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 statement is (a).

Step 1: Calculate moles of H₂SO₄

We need to find the number of moles of \( \mathrm{H}_2\mathrm{SO}_4 \) in the given solution. The molar mass of \( \mathrm{H}_2\mathrm{SO}_4 \) is approximately 98 g/mol. Thus, the number of moles of \( \mathrm{H}_2\mathrm{SO}_4 \) in 0.49 g is calculated as follows: \[ \text{Moles of } \mathrm{H}_2\mathrm{SO}_4 = \frac{0.49\, \text{grams}}{98\, \text{g/mol}} = 0.005\, \text{moles} \]

Step 2: Calculate pH of the solution

Since \( \mathrm{H}_2\mathrm{SO}_4 \) is a strong acid, it dissociates completely in water. Each molecule of \( \mathrm{H}_2\mathrm{SO}_4 \) releases 2 moles of \( \mathrm{H}^+ \) ions: \[ \mathrm{H}_2\mathrm{SO}_4 \rightarrow 2\, \mathrm{H}^+ + \mathrm{SO}_4^{2-} \] Thus, the concentration of \( \mathrm{H}^+ \) ions is \( 2 \times 0.005 = 0.01 \) mol/L. The \( \mathrm{pH} \), which is the negative logarithm of \( \mathrm{H}^+ \) concentration, is calculated as follows: \[ \mathrm{pH} = -\log(0.01) = 2 \] Thus, statement (a) is correct.

Step 3: Determine the conjugate base of H₂S

The conjugate base of an acid is formed by the removal of a proton. For \( \mathrm{H}_2\mathrm{S} \), removing one proton forms \( \mathrm{HS}^- \), not \( \mathrm{S}^{2-} \). Thus, statement (b) is incorrect.

Step 4: Determine Lewis Acid and Base characteristics

\( \mathrm{BF}_3 \) is known as a Lewis acid because it can accept electron pairs due to the incomplete octet of boron. It is not a Lewis base. Thus, statement (c) is incorrect.

Step 5: Identify phenolphthalein behavior in different mediums

Phenolphthalein is a pH indicator that is colorless in acidic medium and turns pink in basic medium. Thus, statement (d) is incorrect.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, and understanding it is key for calculations involving chemical reactions and solutions. It is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
To determine the molar mass, you add together the atomic masses of all the elements in a molecule. For example, sulfuric acid (\(\mathrm{H}_2\mathrm{SO}_4\)) has the following atomic masses: hydrogen (approximately 1 g/mol), sulfur (approximately 32 g/mol), and oxygen (approximately 16 g/mol).

• Calculate for each element: - Hydrogen: \(2 \times 1 = 2\) g/mol - Sulfur: \(1 \times 32 = 32\) g/mol - Oxygen: \(4 \times 16 = 64\) g/mol
• Sum them up: - Total molar mass = \(2 + 32 + 64 = 98\) g/mol

The molar mass is crucial for converting mass to moles, as used in chemical calculations like determining the pH of a solution.

Conjugate Base

A conjugate base is what remains after an acid donates a proton (H⁺) in a chemical reaction. Understanding this concept is important for analyzing acid-base reactions and equilibria.
Take dihydrogen sulfide (\(\mathrm{H}_2\mathrm{S}\)) as an example. When it loses one proton, it forms the conjugate base, bisulfide ion (\(\mathrm{HS}^-\)). Misconceptions may arise, such as assuming a further loss of protons leads directly to the sulfide ion (\(\mathrm{S}^{2-}\)). However, the immediate conjugate base formed after losing one proton is the bisulfide ion.
In chemical reactions:

• Acid Function: Proton donor
• Conjugate Base Formation: - \(\mathrm{H}_2\mathrm{S} \rightarrow \mathrm{HS}^- + \mathrm{H}^+\)

Recognizing and identifying conjugate bases help in balancing equations and predicting reaction behavior.

Lewis Acid

The concept of Lewis acids and bases is based on the ability to accept or donate electron pairs. This framework broadens the definition beyond just protons.
A Lewis acid is a substance that can accept an electron pair, making it an electron-pair acceptor. One classic example is boron trifluoride (\(\mathrm{BF}_3\)).
Boron in \(\mathrm{BF}_3\) has an incomplete octet, which explains why it readily accepts electrons. This makes it a quintessential Lewis acid.

• Lewis Acid Characteristics: - Electron pair acceptor - Has a vacant orbital - Example: \(\mathrm{BF}_3\)

Recognizing a Lewis acid helps in understanding various types of chemical reactions, especially those that don't involve hydrogen ions directly.

pH Indicator

pH indicators are substances that change color depending on the pH level of the solution they are in. They are invaluable for determining whether a solution is acidic or basic.
One well-known pH indicator is phenolphthalein. It remains colorless in acidic to slightly neutral solutions but turns a vibrant pink in basic solutions. This color change is instrumental in titrations, where the endpoint of a chemical reaction is identified visually.

• Behavior in Different Mediums: - Colorless in acidic and neutral (<7 pH) solutions - Pink in basic (>7 pH) solutions

Understanding how pH indicators work aids in conducting experiments and accurately interpreting the acidity or basicity of various solutions.