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

Answer 1

The number of kilowatt-hours of electricity required to produce 4.60kg of metallic sodium from the electrolysis of molten NaCl(s) is 3.13 kWh when the applied emf is 4.50V

An equation for the reaction can be given as follows;

$Na^{+} + e^{-} ---- > Na (s)$

Hence, the moles of Na is equal to the moles of electron used

Therefore, we can calculate the number of moles of sodium as follows;

No of moles = mass ÷ molar mass

No of moles = 4600 g ÷ 23 g/mol     (As 1 kg = 1000 g)

No of moles =  200 mol

As Q = n × F;  where F represents  Faraday's constant

Q = 200 mol × 96500 C

Q = 19,300,000 mol C

The relation between electrical energy and Q is as follows;

E = Q × V

Now we can substitute the given values into the above formula and then calculate the value of electricity as follows;

E = 19,300,000 × 4.50

E = 86,850,000 J

As 1 J = 2.77 × 10^-7 kWh

Therefore;

86,850,000 ÷ 2.77 × 10^-7  kWh = 3.13 kWh

Hence, we can conclude that 3.13 kilowatt-hours of electricity is required to produce 4.60kg of metallic sodium from the electrolysis of molten NaCl(s)

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