Problem 206 - A Complete Resource Book in Chemistry for JEE Main

Question

Equal volumes of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) (c M) solution of \(\mathrm{pH}=5\) is mixed with HCl solution of same \(\mathrm{pH}\). Which of the following is an incorrect statement? (a) Concentration of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) will become \(\mathrm{c} / 2 \mathrm{M}\) after mixing \(\mathrm{HCl}\) with it. (b) Concentration of \(\mathrm{H}^{+}\)after mixing the two solutions is \(10^{-5} \mathrm{M}\). (c) The degree of dissociation of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) is suppressed due to addition of \(\mathrm{HCl}\). (d) Original concentration of \(\mathrm{HCl}\) was \(10^{-5} \mathrm{M}\). Passage-2 Solubility product of an electrolyte at a particular temperature is defined as the product of conc. of its ions in a saturated solution, each conc. raised to the power equal to the number of ions produced on dissociation of one molecule of the electrolyte. \(\mathrm{A}_{\mathrm{x}} \mathrm{B}_{\mathrm{y}} \rightleftharpoons \mathrm{xA}^{+}+\mathrm{yB}^{-}\) \(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{A}^{+}\right]^{\mathrm{x}}\left[\mathrm{B}^{-}\right]^{\mathrm{y}}\) Ionic product of the electrolyte \(\mathrm{A}_{x} \mathrm{~B}_{y}\) is also equal to \(\left[\mathrm{A}^{+}\right]^{\times}\left[\mathrm{B}^{-}\right]^{\mathrm{y}}\) but it is applicable to all types of solutions, which may be saturated or unsaturated.

Step-by-Step Solution

Answer

Option (d) is the incorrect statement.

Step 1: Initial Hydrogen Ion Concentration

Since the pH of both the acetic acid and HCl solutions is 5, the concentration of hydrogen ions in each solution is given by \([H^+] = 10^{-5} \text{ M}\).

Step 2: Mixing Solutions and Concentrations

When equal volumes of acetic acid and HCl solutions are mixed, the total volume doubles, therefore the concentration of each initial solution is halved. The concentration of acetic acid in the new solution is reduced to \(\frac{c}{2}\).

Step 3: Analyzing the Hydrogen Ion Concentration

The final concentration of hydrogen ions is a result of mixing both solutions. Since both solutions initially have \([H^+] = 10^{-5} \text{ M}\), the total \([H^+]\) after mixing (dilution won't change [H+]) is still \(10^{-5} \text{ M}\).

Step 4: Effect on Dissociation

Addition of HCl increases the \([H^+]\) concentration from acetic acid perspective, which suppresses its ionization according to Le Chatelier's principle due to a common ion effect.

Step 5: Check Incorrect Statement

Evaluate each statement given the observations: - (a) is correct as concentration of acetic acid becomes \(\frac{c}{2} \text{ M}\).- (b) is correct as hydrogen ion concentration remains \(10^{-5} \text{ M}\).- (c) is correct as the degree of acetic acid dissociation is suppressed.- (d) is incorrect because original concentration of HCl was \(2 \times 10^{-5} \text{ M}\) due to dilution.

Key Concepts

pH calculation

Understanding pH is essential to grasp the basics of acidic and basic solutions. pH measures the concentration of hydrogen ions ([H^+]) in a solution. This is calculated using the formula:

\[pH = -\log[H^+]\]
For instance, a pH of 5 indicates [H^+] of \(10^{-5}\ \text{M} \). This logarithmic nature means that for every unit change in pH, the [H^+] concentration changes tenfold. A lower pH corresponds to a higher concentration of hydrogen ions, signifying a stronger acid.
When mixing solutions of equal pH, like acetic acid and hydrochloric acid, every molecule of CH₃CO₂H and HCl undergoes dilution because the total volume doubles. While the pH doesn't change with dilution in a scenario where additional ions are not added or removed, the concentration of each specific substance decreases (halved in this case).
Calculating pH after mixing involves understanding how dilution affects concentrations independently.

Le Chatelier's Principle

In chemical equilibrium, changes in conditions such as concentration, temperature, or pressure can shift the equilibrium position according to Le Chatelier's Principle. This principle states that if an external change is applied to a system in equilibrium, the system will adjust to partially oppose that change.
In the context of adding hydrochloric acid to a solution of acetic acid, both release hydrogen ions, causing an increase in [H^+] . When there is a common ion (in this case, H⁺) introduced by both substances, the system will attempt to shift to counteract the increase in [H^+] concentration.
This results in the suppression of acetic acid dissociation to maintain balance. Thus, CH₃CO₂H releases fewer ions, adjusting to the raised hydrogen ion concentration. Recognizing this principle helps to explain observations in more complex solution mixes. It demonstrates the natural corrective dynamics in play when dealing with equilibrium in chemistry.

Solubility product

Solubility product, represented as K_sp, is the constant used to express the solubility of sparingly soluble ionic compounds. It depicts the equilibrium concentration product of the ions produced when a ionic compound dissolves in water at a particular temperature.
Consider a generic salt A_xB_y. When it dissolves, it forms x moles of A⁺ ions and y moles of B^- ions. The equilibrium constant K_sp is expressed as:

\[K_{sp} = [A^+]^x[B^-]^y\]
K_sp aids in predicting whether a precipitate will form when two ionic solutions are mixed. If the ionic product (the actual concentrations multiplied) exceeds K_sp, precipitation occurs, illustrating saturation.
In understanding dynamic equilibria, this is closely related to concentration changes driven by factors such as common ion effect.In our exercise, by considering ion product principles, subtle shifts in equilibria among ions can predict outcomes in scenarios involving varied solubility products. This knowledge enhances problem-solving in real-world chemical scenarios.