The depression in freezing point observed for a formic acid solution of concentration $05\, mL\, L ^{-1}$ is $00405^{\circ} C$ Density of formic acid is $105 \, g \, mL ^{-1}$ The Van't Hoff factor of the formic acid solution is nearly : (Given for water $k _{ f }=186 \, K \, kg \, mol ^{-1}$ )
- $0.8$
- $1.1$
- $1.9$
- $2.4$
The Correct Option is C
Solution and Explanation
To find the Van't Hoff factor (\(i\)) for the formic acid solution, we use the depression in freezing point formula:
\(\Delta T_f = i \cdot K_f \cdot m\)
Where:
- \(\Delta T_f = 0.0405^\circ C\) is the depression in freezing point.
- \(K_f = 1.86 \, K \, kg \, mol^{-1}\) is the cryoscopic constant for water.
- \(m\) is the molality of the solution.
The given concentration of formic acid is \(5 \, mL \, L^{-1}\). First, we calculate the molality.
Step 1: Calculate the mass of formic acid in 1 L of solution.
Density of formic acid = \(1.05 \, g \, mL^{-1}\).
Mass of formic acid in \(5 \, mL\) is:
\(\text{Mass} = \text{Volume} \times \text{Density} = 5 \times 1.05 = 5.25 \, g\)
Step 2: Calculate the number of moles of formic acid.
Molar mass of formic acid (HCOOH) = \(2 \times 1 + 12 + 16 \times 2 = 46 \, g \, mol^{-1}\).
Number of moles = \(\frac{5.25}{46} \approx 0.1141 \, mol\).
Step 3: Calculate the molality.
Since the solution is prepared in 1 liter of water, the mass of water is approximately \(1000 \, g = 1 \, kg\).
Molality \((m) = 0.1141 \, mol \, kg^{-1}\).
Step 4: Calculate the Van't Hoff factor.
Rearranging the formula for Van't Hoff factor:
\(i = \frac{\Delta T_f}{K_f \cdot m} = \frac{0.0405}{1.86 \times 0.1141} \approx 1.9\)
Therefore, the Van't Hoff factor of the formic acid solution is approximately 1.9, which corresponds to the correct option.
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.