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 4.50 kg of metallic sodium from the electrolysis of molten NaCl(s) is ________ when the applied emf is 5.00 V.

Answer 1

Explanation:

The reaction equation will be as follows.

           $Na^{+} + e^{-} \rightarrow Na(s)$

Hence, moles of Na = moles of electron used

Therefore, calculate the number of moles of sodium as follows.

       No. of moles = $\frac{mass}{\text{molar mass}}$

                             = $\frac{4500 g}{23 g/mol}$    (as 1 kg = 1000 g)

                             = 195.65 mol

As,     Q = $n \times F$       where F = Faraday's constant

              = $195.65 mol \times 96500 C$

              = $1.88 \times 10^{7}$ mol C

Relation between electrical energy and Q is as follows.

               E = $Q \times V$

Hence, putting the given values into the above formula and then calculate the value of electricity as follows.

              E = $Q \times V$

                 = $1.88 \times 10^{7} \times 5$

                 = $9.4 \times 10^{7} J$

As 1 J = $2.77 \times 10^{-7}$ kWh

Hence,      $\frac{9.4 \times 10^{7}}{2.77 \times 10^{-7}}$ kWh

                = 3.39 kWh

Thus, we can conclude that 3.39 kilowatt-hours of electricity is required in the given situation.

Answer 2

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