Question

When an electric current is passed through acidified water, $112mL$ of hydrogen gas N.T.P was collected at the cathode in $965$ seconds. The current asset, ampere, is:

Answer 1

Hint: Make use of Faraday's first law of electrolysis which says “In electrolysis, the deposited amount of substance $\left( M \right)$ at electrode is directly proportional to change flow $\left( Q \right)$”.


Complete step by step solution:
Formula use:
$
  M \propto Q \\
  M = WQ \\
 $
We know that,
$Q = it$
$M = Wit$…………. (i)
Where, $M \to $deposited amount of substance
$Q \to $Charge
$i \to $Current (ampere)
$t \to $Time
$W \to $Equivalent mass
We know that
$
  W = \dfrac{{Equivalent{\text{ mass}}}}{{Faraday}} \\
  W = \dfrac{E}{F} \\
  E = \dfrac{{Molar{\text{ mass}}\left( M \right)}}{{Z - factor}} \\
 $
Put the value of $E$in equation
$W = \dfrac{{Molar{\text{ mass}}\left( M \right)}}{{Z - factor \times F}}$
Where
$E \to $Equivalent mass
$F \to $Faraday
Put the value of $W$ in the equation ……(i).
$
  M = \dfrac{{Molar{\text{ mass}}}}{{Z - factor \times F}} \times it \\
  \dfrac{M}{{Molar{\text{ mass}}}} = \dfrac{{it}}{{Z - factor \times F}} \\
 $
We know that,
$Mole = \dfrac{{mass\left( m \right)}}{{Molar{\text{ mass}}}}$
So, $Mole = \dfrac{{it}}{{Z - factor}}$ …….. (ii)
We can use this formula –
Given that,
Volume of ${H_2}$at $NTP = 112ml$
Time$\left( t \right) = 965$second
$1$ Faraday$\left( F \right) = 96,500C$
Reduction at cathode –
$2{H^ + }\left( {aq.} \right) + 2{e^ - }\xrightarrow{{}}{H_2}\left( g \right)$
Z – factor $ = $ transfer of electron $ = 2$
$
  Mole = \dfrac{{Volume{\text{ of }}{{\text{H}}_2}{\text{ at NTP}}}}{{22,400ml}} \\
  Mole = \dfrac{{112}}{{22,400}} = \dfrac{1}{{200}} \\
 $
Put the given value in equation (ii).
$
  Mole = \dfrac{{it}}{{Z - factor \times F}} \\
  \dfrac{1}{{200}} = \dfrac{{1 \times 965}}{{2 \times 96,500}} \\
  i = 1amp \\
 $
Current passed $ = 1amp.$


Note: Firstly you should know about Faraday’s first law.
You derive a formula and put the given value in this formula and you get your answer.