Problem 30 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is correct? (a) the \(\mathrm{pH}\) of one litre solution containing \(0.49 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is \(2.0\) (b) the conjugate base of \(\mathrm{H}_{2} \mathrm{~S}\) is \(\mathrm{S}^{2-}\) (c) \(\mathrm{BF}_{3}\) is lewis base (d) phenolphthalein is colourless in basic medium.

Step-by-Step Solution

Answer

The correct option is (a). The pH is indeed 2.0 for the given solution.

Step 1: Analyze Option (a)

Calculate the number of moles of \( \text{H}_2\text{SO}_4 \) in the 0.49g solution, using the molar mass of \( \text{H}_2\text{SO}_4 \), which is approximately 98 g/mol.Number of moles = \( \frac{0.49}{98} = 0.005 \text{ moles} \).Since the solution is 1 litre, the concentration of \( \text{H}_2\text{SO}_4 \) is 0.005 M. \( \text{H}_2\text{SO}_4 \) is a strong diprotic acid:\[ \text{H}_2\text{SO}_4 \rightarrow 2\text{H}^+ + \text{SO}_4^{2-} \]Thus, the concentration of \( \text{H}^+ \) ions will be 0.01 M, and the pH is:\[ \text{pH} = -\log[\text{H}^+] = -\log(0.01) = 2.0 \].Option (a) is correct.

Step 2: Analyze Option (b)

\( \text{H}_2\text{S} \) is a weak acid. Its conjugate base is formed by removing one proton (one \( \text{H}^+ \) ion).\[ \text{H}_2\text{S} \rightarrow \text{HS}^- + \text{H}^+ \].The conjugate base of \( \text{H}_2\text{S} \) is \( \text{HS}^- \), not \( \text{S}^{2-} \). Thus, option (b) is incorrect.

Step 3: Analyze Option (c)

\( \text{BF}_3 \) is a molecule where boron is electron-deficient. It has only 6 valence electrons around it, making it a Lewis acid, not a base, because it can accept an electron pair.Therefore, option (c) is incorrect.

Step 4: Analyze Option (d)

Phenolphthalein is a pH indicator. It is actually colourless in acidic to neutral solutions and turns pink in basic solutions. Thus, option (d) being "phenolphthalein is colourless in basic medium" is incorrect.

Key Concepts

pH calculation

The concept of pH is central in acid-base chemistry. pH is a scale used to determine the acidity or basicity of an aqueous solution. It is defined as the negative logarithm (-log) of the hydrogen ion concentration. In simple terms, it tells us how many hydrogen ions are present in a solution. For strong acids, like sulfuric acid (\(\text{H}_2\text{SO}_4\)), which dissociates completely in water, the concentration of hydrogen ions (\([\text{H}^+]\)) can be calculated directly from the concentration of the acid. In the exercise example, the concentration of \(\text{H}^+\) ions was calculated to be 0.01 M. Therefore, the pH is calculated as:\[ \text{pH} = -\log(0.01) = 2.0 \]Understanding pH calculations is crucial because it impacts various fields such as biology, environmental science, and chemistry. Here are a few friendly reminders:- A pH lower than 7 indicates an acidic solution.- A pH higher than 7 indicates a basic solution.- A pH of 7 is considered neutral.

Conjugate acids and bases

In acid-base chemistry, the terms conjugate acid and conjugate base are often used to discuss the species that arise when a compound gains or loses a proton (\(\text{H}^+\)). When an acid donates a proton, what remains is its conjugate base. Conversely, when a base accepts a proton, what forms is its conjugate acid.Take for example hydrogen sulfide (\(\text{H}_2\text{S}\)), a weak acid. When \(\text{H}_2\text{S}\) donates a proton, it forms its conjugate base:\[ \text{H}_2\text{S} \rightarrow \text{HS}^- + \text{H}^+ \]Thus, the conjugate base of \(\text{H}_2\text{S}\) is \(\text{HS}^-\), not \(\text{S}^{2-}\), as commonly misunderstood. Understanding this concept is useful for predicting the behavior of molecules in chemical reactions.Key points to remember:- The conjugate base forms when an acid loses a proton.- The conjugate acid forms when a base gains a proton.- This exchange is central to buffer solutions, where weak acids and bases maintain pH stability.

Lewis acids and bases

The Lewis theory expands on the definitions of acids and bases, focusing on electron pair transfer. A Lewis acid is a species that accepts an electron pair, while a Lewis base donates an electron pair. This broader understanding goes beyond the traditional "protons" concept.For instance, \(\text{BF}_3\) (boron trifluoride) is a classic example of a Lewis acid. Boron, in \(\text{BF}_3\), has only 6 valence electrons, making it electron-deficient. It can accept an electron pair from a Lewis base to fulfill its electron shell. Often learners mistakenly categorize \(\text{BF}_3\) as a Lewis base because they traditionally think of bases as electron donors.Here's what to keep in mind:- Lewis acids accept electron pairs.- Lewis bases donate electron pairs.- This concept is crucial for understanding reactions like ligand binding in coordination chemistry and enzyme-substrate interactions in biology. With these structured understandings, the Lewis model helps explain many reactions beyond the capacity of traditional acid-base definitions.