Question

Name the law or principle to which the following observations confirm:
$(1)$ When water is added to a $1.0M$ aqueous solution of acetic acid, the number of hydrogen ions $({H^ + })$ increases.
 $(2)$When $9650C$ of electricity is passed through a solution of copper sulphate, $3.175g$ of copper is deposited on the cathode (atomic weight of $Cu = 63.5$).
$(3)$ When ammonium chloride is added to a solution of ammonium hydroxide, the concentration of hydroxyl ions decreases.

Answer 1

Hint: To solve this question first we should know that acetic acid does not dissociate completely because it is a weak acid, secondly if atomic weight and amount of charge deposited given then we can find the amount deposited and when there is common ions in two compound then there may be common ion effect.

Complete step by step answer:
Solving for $(1)$: Acetic acid is a weak acid. As we can see in one that by adding water in acetic acid the number of hydrogen ions increases . We can relate this to ostwald dilution law because we are diluting the solution by adding more water.
Ostwald dilution law states that the degree of dissociation of a weak electrolyte is inversely proportional to the square root of it’s concentration. This law can be given as :
$\alpha = \sqrt {\dfrac{K}{C}} $
Where $\alpha = $ degree of dissociation
$K = $ dissociation constant
$C = $ concentration of solute in solution.
As we can see, the concentration($C$) of acetic acid becomes less as we are adding water in the solution. From the formula it is clear that concentration of solute is inversely proportional to degree of dissociation. As concentration decreases, the degree of dissociation increases. That is there will be more $({H^ + })$ ions according to given equation:
$C{H_3}COOH \rightleftharpoons C{H_3}CO{O^ - } + {H^ + }$
Hence we can conclude that the $(1)$ part of question depicts the ostwald dilution law.
Solving for ($2$):
In this question, the charge passed and the amount of substance is given. So, we can relate it with Faraday’s first law.
Faraday’s first law states that mass of the substance that is deposited on any electrode is directly proportional to the charge passed through it. This law can be written as :
$M$$\alpha $$Q$
$M = zQ$ $ - (1)$
Where $M = $ mass of substance deposited
$Q = $ charge passed through electrode
$z = $ electrochemical constant.
Also, $z = \dfrac{{atomic{\text{ weight}}}}{{Valency \times 96500}}$
For copper it has a valency $2$ , atomic weight of copper is $63.5$ and given charge is $9650C$.
So, for copper $z = \dfrac{{63.5}}{{2 \times 96500}}$
Now, by putting all these values in equation one we get:
$M = \dfrac{{63.5 \times 9650}}{{2 \times 96500}}$
$M = 3.175g$
As this question can be proved by this law. Hence, part $ - (2)$ depicts Faraday’s first law.
Solving for $ - (3)$:
In this option, when we add ammonium chloride to a solution of ammonium hydroxide, the concentration of hydroxyl ion decreases due to the common ion effect. According to which when we add a solution of strong electrolyte to the solution of weak electrolyte and there is a common ion between them and then the ionisation of weak electrolyte is suppressed.
In given question, the equations for it can be given as :
$
  N{H_4}Cl \rightleftharpoons NH_4^ + + O{H^ - } \\
  N{H_4}OH \rightleftharpoons NH_4^ + + C{l^ - } \\
 $
Thus part $(3)$ depicts the common ion effect.


Note:
 In this type of question, we need to remember that for common ion effects the two given electrolytes must have one ion in common and in faraday’s first law the value $96500C$ is also known as $1$ faraday.