sec = 3.6 x 10^6 joules, so if you divide 1.16 x 10^8 joules by 3.6 x 10^6 joules /Kw-hr, you get 32.2 Kw-hr.