The solution from the following with highest depression in freezing point/lowest freezing point is
- 180 g of benzoic acid dissolved in benzene
- 180 g of acetic acid dissolved in benzene
- 180 g of acetic acid dissolved in water
- 180 g of glucose dissolved in water
The Correct Option is C
Approach Solution - 1
To determine which solution has the highest depression in freezing point, we need to consider the colligative properties of solutions, specifically the freezing point depression.
Colligative Properties: Freezing point depression is given by the formula:
ΔTf = i · Kf · m
where ΔTf is the depression in freezing point, i is the van 't Hoff factor (number of particles the solute breaks into), Kf is the cryoscopic constant of the solvent, and m is the molality of the solution.
Analyzing Each Option:
- Option (3): 180 g of acetic acid in water. Acetic acid partially ionizes in water (i ≈ 1). The molality will be relatively high as the solvent is water.
- Option (2): 180 g of acetic acid in benzene. Acetic acid does not ionize in benzene (i = 1). Benzene has a lower Kf than water, leading to a lesser depression.
- Option (1): 180 g of benzoic acid in benzene. Similar to option (2), it does not ionize, and its effect will be limited by benzene’s lower Kf.
- Option (4): 180 g of glucose in water. Glucose does not ionize (i = 1), but its molar mass is higher, leading to a lower molality compared to acetic acid.
Conclusion: Given that acetic acid has a higher molar mass than glucose and ionizes in water, it will result in a greater freezing point depression.
Thus, the solution with the highest depression in freezing point is: 180 g of acetic acid dissolved in water.
Approach Solution -2
To determine which solution has the highest depression in freezing point or lowest freezing point, we need to consider the concept of colligative properties, specifically the depression of freezing point.
Depression in Freezing Point:
The depression in freezing point (\(ΔT_f\)) is given by the formula:
\(ΔT_f = i \cdot K_f \cdot m\)
- \(i\) is the van 't Hoff factor (number of particles the solute splits into)
- \(K_f\) is the freezing point depression constant of the solvent
- \(m\) is the molality of the solution
The greater the number of particles (\(i \cdot m\)), the greater the depression of freezing point, and consequently, the lower the freezing point of the solution.
Evaluation of Options:
- 180 g of benzoic acid dissolved in benzene:
- Benzoic acid in benzene forms a dimer, effectively lowering \(i\) to about 0.5.
- 180 g of acetic acid dissolved in benzene:
- Acetic acid similarly forms a dimer in benzene, which also results in a lower \(i\).
- 180 g of acetic acid dissolved in water:
- Acetic acid partially ionizes in water to form acetate ions and protons, increasing \(i\) since it dissociates into multiple particles.
- 180 g of glucose dissolved in water:
- Glucose, being a non-electrolyte, does not dissociate in water and \(i\) remains 1.
Considering the dissociation and ionization:
- Acetic acid in water increases the number of solute particles due to partial ionization.
- This results in a higher \(i \cdot m\) value compared to others, leading to the greatest depression of freezing point.
Conclusion: The solution with 180 g of acetic acid dissolved in water exhibits the highest depression in freezing point due to its ability to ionize, leading to the lowest freezing point.
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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.