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 4.60 kg of metallic sodium from the electrolysis of molten NaCl(s)is __________ when the applied emf is 4.50 V.

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The number of moles of sodium produced is:$$4.60	ext{ kg Na}	imes\frac{1000	ext{ g Na}}{1	ext{ kg Na}}	imes\frac{1	ext{ mol Na}}{22.99	ext{ g Na}}=200	ext{ mol Na}$$The half-reaction for the production of sodium is:$$Na^+(l)+e^-ightarrow Na(s)$$The number of moles of electrons required is:$$200	ext{ mol Na}	imes\frac{1	ext{ mol e}^-}{1	ext{ mol Na}}=200	ext{ mol e}^-$$The number of coulombs required is:$$200	ext{ mol e}^-	imes\frac{96,485	ext{ C}}{1	ext{ mol e}^-}=1.93	imes10^7	ext{ C}$$The number of kilowatt-hours of electricity required is:$$1.93	imes10^7	ext{ C}	imes\frac{4.50	ext{ V}}{1000	ext{ W}}	imes\frac{1	ext{ h}}{3600	ext{ s}}=\boxed{24.1	ext{ kWh}}$$

The Town of Natrium, West Virginia, Derives Its Name from the Sodium