In the electrolysis of acidified water using platinum electrodes, \(1 dm ^{3}\) of oxygen was collected at s.t.p. by passing \(4.5\) amperes into the electrolytic cell. Calculate the time required to set this amount of gas free. [Molar volume of gas at s.t.p. \(=22.4 dm ^{3}, 1\) Faraday \(=96500\) coloumbs]
A. \(40.4\) mins B. \(63.8\) mins C. \(55.5\) mins D. \(5.68\) mins
Correct Answer: B
Explanation
The electrolysis of acidified water is represented by: \(4 OH ^{-} \rightarrow 2 H _{2} O + O _{2}+4 e ^{-}\) 1 mole of involves \(1 F\) of electricity. Thus 1 mole of \(O _{2}\) is produced by \(4 F\). i.e. \(22.4 dm ^{3}\) of ox- ygen requires \(4 F .1 dm ^{3}\) will require \((4 / 22.4) F =0.1786 F\) \begin{aligned} &0.1786 F =(0.1786 \times 96500) C\\ &=17232.14 C\\ &Q=I \times t, t=\frac{Q}{I}=\left(\frac{17232.14}{4.5}\right) s\\ &=3829.37 s =63.82 min \end{aligned}