Question

If you dissolve equal molar amounts of \(\mathrm{NaCl}\) and \(\mathrm{CaCl}_{2}\) in water, the \(\mathrm{CaCl}_{2}\) lowers the freezing point of the water almost 1.5 times as much as the NaCl. Why?

Short answer

CaCl₂ lowers the freezing point more because it produces more ions than NaCl when dissolved.

Step-by-step solution

Understanding Colligative Properties

Colligative properties depend on the number of solute particles in a solution, not on their identity. One such property is the freezing point depression, which is observed when a solute is added to a solvent, lowering the freezing point of the solution.

Examining the Dissociation of Solutes

Upon dissolving, NaCl dissociates into two ions: Na⁺ and Cl⁻. Therefore, 1 mole of NaCl produces 2 moles of particles in solution. CaCl₂, however, dissociates into three ions: one Ca²⁺ and two Cl⁻ ions. Thus, 1 mole of CaCl₂ results in 3 moles of particles.

Calculating the Freezing Point Depression

The freezing point depression (ΔT_f) is calculated using the formula: ΔT_f = i imes K_f imes m, where i is the van 't Hoff factor, K_f is the freezing point depression constant, and m is the molality. For NaCl, i = 2, and for CaCl₂, i = 3.

Comparing Effects of NaCl and CaCl₂

Given equal molar amounts, CaCl₂ will cause a greater freezing point depression than NaCl because it produces more particles ( i = 3 vs. i = 2). Consequently, the ΔT_f for CaCl₂ is about 1.5 times the ΔT_f for NaCl, as 3/2 = 1.5.

Key concepts

Freezing Point Depression

Freezing point depression is a fascinating colligative property. It is a phenomenon where the addition of a solute to a solvent causes the solution to freeze at a lower temperature than the pure solvent. This occurs because solute particles interfere with the process of ice formation, requiring more energy (in the form of lower temperatures) to arrange the liquid molecules into the solid phase.

When trying to understand why this happens, imagine adding salt to icy roads. The salt particles disrupt the order the water molecules need to form ice, effectively lowering the freezing point. The same principle occurs when solutes like \(\text{NaCl}\) or \(\text{CaCl}_{2}\) are dissolved in water. The more particles added, the greater the interference, leading to a greater depression of the freezing point.

In essence, whenever solute particles are introduced, the orderly structure necessary for ice formation is disturbed. This universally results in a lower freezing point for the solution.

Van 't Hoff Factor

The Van 't Hoff factor \( (i) \) is a crucial aspect of colligative properties. It quantifies the number of particles a solute produces when it dissolves. For ionic compounds, this involves dissociation into ions.

For example, \(\text{NaCl}\) dissociates into two ions: \(\text{Na}^+\) and \(\text{Cl}^-\). This gives it a \(i\) factor of 2. Meanwhile, \(\text{CaCl}_{2}\) breaks into three ions: one \(\text{Ca}^{2+}\) and two \(\text{Cl}^-\). Thus, \(\text{CaCl}_{2}\) has a \(i\) factor of 3.

Why is this factor important? Because it directly affects colligative properties like freezing point depression. The calculation \( \Delta T_f = i \times K_f \times m \) highlights this, where a higher \(i\) results in greater lowering of the freezing point. Hence, \(\text{CaCl}_{2}\), with a \(i\) of 3, affects the freezing point more significantly than \(\text{NaCl}\) with a \(i\) of 2.

Dissociation in Solution

Dissociation in solution is a process where an ionic compound separates into its constituent ions. This is crucial for understanding the impact of solutes on colligative properties.

In the example given, when \(\text{NaCl}\) is added to water, it dissociates into \(\text{Na}^+\) and \(\text{Cl}^-\). Similarly, \(\text{CaCl}_{2}\) dissociates into \(\text{Ca}^{2+}\) and two \(\text{Cl}^-\) ions. The number of ions released upon dissociation significantly influences how the solution behaves.

Why does this happen? Water is a polar solvent, meaning its molecules have an uneven distribution of charges. This allows them to surround and pull apart the ions of the solute. As a result, the total number of particles increases, amplifying colligative properties like freezing point depression.

In summary, dissociation increases the number of solute particles in a solution. The more particles present, the greater the impact on properties like freezing point, explaining why \(\text{CaCl}_{2}\) is more effective at lowering freezing points than \(\text{NaCl}\).