Question

The pH of 1N aqueous solutions of HCl, $C{{H}_{3}}COOH$and HCOOH follows the order.
(A) $HCl\,>\,HCOOH\,>\,C{{H}_{3}}COOH$
(B) $HCl\,=\,HCOOH\,>C{{H}_{3}}COOH$
(C) $C{{H}_{3}}COOH\,>\,HCOOH\,>\,HCl$
(D) $C{{H}_{3}}COOH\,=\,HCOOH\,>\,HCl$

Answer 1

To solve the above given question we should know the relation between pH and acidic strength. And we should know the stability of the conjugate base formed and the factors that affect the stability of the conjugate base formed.
The pH is inversely proportional to the acidic strength.
$pH\,\alpha \,\dfrac{1}{Acidic\,strength}$

Complete step-by-step answer: In the question three acids of 1N aqueous solution is given and we have to predict the order of the pH value of the three acids,
First we should know the relation between the pH and the acidic strength of the acids.
$pH=-\log \left[ {{H}^{+}} \right]$
$pH\alpha \dfrac{1}{Acidic\,strength}$
The dissociation of three acids are as follows:
$HCl\to {{H}^{+}}+C{{l}^{-}}$
$C{{H}_{3}}COOH\rightleftharpoons C{{H}_{3}}CO{{O}^{-}}+{{H}^{+}}$
$HCOOH\rightleftharpoons HCO{{O}^{-}}+{{H}^{+}}$
Now we have to know how acidic strength is related to stability of the conjugate base formed.
Conjugate base is the anion formed during the dissociation of the acids.
$\text{acidic}\,\text{strength}\,\text{ }\\!\\!\alpha\\!\\!\text{ }\,\text{stability \,of}\,\text{conjugate}\,\text{base}$
The stability of the conjugate base depends on many factors like, size of the anion formed, mesomeric effect (-M effect) i.e. the groups that has the ability to attract the negative charge or electrons towards itself is attached with the conjugate base, inductive effect (-I effect) is phenomenon in which the negative charge is delocalized.
Let us compare the three conjugate bases by the dissociation.
In HCl, $C{{l}^{-}}$is the anion formed it is comparatively bigger in size than the other two conjugate bases.
In$C{{H}_{3}}COOH$, $C{{H}_{3}}CO{{O}^{-}}$is the conjugate base and in$HCOOH$, $HCO{{O}^{-}}$is the conjugate base formed.
As $C{{l}^{-}}$is comparatively bigger in size than the other two, it will have the highest acidic strength.
Now comparing $C{{H}_{3}}CO{{O}^{-}}$ and$HCO{{O}^{-}}$, $C{{H}_{3}}CO{{O}^{-}}$will be less stable as the group attached is methyl group which shows the +I effect and the density of the negative charge increases by which the stability decreases. Hence $HCO{{O}^{-}}$will be more acidic and stable than $C{{H}_{3}}CO{{O}^{-}}$
Hence the strength of acidity order will be: $HCl\,>\,HCOOH\,>\,C{{H}_{3}}COOH$
But the acidity is inversely proportional to pH, hence the order of pH will be as follows:
$C{{H}_{3}}COOH\,>\,HCOOH\,>\,HCl$

So the correct answer for the above given question is option (c).

Note: Always compare all the factors that decide the stability of the conjugate base and if any of the parameters like –I effect or –M effect is almost similar in the cases then the size factor will overweigh the other effects.
+I and +M effect destabilizes the conjugate bases whereas –I and –M effect stabilizes the anion.
We can also say the order easily if we know the $p{{K}_{a}}$values of the acids.