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Sagot :
Answer:
Mass of sodium produced = 2.74 × 10⁵ g of Na
Mass of chlorine produce = 4.24 × 10⁵ g of Cl₂
Explanation:
In the electrolysis of molten NaCl as described above, the quantity of charge used is given by the formula, Q = I × t
Where I isnthe current passed in amperes and t is time in seconds.
Q = 4.0 × 10⁴ A × (8 × 60 × 60) s = 1.152 × 10⁹ C
Equation for the discharge of sodium is; Na+ + e- ---> Na (s)
One mole of electrons is required to discharge one mole of Na
One mole of electron = 1 faraday = 96500 C
One mole of Na has a mass of 23 g
96500 C produces 23 g of Na
1.152 × 10⁹ C will produce 23 g × 1.152 × 10⁹ C / 96500 C = 2.74 × 10⁵ g of Na
Equation for the discharge of chlorine gas is; 2 Cl- ---> Cl₂(g) + 2e-
Two mole of electrons are required to discharge one mole of chlorine gas
Two moles of electron = 2 faraday = 2 × 96500 C = 193000
One mole of Cl₂ has a mass of 71 g
193000 C produces 71 g of Cl₂
1.152 × 10⁹ C will produce 71 g × 1.152 × 10⁹ C / 193000 C = 4.24 × 10⁵ g of Cl₂
The amount of Na produced is 274551 g and the amount of Cl₂ produced is 423763.5 g.
Current passed through the cell = [tex]4.0\times10^4 A[/tex]
Time = 8 Hours
We have to calculate the amount of Na and [tex]Cl_2[/tex] produced in 8 hours in the downs cell.
What is a down cell?
The Downs process is an electrochemical method for the commercial preparation of metallic sodium, in which molten NaCl is electrolyzed in a special apparatus called the Downs cell.
The total charge passed through the cell is calculated by the given formula as
Charge(Q) = Current(I) × time(t)
Q = [tex]4.0\times10^4 A \times t[/tex]
[tex]t = 8 \times 60\times 60[/tex] sec
t = 28800 sec
Q = [tex]4.0\times10^4 A \times 28800[/tex] sec
Q = [tex]115200\times 10^4 A\ sec[/tex]
We know that, Ampere = Coulombs per sec
Q = [tex]115200\times 10^4\ C[/tex]
1 mol of electrons 96500 C charge
Therefore, the number of mols of electrons carries this [tex]115200\times 10^4\ C[/tex] charge = [tex]\frac{115200\times10^4}{96500}[/tex] = 1.1937 × 10⁴ = 11937 mol electrons
In the Down's cell
Half cell reactions are:
Reduction half-reaction: [tex]2Na^+(aq)+2e^- \to 2Na(s)[/tex]
Oxidation half-reaction: [tex]2Cl^-(aq)\to Cl_2(g) + 2e^-[/tex]
We know that no. of moles = [tex]\frac{given \ mass}{molar \ mass}[/tex]
Molar mass of Na = 23 g/mol
The mass of Na formed = 11937 mol × 23 g/mol = 274551 grams
The molar mass of Cl₂ = 71 g/mol
The mass of Cl₂ = [tex]\frac{11937}{2}\times 71 = 423763.5 \ grams[/tex]
Hence, the amount of Na produced is 274551 g and the amount of Cl₂ produced is 423763.5 g.
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