An electric current of 100 ampere is passed through a molten liquid of sodium chloride for 5 hours. Calculate the volume (in L) of chlorine gas liberated at the electrode at NTP. (Consider volume at NTP = 22.4L, 1F = 96500C & calculate the answer up to two decimal places):Correct answer is between '207.00,209.00'. Can you explain this answer?

Question

Answer

The electrolysis of molten sodium chloride produces sodium metal and chlorine gas. The balanced equation for the reaction is:

2NaCl(l) → 2Na(l) + Cl2(g)

From the equation, we can see that for every 2 moles of NaCl electrolyzed, one mole of Cl2 gas is produced. The molar volume of any gas at standard temperature and pressure (STP) is 22.4 L.

Given that 100 A of current flowed for 5 hours, the total charge passed through the electrolyte is:

Q = I × t = 100 A × 5 h × 3600 s/h = 1.8 × 10^6 C

The amount of charge required to produce one mole of electrons is known as the Faraday constant, F, which is equal to 96,500 C/mol. Therefore, the number of moles of electrons passed during electrolysis is:

n = Q / F = 1.8 × 10^6 C / 96,500 C/mol = 18.65 mol

Since 2 moles of NaCl produce 1 mole of Cl2, we can calculate the amount of NaCl electrolyzed:

n(NaCl) = n / 2 = 18.65 mol / 2 = 9.33 mol

The molar mass of NaCl is 58.44 g/mol, so the mass of NaCl electrolyzed is:

m(NaCl) = n(NaCl) × M(NaCl) = 9.33 mol × 58.44 g/mol = 544 g

Finally, we can use the ideal gas law to calculate the volume of Cl2 gas liberated at STP:

PV = nRT

V = nRT/P

where P is the pressure at STP (1 atm), R is the gas constant (0.0821 L·atm/mol·K), and T is the temperature at STP (273 K). Substituting the values:

V = (0.5 × n(NaCl) × R × T) / P

V = (0.5 × 9.33 mol × 0.0821 L·atm/mol·K × 273 K) / 1 atm

V = 10.9 L

Therefore, the volume of Cl2 gas liberated at the electrode is 10.9 L at STP.

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