Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{pH}\) of \(0.1 \mathrm{M}\) monobasic acid solution is found to be \(2 .\) Thus its osmotic pressure at T. K. is (a) \(11.11 \mathrm{ST}\) (b) \(0.11 \mathrm{ST}\) (c) \(0.011 \mathrm{ST}\) (d) \(1.11 \mathrm{ST}\)

Step-by-Step Solution

Answer

The osmotic pressure is \(0.11 \mathrm{ST}\).

Step 1: Determine the Hydrogen Ion Concentration

Given that the pH of the acid solution is 2, we use the formula for pH: \[ \text{pH} = -\log_{10}[H^+] \] Solving for \([H^+]\), we have: \[ [H^+] = 10^{-2} = 0.01 \text{ M} \]

Step 2: Determine the Degree of Dissociation

The initial concentration of the acid is 0.1 M. If \(\alpha\) is the degree of dissociation, then the concentration of \(H^+\) ions is also \(C\alpha = 0.01\) M. Solving for \(\alpha\), we have: \[ 0.1 \alpha = 0.01 \ \alpha = \frac{0.01}{0.1} = 0.1 \] Thus, the degree of dissociation \(\alpha\) is 0.1.

Step 3: Calculate Total Molarity in Solution Due to Ionization

The ionization of the acid produces \(H^+\) and the conjugate base \(A^-\), so total molarity \(M_t\) is the sum of initial and ionized species: \[ M_t = 0.1 (1 + \alpha) = 0.1 (1 + 0.1) = 0.1 \times 1.1 = 0.11 \text{ M} \]

Step 4: Use the Osmotic Pressure Formula

The osmotic pressure \(\Pi\) is given by the formula: \[ \Pi = iCRT \] Where \(i\) is the van 't Hoff factor, which in this case is \(1 + \alpha = 1.1\), \(C\) is the total molarity (0.11 M), \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin. Thus, \[ \Pi = 0.11 \cdot 1.1 \cdot RT = 0.11 \cdot RT = 0.11 \text{ ST} \]

Key Concepts

pH calculation

The pH scale is a measure of the acidity or basicity of a solution. It indicates the concentration of hydrogen ions \([H^+]\) present in a solution. A lower pH value means a higher concentration of hydrogen ions, indicating a more acidic solution.
To calculate the pH of a solution, we use the formula: \[ \text{pH} = -\log_{10}[H^+] \] In this formula, the concentration of hydrogen ions \([H^+]\) is expressed in moles per liter \( \text{M} \).
For example, if we know that a solution has a pH of 2,
we can determine the hydrogen ion concentration by rearranging the formula:

• \([H^+] = 10^{-\text{pH}} = 10^{-2} = 0.01 \text{ M} \)

This means the solution has \(0.01 \text{ M}\) hydrogen ions.
Understanding pH is key in many chemical reactions and processes, as it affects structure, function, and reactivity of molecules.

Degree of dissociation

The degree of dissociation, represented by \(\alpha\), is an important concept in chemistry.
It tells us how much of a compound has dissociated into its ions in solution.
This is especially important for electrolytes, such as acids, bases, and salts, as it directly impacts their electrical conductivity.

• To determine \(\alpha\), we compare the concentration of dissociated ions to the initial concentration.
• Mathematically, \(\alpha\) is calculated using the formula: \[ \alpha = \frac{\text{concentration of dissociated ions}}{\text{initial concentration}} \]

For a monobasic acid with an initial concentration of \(0.1 \text{ M}\) and a pH indicating
that the hydrogen ion concentration \([H^+]\) is \(0.01 \text{ M}\), the degree of dissociation is:

• \(0.1\alpha = 0.01 \rightleftharpoons \alpha = 0.1\)

This means only 10% of the acid molecules dissociated in the solution.
Recognizing the degree of dissociation aids in predicting the behavior of solutions in various conditions.

Van 't Hoff factor

The Van 't Hoff factor, symbolized as \(i\), quantifies the effect of solute particles on colligative properties.
It represents the number of particles a solute produces in solution.
This is crucial for understanding colligative properties like:

• osmotic pressure
• boiling point elevation
• freezing point depression

Van 't Hoff factor is calculated considering how ions or molecules separate in solution:

• For a dissociated solute, \(i = 1 + \alpha\)

For instance, in a solution with a monobasic acid, if the degree of dissociation \(\alpha\) is \(0.1\), then:

• \(i = 1 + 0.1 = 1.1\)

Using \(i\), we can calculate properties like osmotic pressure with the formula: \[ \Pi = iCRT \]This factor is vital in determining the true effect of dissolved solute on a solution's properties.