Freezing Point Depression of a KBr Solution: An In-Depth Analysis

Introduction

The concept of freezing point depression is a fundamental principle in physical chemistry, particularly in understanding the behavior of solutions. This principle is often applied in various practical scenarios, such as antifreeze in vehicles or understanding the properties of brine solutions. This article aims to provide a detailed analysis of the freezing point depression of a solution prepared by dissolving 15 grams of KBr (potassium bromide) in 100 ml of water, given the freezing point depression constant for water (Kf) as 1.86 K kg/mol.

Understanding the Problem

When we prepare a solution by dissolving 15 grams of KBr in 100 ml of water, the first step is to calculate the molality of the solution, which is defined as the number of moles of solute per kilogram of solvent.

Step 1: Calculate the Moles of KBr

To find the moles of KBr, we need to use its molar mass. The molar mass of KBr (potassium bromide) is approximately 117.9 g/mol. Therefore, the moles of KBr can be calculated as:

[ text{Moles of KBr} frac{15 text{ g}}{117.9 text{ g/mol}} 0.127 text{ moles} ]

Step 2: Consider the Ionic Dissociation

KBr dissolves in water and dissociates into K? and Br? ions in a one-to-one ratio. This means that the total number of particles in the solution will be twice the moles of KBr, as each KBr molecule dissociates into two ions.

[ text{Moles of particles} 2 times text{moles of KBr} 2 times 0.127 text{ moles} 0.254 text{ moles} ]

Step 3: Determine the Molality

The molality of the solution is the moles of KBr present per kilogram of water. Given that 100 ml of water is approximately 0.1 kg, the molality can be calculated as:

[ text{Molality} frac{0.254 text{ moles}}{0.1 text{ kg}} 2.54 text{ m} ]

Freezing Point Depression Calculation

Freezing point depression is the decrease in the freezing point of a solution relative to the pure solvent. The relationship between freezing point depression and molality is given by:

[ Delta T_f K_f times m ]

Where:

(Delta T_f): Freezing point depression (K_f): Freezing point depression constant for water (1.86 K kg/mol) (m): Molality of the solution

Substituting the given values, we get:

[ Delta T_f 1.86 text{ K kg/mol} times 2.54 text{ m} 4.72 text{ K} ]

The freezing point of the solution will be:

[ T_f T_{text{freezing point of water}} - Delta T_f 0 - 4.72 text{ K} -4.72 text{ K} ]

Conclusion

In summary, the solution prepared by dissolving 15 grams of KBr in 100 ml of water has a freezing point that is depressed to -4.72 K due to the solute dissociation and the freezing point depression constant of water. This analysis demonstrates the practical application of colligative properties, specifically freezing point depression, in understanding the behavior of solutions and their thermal properties.

Keywords

freezing point depression, molality, KBr solution