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# How many faradays of charge is transferred to produce 11.2 mL of ${{H}_{2}}$ at STP in the following reaction, $NaH+{{H}_{2}}O\text{ }\to \text{ }NaOH+{{H}_{2}}\uparrow$(A) 1(B) 0.5(C) 2(D) 2.5

Last updated date: 17th Jun 2024
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Hint: Try to recall the concept of electrolysis given in the chapter electrochemistry. In the reaction provided, find the number of electrons involved for 1 mole of reactant. With this, you can now substitute the values in the formula for Faraday's first law of electrolysis.

Complete step by step solution:
Electrochemistry is the branch of physical chemistry that mainly deals with the relationship between electricity and identifiable chemical change.
An electrochemical reaction is a chemical reaction in which current is externally supplied or produced through a spontaneous chemical reaction.
Chemical reactions where electrons are directly transferred between the constituent molecules or atoms are called oxidation-reduction or rather redox reactions.
Faraday’s First Law of Electrolysis states that the chemical deposition of a substance due to the flow of current through an electrolyte is directly proportional to the quantity of electricity passed through it.
\begin{align} & {{\text{m}}_{{}}}{{\propto }_{{}}}Q \\ & {{m}_{{}}}{{=}_{{}}}Z.Q \\ \end{align}
Where,
$m$ is the mass of electrolyte deposited,
$Q$ is the quantity of electricity
$Z$ is the constant of proportionality and is known as the electrochemical equivalent.
We will now write the reaction and identify the amount of charge required.
$NaH+{{H}_{2}}O\text{ }\to \text{ }NaOH+{{H}_{2}}\uparrow$
In the above reaction, we find that there is a change in the oxidation state of 1 for every mole of reactant.
$1$ mole of any substance occupies $22.4 L$ volume at STP. So, $11.2 L$ of ${{H}_{2}}$ is occupied by $0.5$ moles of reactant.
So, $0.5$ moles of electrons are used in the reaction. The number of faradays of charge is transferred to produce $11.2$ $mL$ of ${{H}_{2}}$ at STP in the following reaction is $0.5$.

Therefore, the correct answer is option (B).

Note: The term faraday is used in chemistry and farad used in physics. One Farad is defined as the capacitance across two plates when charged to 1 coulomb and the potential difference is 1 volt. On the other hand, one faraday is the magnitude of the charge of 1 mole of electrons. Although both terms are in honour of the same scientist, they are two completely different terms.