Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The observed osmotic pressure for a \(0.10 \mathrm{M}\) solution of \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{SO}_{4}\right)_{2}\) at \(25^{\circ} \mathrm{C}\) is \(10.8 \mathrm{~atm} .\) The expected and experimental (observed) values of van't Hoff factor \((i)\) will be respectively: \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\) (a) 5 and \(4.42\) (b) 4 and \(4.00\) (c) 5 and \(3.42\) (d) 3 and \(5.42\)

Step-by-Step Solution

Answer

The expected and observed Van't Hoff factors are 5 and 4.42, respectively. The answer is (a) 5 and 4.42.

Step 1: Determine the expected Van't Hoff factor

The compound \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{SO}_{4}\right)_{2}\) dissociates in water to form ions. The dissociation equation is:\[\mathrm{Fe}^{2+} + 2\mathrm{NH}_{4}^{+} + 2\mathrm{SO}_{4}^{2-}\]This gives a total of 5 ions per formula unit, which means the expected Van't Hoff factor, \(i_{expected}\), is 5.

Step 2: Use the osmotic pressure equation to find experimental Van't Hoff factor

The osmotic pressure (\(\Pi\)) is given by the formula: \[ \Pi = i \times C \times R \times T \]where \(i\) is the Van't Hoff factor, \(C\) is the molarity (0.10 M), \(R\) is the gas constant (0.082 L atm K\(^{-1}\) mol\(^{-1}\)), and \(T\) is the temperature in Kelvin (25°C = 298 K).Rearrange the formula to solve for \(i_{observed}\):\[ i_{observed} = \frac{\Pi}{C \times R \times T} \]Substitute the given values:\[ i_{observed} = \frac{10.8}{0.10 \times 0.082 \times 298} \]

Step 3: Calculate the observed Van't Hoff factor

Continuing from Step 2, calculate:\[ i_{observed} = \frac{10.8}{2.444} \approx 4.42 \]The observed Van't Hoff factor is approximately 4.42.

Step 4: Compare the expected and observed Van't Hoff factors

The expected Van't Hoff factor was calculated to be 5. The experimental (observed) Van't Hoff factor is approximately 4.42. Compare these values to select the correct option.

Key Concepts

Osmotic Pressure

Osmotic pressure is a vital concept in chemistry, especially when dealing with solutions and their colligative properties. It refers to the pressure required to stop the process of osmosis, which is the movement of solvent molecules through a semipermeable membrane from a less concentrated solution into a more concentrated one. Osmotic pressure is influenced by the concentration of solute particles in a solution. Higher concentration means more significant osmotic pressure. Understanding osmotic pressure helps explain various biological and chemical phenomena, such as the way cells maintain their shape and how plants uptake water.
It is important to remember that osmotic pressure is not dependent on the identity of solute particles but rather on their number. This characteristic categorizes it as a colligative property.

Dissociation in Solutions

When ionic compounds dissolve in water, they dissociate into their respective ions. This process is fundamental to understanding how ionic solutions act differently than non-ionic solutions. For example, our compound \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{SO}_{4}\right)_{2}\) dissociates in water to form five ions: one \(\mathrm{Fe}^{2+}\), two \(\mathrm{NH}_{4}^{+}\), and two \(\mathrm{SO}_{4}^{2-}\).
The degree of dissociation in a solution affects its colligative properties, including osmotic pressure. The more ions produced, the more drastic the effect on properties like boiling point elevation or freezing point depression. The Van't Hoff factor, \(i\), indicates the number of particles a compound forms in a solution and is crucial for calculating these properties.

Ionic Compounds

Ionic compounds consist of positive and negative ions bound together by ionic bonds. These bonds form due to the electrostatic attraction between oppositely charged ions. A characteristic feature of ionic compounds is their ability to dissociate into ions when dissolved in water. When compounds like \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2}\left(\mathrm{SO}_{4}\right)_{2}\) dissolve, they split into their constituent ions. This dissociation increases the total number of particles in a solution, heavily influencing its colligative properties, such as osmotic pressure.
Ionic compounds tend to have high melting and boiling points because of their strong ionic bonds. Additionally, their ability to conduct electricity when dissolved or molten is another notable property, owing to the movement of free ions.

Osmotic Pressure Formula

The formula for osmotic pressure (\(\Pi\)) is crucial for calculating and understanding how solutes affect solution properties. It is given by:\[ \Pi = i \times C \times R \times T \]where:

• \(\Pi\) is the osmotic pressure.
• \(i\) is the Van't Hoff factor, representing the number of particles the solute forms in solution.
• \(C\) is the molarity of the solution (in moles per liter).
• \(R\) is the gas constant, valued at 0.082 L atm K\(^{-1}\) mol\(^{-1}\).
• \(T\) is the temperature in Kelvin.

This equation is similar to the ideal gas law and is essential for practical applications in chemistry and biology. For instance, it helps predict the movement of water across cell membranes and the behavior of solutions in different environmental conditions. Understanding this formula allows predicting osmotic pressure based on solute concentration and temperature variables, offering valuable insights into solution behavior.