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

Option (a) is correct; the other options are incorrect.

Step 1: Analyze Option (a)

First, determine the \( ext{pH}\) of the solution. The molecular weight of \( ext{H}_2 ext{SO}_4\) is 98 g/mol. Calculate the molarity by dividing the mass of the acid by its molar mass and the volume of the solution (which is 1 liter). \[ \text{Molarity of } \text{H}_2\text{SO}_4 = \frac{0.49 \, \text{g}}{98 \, \text{g/mol} \times 1 \, \text{L}} = 0.005 \, \text{M} \]Since each \( ext{H}_2 ext{SO}_4\) dissociates into two protons (H\(^+\)), the proton concentration is \([H^+] = 2 \times 0.005\) M = 0.01 M. \( ext{pH}\) is calculated using the formula: \[ \text{pH} = -\log [H^+] = -\log (0.01) = 2 \]. \Thus, option (a) is correct.

Step 2: Analyze Option (b)

Identify the conjugate base of \( ext{H}_2 ext{S}\). The conjugate base of an acid is the species that remains after the acid donates a proton (H\(^+\)). Therefore, when \( ext{H}_2 ext{S}\) loses one \(H^+\), it forms \( ext{HS}^-\), which is the correct conjugate base. If \( ext{H}_2 ext{S}\) loses both protons, \( ext{S}^{2-}\) would be formed, but this requires removing two protons, which is incorrect to be mentioned as the conjugate base.

Step 3: Analyze Option (c)

Determine whether \( ext{BF}_3\) is a Lewis base. Lewis bases are electron pair donors. However, \( ext{BF}_3\) is an electron-deficient molecule because boron has only six electrons in its valence shell. This makes \( ext{BF}_3\) act as a Lewis acid as it can accept electron pairs.

Step 4: Analyze Option (d)

Check the color change of phenolphthalein. Phenolphthalein is a pH indicator, which is colorless in acidic solutions and turns pink or fuchsia in basic solutions when the pH is above 8.2. Therefore, in basic medium, phenolphthalein is not colorless.

Key Concepts

pH Calculation

Understanding how to calculate the pH of a solution is crucial in chemistry. pH is a measure of the hydrogen ion concentration in a solution. The pH scale generally ranges from 0 to 14, with lower numbers being more acidic and higher numbers being more basic. Neutral solutions, like pure water, have a pH of 7. To calculate pH, you use the formula: \[ \text{pH} = -\log [H^+] \]where \([H^+]\) is the concentration of hydrogen ions in the solution in moles per liter (mol/L). For example, if the \([H^+]\) is \(0.01\, M\), the pH is 2 because \[ \text{pH} = -\log (0.01) = 2 \]. When dealing with strong acids like sulfuric acid \(\mathrm{H}_2\mathrm{SO}_4\), which dissociates completely, it is important to consider the amount of \(\text{H}^+\) ions each molecule releases. Sulfuric acid releases two \(\text{H}^+\) ions, so you multiply the molarity of the acid by two to find the \([H^+]\). This is why careful calculation of the acid's contribution to \([H^+]\) is key to finding the correct pH.

Conjugate Base Identification

The concept of a conjugate base stems from the Brønsted-Lowry acid-base theory, which emphasizes the exchange of protons (\(\text{H}^+\)). When an acid donates a proton, what remains is its conjugate base. A helpful way to remember this is:

• A conjugate base is simply the original acid minus a proton (\(\text{H}^+\)).

For instance, if we consider \(\mathrm{H}_2\mathrm{S}\) (hydrogen sulfide), when it donates one proton, it becomes \(\mathrm{HS}^-\), which is its conjugate base. It's important to note that removing one more proton could result in \(\mathrm{S}^{2-}\), but this is not typically referred to as the conjugate base in typical reactions where only one proton is lost. Understanding conjugate bases helps explain the reactivity and strength of acids. Moreover, it provides insights into equilibrium expressions in chemical reactions, making it an essential aspect of acid-base chemistry.

Lewis Acid-Base Theory

The Lewis acid-base theory expands beyond the traditional proton donation and acceptance seen in the Brønsted-Lowry theory. Instead, it focuses on the transfer of electron pairs.

• A **Lewis acid** is a species that can accept an electron pair.
• A **Lewis base** is a species that can donate an electron pair.

Consider \(\mathrm{BF}_3\) (boron trifluoride), which is a great example of a Lewis acid. Boron, being electron-deficient with only six electrons in its outer shell, readily accepts electron pairs, thus making it a Lewis acid. This ability to accept electron pairs is critical in many chemical reactions, particularly in catalysis and complexation reactions.Recognizing Lewis acids and bases allows chemists to predict and understand reactions, particularly those involving coordination compounds and other non-proton-exchange processes.

pH Indicators

pH indicators are substances that change color depending on the acidity or basicity of a solution. They are valuable tools in laboratories and classrooms for determining pH visually without sophisticated equipment. One common pH indicator is **phenolphthalein**, which demonstrates a clear color transition:

• It is colorless in acidic solutions (pH below 8.2).
• In basic solutions (pH above 8.2), it turns pink or fuchsia.

This change helps identify the transition from an acidic to a basic environment. Phenolphthalein is frequently used in titrations, a laboratory method used to determine the concentration of an unknown acid or base by neutralization. Understanding how pH indicators work, and noting their specific color change points, is crucial when selecting the right indicator for various chemical analyses. They offer simplicity and visual clarity, making them an essential tool in both educational and professional settings.