Answer
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Hint: $NaOH$ is a strong base, it dissociates completely in an aqueous solution to give $N{a^ + }$ and $O{H^ - }$ ions. Water molecules undergo self-ionization to form ${H^ + }$ and $O{H^ - }$ions. Due to the common ion effect of $O{H^ - }$ ions, the degree of dissociation of water decreases in the presence of $NaOH$.
Complete step by step answer:
$NaOH$ is a strong base, it undergoes complete dissociation in water, the dissociation of $NaOH$ is given by the following equation:
According to the given concentration of $NaOH$ at ${25^ \circ }C$, which is ${10^{ - 7}}M$, we get a pH of $7$
$
[O{H^ - }] = [NaOH] \\
[O{H^ - }] = {10^{ - 7}} \\
pOH = - \log [O{H^ - }] = - \log ({10^{ - 7}}) \\
pOH = 7 \\
\Rightarrow pH = 14 - 7 = 7 \\
$
But, the pH was found to exist between $7$ to $7.3$, which is slightly alkaline.
Water is a weak electrolyte, it does not completely dissociate, the dissociation of water is given by the following equation:
${H_2}O\,\,(l)\,\, \rightleftharpoons \,\,{H^ + }\,(aq)\,\, + \,\,\,O{H^ - }\,(aq)$
$O{H^ - }$ ions are formed in both the dissociation of $NaOH$and water. The concentration of $O{H^ - }$ ions increases when $NaOH$ dissociates in an aqueous solution. The $O{H^ - }$ions combine with ${H^ + }$ to form water and shift the above equilibrium to the left. Since the concentration of $O{H^ - }$ is increasing and the ${H^ + }$ ions are decreasing, the solution becomes slightly alkaline and the pH becomes higher than $7$ i.e., between $7$ to $7.3$.
The reason for the slightly alkaline pH is the common ion effect. The common ion effect is the decrease in the degree of dissociation of a weak electrolyte in the presence of a strong electrolyte having a common ion.
Here the common ion is $O{H^ - }$ion and water is the weak electrolyte whose degree of ionization is decreased in the presence of a strong electrolyte which is $NaOH$.
So, the correct option is (A): Both (R) and (A) are true and reason is the correct explanation of assertion.
Note:
Common ion-effect is the consequence of Le Chatelier’s principle. It states that if a system in equilibrium is subjected to a change of concentration, temperature, or pressure, the equilibrium shifts in a direction that tends to undo the effect of the change imposed. So, here when the $O{H^ - }$ ions increases, then according to Le Chatelier’s principle, the effect will be to decrease the concentration of $O{H^ - }$. This is only possible if $O{H^ - }$ interacts with ${H^ + }$ to form water and the equilibrium shifts in the backward direction.
Complete step by step answer:
$NaOH$ is a strong base, it undergoes complete dissociation in water, the dissociation of $NaOH$ is given by the following equation:
According to the given concentration of $NaOH$ at ${25^ \circ }C$, which is ${10^{ - 7}}M$, we get a pH of $7$
$
[O{H^ - }] = [NaOH] \\
[O{H^ - }] = {10^{ - 7}} \\
pOH = - \log [O{H^ - }] = - \log ({10^{ - 7}}) \\
pOH = 7 \\
\Rightarrow pH = 14 - 7 = 7 \\
$
But, the pH was found to exist between $7$ to $7.3$, which is slightly alkaline.
Water is a weak electrolyte, it does not completely dissociate, the dissociation of water is given by the following equation:
${H_2}O\,\,(l)\,\, \rightleftharpoons \,\,{H^ + }\,(aq)\,\, + \,\,\,O{H^ - }\,(aq)$
$O{H^ - }$ ions are formed in both the dissociation of $NaOH$and water. The concentration of $O{H^ - }$ ions increases when $NaOH$ dissociates in an aqueous solution. The $O{H^ - }$ions combine with ${H^ + }$ to form water and shift the above equilibrium to the left. Since the concentration of $O{H^ - }$ is increasing and the ${H^ + }$ ions are decreasing, the solution becomes slightly alkaline and the pH becomes higher than $7$ i.e., between $7$ to $7.3$.
The reason for the slightly alkaline pH is the common ion effect. The common ion effect is the decrease in the degree of dissociation of a weak electrolyte in the presence of a strong electrolyte having a common ion.
Here the common ion is $O{H^ - }$ion and water is the weak electrolyte whose degree of ionization is decreased in the presence of a strong electrolyte which is $NaOH$.
So, the correct option is (A): Both (R) and (A) are true and reason is the correct explanation of assertion.
Note:
Common ion-effect is the consequence of Le Chatelier’s principle. It states that if a system in equilibrium is subjected to a change of concentration, temperature, or pressure, the equilibrium shifts in a direction that tends to undo the effect of the change imposed. So, here when the $O{H^ - }$ ions increases, then according to Le Chatelier’s principle, the effect will be to decrease the concentration of $O{H^ - }$. This is only possible if $O{H^ - }$ interacts with ${H^ + }$ to form water and the equilibrium shifts in the backward direction.
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