Question

Sodium metal is produced from molten sodium chloride in an electrolysis device called a Downs cell. (There is molten calcium chloride in the device too, because the mixture has a much lower melting point than pure sodium chloride, but the calcium chloride plays no role in this problem. Sodium ions are reduced to liquid sodium metal at the cathode that is submerged in the molten liquid. Chloride ions are oxidized to di-chlorine gas at an anode designed to allow the gas to escape without ever coming into contact with the highly reactive sodium metal. How many amps must be passed per hour through a Downs cell that generates 30.0 kg per hour of sodium metal?

Answer 1

To produce 30.0 kg of sodium metal per hour in a Downs cell, about 34,959.94 amps need to be passed through the cell each hour, based on the electrochemical requirement of 1 Faraday (96,485 coulombs) to produce 1 mole of sodium.

Step-by-step explanation:

The student has asked how many amps must be passed per hour through a Downs cell that generates 30.0 kg of sodium metal per hour. To solve this, we'll use the information about the electrolysis of sodium chloride and the electrochemical equivalents.

Firstly, we know that the electrochemical reaction at the cathode is:
Na+ + e− → Na(l), and the molar mass of sodium (Na) is 22.99 g/mol.

To produce 1 mole of sodium, 1 Faraday (96,485 coulombs) of charge is required. Given that 1 ampere is equal to 1 coulomb per second, we can calculate the current needed to produce the 30.0 kg of sodium per hour.

We start by converting 30.0 kg to grams and then to moles:

• 30.0 kg Na x 1000 g/kg = 30,000 g Na
• 30,000 g Na / 22.99 g/mol = 1,304.48 mol Na

Now, we calculate the total charge:

• 1,304.48 mol Na x 96,485 C/mol = 125,853,776 C

Since 1 hour is 3600 seconds, we can find the current I (in amperes):

• 125,853,776 C / 3600 s = 34,959.94 A

Therefore, 34,959.94 amps must be passed per hour through the Downs cell to produce 30.0 kg of sodium metal per hour.