Answer:
The correct answer is 17.845 hours.
Explanation:
To solve the question, that is, to determine the hours required there is a need to combine the Faraday's law of electrolysis with the Ideal gas law.
Based on Faraday's law, m = Mit/nF
Here m is the mass in grams, M is the molecular mass, i is the current in amperes, t is time, n is the number of moles of electron per mole of oxygen formed and F is the Faraday's constant (the value of F is 96487 coulombs/mole).
From the above mentioned equation,
t = mnF/Mi ------(i)
Now based on ideal gas law's, PV = nRT or PV = m/M RT, here n = mass/molecular mass.
So, from the above gas law's equation, m = PVM/RT
Now putting the values of m in the equation (i) we get,
t = PVMnF/MiRT = PVnF/iRT
Based on the given information, the value of P is 750 torr or 750/760 atm = 0.98 atm, the value of v is 15.0 L, T is 30 degree C or 273 + 30 K = 303 K, i is 3.55 Amperes, and the value of R is 0.0821 atm L/mol K.
1 mole of oxygen gives 2 moles of electrons, therefore, 2 moles of oxygen will give 4 moles of electrons.
Now putting the values we get,
t = PVnF/iRT
= 0.98 atm × 15.0 L × 4 moles of electron × 96487 coulombs per mole / 3.55 coulomb per sec × 0.0821 atm L per mole-K × 303 K
= 64243.81 secs or 64243.81/3600 hr
= 17.845 hours
