the electrolysis of an acetate solution produces ethane and carbon dioxide acc to the reaction

2CH3COO- gives C2H6+2CO2+2e-

The efficiency of reaction is 82%. What volume of C2H6 and CO2 would be produced at 27oCand 740mm pressure if a current of 0.5 ampere is passed through the solution for 7hours?

The overall reaction occurring is as follows:

2CH₃COO^- ------->  C₂H₆ + 2CO₂+2e^-

as we can see that to reduce 1 molecule of CH₃COO^- we need 1 electron.

The total no. of moles of electrons passed:
Current x time (s) / 96500 =
0.5 x (7x60x60)/96500 =

12600/96500 = 0.1305 moles

However efficiency is given at 82% hence the actual no. moles of CH₃COO^- neutralised will be
0.1305 x 0.82 = 0.107 moles

As we can see for the above reaction that 2 moles of CH₃COO^- gives 1 mole of C₂H₆ and 2 moles if CO₂
Thus 0.107 moles of CH₃COO^- will give 0.053 moles of C₂H₆ and 0.107 moles if CO₂

As we know that under ideal conditions:
PV = nRT
Thus V = nRT/P

here n= 0.053, P = 760 mm Hg = 1 atm.
R = 0.0821
T = 27 ⁰C = 273 + 27 = 300K

V = 0.053 x 0.0821 x 300 /1
= 1.305 litres of C₂H₆

Similarly for CO₂,
The value of n = 0.107
Hence volume will be: 2.63 litres