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 \(\mathrm{HCl}\) 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 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 \(10^{-5} \mathrm{M}\).

Step-by-Step Solution

Answer

Statement (b) is incorrect.

Step 1: Understanding the Problem

We are given two solutions, one of acetic acid \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) and another of \(\mathrm{HCl}\), each with a pH of 5. These solutions are mixed in equal volumes. We need to determine which statement about the solutions after mixing is inaccurate.

Step 2: Determine pH and \( \mathrm{H}^+ \) Concentration of the Original Solutions

Both solutions initially have a pH of 5. This means the concentration of hydrogen ions in each solution is \[\left[\mathrm{H}^{+}\right] = 10^{-5} \, \mathrm{M}.\]

Step 3: Derive Post-mix Concentrations

After mixing equal volumes, the concentration of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) becomes half, changing from \(\mathrm{c}\) to \(\frac{\mathrm{c}}{2}\). The concentration of \(\mathrm{H}^{+}\) before mixing being \(10^{-5} \, \mathrm{M}\) means \(\mathrm{H}^{+}\) will also effectively mix without change if dissociation effects are minimal.

Step 4: Analyze Statement (a)

According to (a), the concentration of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) becomes \(\frac{\mathrm{c}}{2} \, \mathrm{M}\), which should be true after equal volume mixing.

Step 5: Analyze Statement (b)

(b) claims \(\left[\mathrm{H}^{+}\right] = 10^{-5} \, \mathrm{M}\) after mixing. Since both solutions contribute equally to the \(\mathrm{H}^+\) concentration, and \(\mathrm{HCl}\) is a strong acid, the post-mix concentration should reflect higher than the weak acid's equilibrium condition, likely leading to a concentration greater than \(10^{-5} \, \mathrm{M}\).

Step 6: Analyze Statement (c)

Statement (c) says that the degree of dissociation of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\) is suppressed by \(\mathrm{HCl}\). This is expected because adding a strong acid suppresses the ionization of a weak acid (common ion effect). Hence, (c) is correct.

Step 7: Analyze Statement (d)

(d) states that the original concentration of \(\mathrm{HCl}\) was \(10^{-5} \, \mathrm{M}\) based on an initial pH of 5, which matches the calculated \(\mathrm{H}^+\) concentration in Step 2. Hence, this statement is true.

Step 8: Identify the Incorrect Statement

Given the analyses, the incorrect statement is (b) because after mixing, the effective \(\mathrm{H}^+\) ion concentration should be higher due to \(\mathrm{HCl}\) being a strong acid, unlike the weak acetic acid.

Key Concepts

pH calculations

Calculating pH is a fundamental concept in understanding acid-base equilibria. pH is a scale used to specify how acidic or basic a water-based solution is. It is calculated using the formula: \[ \text{pH} = -\log_{10} [\mathrm{H}^+] \]where \([\mathrm{H}^+]\) is the concentration of hydrogen ions in the solution. For instance, in a solution with a pH of 5, \([\mathrm{H}^+]\) would be \(10^{-5} \mathrm{M}\). This means every liter of the solution contains \(0.00001\) moles of hydrogen ions.

Key points about pH calculations:

• A lower pH value indicates a higher concentration of hydrogen ions, meaning a more acidic solution.
• A higher pH indicates fewer hydrogen ions and a more basic solution.
• The pH scale typically goes from 0 to 14, with 7 being the neutral point (like pure water).

Calculating pH helps in understanding the acidity and basicity of a solution and plays a crucial role in predicting the behavior of acids and bases when they interact in a solution.

Acid dissociation

Acid dissociation refers to the process by which an acid releases hydrogen ions when dissolved in water. This process is characterized by the acid dissociation constant, \(K_a\), which measures the strength of an acid in solution. The stronger the acid, the more it dissociates and the higher its \(K_a\) value.

The basics of acid dissociation:

• Strong acids: Completely dissociate in solution, releasing a high concentration of hydrogen ions. HCl is an example of a strong acid.
• Weak acids: Partially dissociate, establishing an equilibrium between the undissociated acid and the ions in solution. Acetic acid (\(\mathrm{CH}_3\mathrm{CO}_2\mathrm{H}\)) is a weak acid.

For example, in a solution of acetic acid, most of the acid remains in its molecular form, with only a small fraction dissociating into \(\mathrm{CH}_3\mathrm{CO}_2^-\) and \(\mathrm{H}^+\). This partial dissociation is what causes weak acids to have a less intense "acidic" effect compared to strong acids.Understanding acid dissociation helps predict how an acid will behave when mixed with other substances, like another acid or a base. It also helps explain phenomena like buffering capacity and the impact of the common ion effect.

Common ion effect

The common ion effect is a principle in chemistry that describes the reduction in solubility or ionization of an ionic compound when a solution already contains an ion that is a component of the compound. In the context of acid-base chemistry, the common ion effect is seen when the ionization of a weak acid is suppressed by the presence of a strong acid in the solution.

Here's how the common ion effect works:

• When a strong acid like HCl is added to a solution containing a weak acid like acetic acid, the concentration of \(\mathrm{H}^+\) ions in the solution increases.
• This additional \(\mathrm{H}^+\) from the strong acid shifts the equilibrium, reducing the overall dissociation of the weak acid.
• As a result, the weak acid loses its ability to release more \(\mathrm{H}^+\) ions, thereby decreasing its effective acidic strength.

For instance, when HCl is mixed with acetic acid, the extra \(\mathrm{H}^+\) ions from HCl will cause fewer acetic acid molecules to dissociate.Understanding the common ion effect is essential for predicting the outcome of mixing different acidic solutions and explains why weak acids behave differently in the presence of strong acids.