A silver coulometer is in series with a cell electrolyzing water. In a time of 1 minute at a constant current 1.08 g silver get deposited on the cathode of the coulometer. What total volume (in mL at 1atm, 273K) of the gases would have produced in other cell. In this cell that the anodic and cathodic efficiencies were `90%` and 80% respectively. Assume the gases collected are dry. (Ag = 108) (molar volume of any ideal gas at 1atm and 273K = 22.4L)

Answer

140

Explanation

Charge passed `=0.01` faraday
At the anode `(H_(2)Oto(1)/(2)O_(2)+2H^(+)+2e^(-))` with `90%` efficiency `0.01xx0.9` F have been used and will produce `(1)/(4)xx0.01xx0.9` mole of `O_(2)` i.e., `0.00225molO_(2)`
At the cathode `2H_(2)Ooverset(+2e^(-))toH_(2)+2OH^(-)`
Moles of `H_(2)` produced `=(0.01xx0.8)/(2)mol=0.004mol`
Total moles produced of gases `=0.004+0.00225=0.00625mol`
vol. at STP `=0.00625xx22400mL=140mL`