Question

The freezing-point depression of a 0.091-m solution of CsCl is \(0.320^{\circ} \mathrm{C} .\) The freezing-point depression of a \(0.091-m\) solution of \(\mathrm{CaCl}_{2}\) is \(0.440^{\circ} \mathrm{C}\). In which solution does ion association appear to be greater? Explain.

Short answer

Ion association appears to be greater in the 0.091-m CsCl solution compared to the 0.091-m CaCl2 solution, as the freezing-point depression value is lower for the CsCl solution (0.320°C) than for the CaCl2 solution (0.440°C).

Step-by-step solution

First, compare the freezing-point depression values for each solution: - 0.320°C for 0.091-m CsCl - 0.440°C for 0.091-m CaCl2 Since the molality is the same for both solutions, we can directly compare their freezing-point depression values. #Step 2: Determine which solution has the greater ion association#

The greater ion association corresponds to a lower freezing-point depression value. Given the comparison in Step 1, it's clear that the 0.091-m CsCl solution has a lower freezing-point depression value (0.320°C) than the 0.091-m CaCl2 solution (0.440°C). Thus, ion association appears to be greater in the CsCl solution. In conclusion, ion association appears to be greater in the 0.091-m CsCl solution compared to the 0.091-m CaCl2 solution.

Key concepts

Ion Association

Ion association refers to the phenomenon where ions in a solution come together to form neutral pairs or clusters instead of remaining completely dissociated as separate ions. This can impact properties like the freezing-point depression of a solution. Ion association reduces the effect that ions have on the colligative properties of a solution.
When there is high ion association, fewer ions are available to decrease the vapor pressure, leading to less freezing-point depression. In the exercise, since the CsCl solution exhibited a lower freezing-point depression, it suggests that ion association is more significant in this solution compared to the CaCl2 solution.
Understanding ion association helps in correlating the physical properties of solutions with the degree of ionic dissociation, which is crucial in predicting the behavior of ions in varying chemical and physical conditions.

Molality

Molality is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality is not affected by changes in temperature or pressure because it relies on the mass of the solvent rather than the total volume of the solution. For calculations involving colligative properties, such as freezing-point depression, molality is often preferred.
To calculate molality, you follow these steps:

• Determine the moles of solute present in the solution.
• Measure the mass of the solvent in kilograms.
• Divide the number of moles of solute by the mass of the solvent to find molality.

In the exercise, both solutions of CsCl and CaCl2 have the same molality (0.091 m). This allows for a direct comparison of their freezing-point depressions and the effects of ion association.

CsCl

Cesium chloride (CsCl) is a chemical compound composed of cesium and chloride ions. CsCl is important in studying freezing-point depression due to its simple 1:1 ion ratio.
The presence of CsCl causes a smaller freezing-point depression in the provided exercise, indicating possible greater ion association compared to CaCl2. This means the interactions between cesium and chloride might be strong enough to form ion pairs, decreasing the number of effective particles in the solution.
Knowing how CsCl behaves in solutions provides insight into its properties in various applications, including its use in density gradient centrifugation and as an electrolyte in experiments.

CaCl2

Calcium chloride (CaCl2) is a salt consisting of calcium and chloride ions. It’s commonly used for ice melting and as a de-icing agent. In a solution, CaCl2 dissociates into three ions: one calcium ion and two chloride ions, having a 1:2 molar ratio.
In the context of freezing-point depression, CaCl2 typically demonstrates a more significant decrease in temperature than a compound with fewer dissociated ions. The exercise shows that CaCl2 solution has a greater freezing-point depression than CsCl at the same molality, suggesting lower ion association and, therefore, a higher number of free ions affecting the freezing point.
Understanding how CaCl2 behaves in solution is crucial for its practical applications, like road salting, as well as for theoretical predictions in chemistry regarding electrolyte solutions.