Question

How much time in hours is required for a current of \[2amp\] to decompose electrolytically \[18gm\] of water?
A. 96500
B. 9650
C. 26.8
D. 2.68

Answer 1

Hint: Current is defined as the rate of flow of electric charge per unit time. Water has the molecular formula \[{H_2}O\] and hence, it has two hydrogens and one oxygen. When water decomposes on passing current, it forms hydrogen and oxygen molecules.

Complete step by step answer:
The decomposition of a water molecule can be written as,
\[2{H_2}O \to 2{H_2} + {O_2}\]
Mole can be calculated by dividing the weight of the substance by its molecular weight.
\[Mole = \dfrac{{18gm}}{{18gm/mol}}\]
\[ \Rightarrow Mole = 1\]
Therefore, one mole of water is used in the electrolytic reaction.
 It is also clear that one mole of water needs two electrons to decompose into two hydrogens and one oxygen molecule since water contains two hydrogen atoms and one oxygen atom.
Electric charge passed through the circuit can be calculated as,
\[Q = nF\]
Where,
Q- Electric charge
n- Number of electrons involved
F-Faraday’s constant and it has value of \[96,500C\]
Here, \[n = 2\]. Thus, “Q” can be calculated as,
\[Q = 2 \times 96,500C\]
\[ \Rightarrow Q = 193000C\]
Thus, charge passed through the circuit, \[Q = 193,000C\]
It is known that electric current can be calculated by dividing flow of charge per unit time.
\[I = \dfrac{Q}{t}\]
\[ \Rightarrow 2amp = \dfrac{{19300C}}{t}\]
\[ \Rightarrow t = \dfrac{{19300C}}{{2amp}}\]
\[ \Rightarrow t = \dfrac{{19300C}}{{2C{s^{ - 1}}}}\]
Since it is known that \[A = C/s\]
where, A-ampere
C- coulomb
 s- second
Thus, \[1hr = 3600s\]
\[ \Rightarrow t = \dfrac{{19300}}{{2 \times 3600}}hr\]
\[ \Rightarrow t = 26.8hr\]
Thus, \[26.8hour\] is required for a current of \[2amp\] to decompose electrolytically \[18gm\] of water.

So, the correct answer is Option C.

Note: When an electric current passes through an electrolytic solution, the decomposition reaction occurs. When a water molecule ionizes, it forms protons and hydroxyl ions. In a water molecule, the positive ion is proton whereas the negative ion is the hydroxyl ion. When the current passed through the electrolyte solution, the positive ion passed towards the cathode and the negative ion passed towards the anode. The anode is a positive charge electrode and thus, it attracts anion towards them whereas the cathode is a negative charge electrode and thus, it attracts cations towards them.