Problem 54 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements about \(\mathrm{pH}\) and \(\mathrm{H}^{+}\) ion concentration is incorrect? (a) addition of one drop of concentrated HCl in \(\mathrm{NH}_{4} \mathrm{OH}\) solution decreases \(\mathrm{pH}\) of the solution (b) a solution of the mixture of one equivalent of each of \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(\mathrm{NaOH}\) has a \(\mathrm{pH}\) of 7 (c) \(\mathrm{pH}\) of pure neutral water is not zero (d) a cold and concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) has lower \(\mathrm{H}^{+}\)ion concentration than a dilute solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

Statements (b) and (d) are incorrect.

Step 1: Review Statement A

Statement (a) claims that adding one drop of concentrated HCl to an \( \mathrm{NH}_{4} \mathrm{OH} \) solution decreases the \( \mathrm{pH} \). \( \mathrm{HCl} \) is a strong acid and \( \mathrm{NH}_4\mathrm{OH} \) is a weak base; the addition of an acid to a base will indeed lower the \( \mathrm{pH} \) of the solution. Therefore, statement (a) is correct.

Step 2: Evaluate Statement B

Statement (b) discusses a mixture of one equivalent of \( \mathrm{CH}_{3} \mathrm{COOH} \) and \( \mathrm{NaOH} \). \( \mathrm{CH}_{3} \mathrm{COOH} \) is a weak acid and \( \mathrm{NaOH} \) is a strong base. When mixed in equivalent amounts, they react to form water and \( \mathrm{CH}_{3} \mathrm{COONa} \) which results in a basic solution due to the presence of the conjugate base \( \mathrm{CH}_{3} \mathrm{COO}^- \). The \( \mathrm{pH} \) will be greater than 7, so the statement that the \( \mathrm{pH} \) is 7 is incorrect.

Step 3: Analyze Statement C

Statement (c) asserts that the \( \mathrm{pH} \) of pure neutral water is not zero. In pure water, both \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) ion concentrations are equal at \( 1 \times 10^{-7} \) M, resulting in a \( \mathrm{pH} \) of 7, not zero. Thus, statement (c) is correct.

Step 4: Check Statement D

Statement (d) compares the \( \mathrm{H}^+ \) ion concentration of cold, concentrated \( \mathrm{H}_2\mathrm{SO}_4 \) with a dilute solution. Concentrated \( \mathrm{H}_2\mathrm{SO}_4 \) has a much higher \( \mathrm{H}^+ \) concentration than a dilute solution, contrary to the statement. Therefore, statement (d) is incorrect.

Key Concepts

Acid-Base Reaction

When we mix acids and bases, we are participating in an acid-base reaction. These reactions are fundamental to understanding chemistry and have various applications in everyday life. An acid-base reaction can be identified because acids will donate a proton (\( \mathrm{H}^+ \)) while bases will accept a proton.In many situations, this process occurs in aqueous solutions:

• A strong acid, like hydrochloric acid (\( \mathrm{HCl} \)), will completely dissociate in water to release \( \mathrm{H}^+ \) ions.
• A weak base, such as ammonium hydroxide (\( \mathrm{NH}_4\mathrm{OH} \)), partially accepts \( \mathrm{H}^+ \) ions from the solution.
• This interaction modifies the \( \mathrm{H}^+ \) concentration and often results in a \( \mathrm{pH} \) change.

Recognizing the type of acid and base involved allows us to predict how the \( \mathrm{pH} \) of a solution will change.

Neutralization

Neutralization is a specific type of acid-base reaction where an acid and a base mix to form water and a salt. This reaction typically brings the solution closer to neutral, but certain aspects affect the final \( \mathrm{pH} \).Consider the case of mixing equal parts of acetic acid (\( \mathrm{CH}_3\mathrm{COOH} \)) and sodium hydroxide (\( \mathrm{NaOH} \)):

• The acetic acid is a weak acid and does not completely break down in water.
• In contrast, sodium hydroxide is a strong base, fully dissociating to contribute \( \mathrm{OH}^- \) ions.
• When mixed, the resultant salt (sodium acetate) can make the solution slightly basic, thus pushing the \( \mathrm{pH} \) over 7.

In essence, neutralization doesn't always result in a neutral solution (\( \mathrm{pH} \) of 7), especially if the reactants are a weak acid mixed with a strong base.

Strong Acids vs Weak Bases

The behavior of acids and bases in solutions largely determines their impact on \( \mathrm{pH} \). Strong acids and weak bases interact differently:- **Strong Acids**: These dissociate completely in water, providing a high concentration of \( \mathrm{H}^+ \) ions. This makes the \( \mathrm{pH} \) lower, indicating an acidic solution.- **Weak Bases**: In contrast, weak bases do not fully dissociate and are less efficient at "soaking up" protons. This means they only slightly increase the \( \mathrm{pH} \), making them less effective at neutralizing acids.When a strong acid is introduced into a solution of a weak base, as seen in statement (a), the \( \mathrm{H}^+ \) concentration will increase, driving down the \( \mathrm{pH} \) rapidly. This is why you can expect a noticeable change in \( \mathrm{pH} \) when adding a strong acid to a weak base.

pH of Water

The \( \mathrm{pH} \) of water is a key concept in understanding acidity and basicity. Pure water, at room temperature, has a \( \mathrm{pH} \) of 7. This number represents neutrality, where the concentration of \( \mathrm{H}^+ \) ions equals that of \( \mathrm{OH}^- \) ions.However, it's crucial to recognize that the \( \mathrm{pH} \) of water is not always stable at 7:

• Factors such as temperature changes can affect the number of \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) ions, thus altering the \( \mathrm{pH} \).
• Even though pure water at normal conditions has a \( \mathrm{pH} \) of 7, this does not imply that water can't have a different \( \mathrm{pH} \) with impurities or dissolved substances present.

Understanding these aspects highlights why statement (c) is indeed correct, as the \( \mathrm{pH} \) of pure neutral water is not zero, but 7.