devarshi-dt-logo

Question:

How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66g of diborane?

1.6 hours

6.4 hours

3.2 hours

0.8 hours

Solution:

B2H6 + 3O2 → B2O3 + 3H2O
Moles of O2 required = 3 × moles of B2H6
Molecular weight of B2H6 = 2(10.8) + 6(1) = 27.6 g/mol
Moles of B2H6 = 27.66 g / 27.6 g/mol = 1 mol
Moles of O2 required = 3 × 1 mol = 3 mol
Oxygen is produced by the electrolysis of water:
2H2O → 2H2 + O2
From the stoichiometry, 1 mole of O2 is produced from 4 moles of electrons.
Thus, 3 moles of O2 require 12 moles of electrons.
Charge = moles of electrons × Faraday's constant = 12 mol × 96500 C/mol = 1158000 C
Current = 100 A
Time (t) = Charge / Current = 1158000 C / 100 A = 11580 s
Time in hours = 11580 s / 3600 s/hr ≈ 3.2 hours
So, the correct option is 3.2 hours