Question

The enthalpies of neutralization of a weak base $AOH$ and a strong base $BOH$ by $HCl$ are $ - 12250cal/mol$ and $ - 13000cal/mol$ respectively. When one mole of $HCl$ is added to a solution containing 1 mol of $AOH$ and 1 mol of $BOH$, the enthalpy change was $ - 12500cal/mol$ . In what ratio the acid is distributed between $AOH$ and $BOH$?

Answer 1

Hint: Enthalpy is defined as the quantity which describes the change in heat and work done when a reaction occurs in respect to pressure and volume and the enthalpy of neutralization is the change in enthalpy during a neutralization reaction between and acid and base react to give water and salt. Thus, an acid neutralizes a base and vice-versa.

Complete step by step answer:
Enthalpy is a thermodynamic property which is calculated as the sum of internal energy of a system and the product of pressure and volume. It is a quantity to measure the heat and work which are added or removed from a system when a reaction occurs.
$H = E + PV$
Where $H$ is the enthalpy, $E$ is the internal energy and $PV$ is the product of volume and pressure.
The enthalpy of neutralization is the change in enthalpy when an acid and a base react with each other to give neutralization reaction which gives water and salt as a product. Heat is given out during the reaction of an acid with a base and thus, the enthalpy of neutralization is negative. Strong acids and strong bases are ionized in a dilute solution completely and therefore, the enthalpy of neutralization of a strong acid and a strong base is constant.
For the above question it is given that,
Enthalpy of $AOH = - 12250cal/mol$ and of $BOH = - 13000cal/mol$
When an acid is added in a solution of $AOH$ and $BOH$ then the enthalpy = $ - 12500cal/mol$
Energy required for dissociation of one mol weak base = $13000 - 12250$
$ \Rightarrow 750cal/mol$
$\Delta {H_{dissociation}}$ of mixture = $13000 - 12500$
$ \Rightarrow 500cal$
Thus, the ratio of dissociation of weak base is equal to ratio of acid neutralizing weak base
$ \Rightarrow \dfrac{{500}}{{750}} = \dfrac{2}{3}$
Therefore, ratio of acid neutralizing strong base $ = \dfrac{1}{3}$
Thus, $\dfrac{{AOH}}{{BOH}} = \dfrac{{\dfrac{2}{3}}}{{\dfrac{1}{3}}}$
$ \Rightarrow 2:1$

Note:
A base is said to be a strong base if it is completely ionised in a solution and is completely dissociated in an aqueous solution and if it is not completely ionised then it is known as a weak base which is partially dissociated. Calcium hydroxide is a strong base whereas ammonia is a weak base.