Question

The freezing points of two \(\mathrm{NaCl}\) solutions were determined to be \(-1.15^{\circ} \mathrm{C}\) for solution \(\mathrm{A}\) and \(-4.10^{\circ} \mathrm{C}\) for solution B. Which solution has the highest concentration of \(\mathrm{NaCl}\) ?

Short answer

Solution B has the highest concentration of NaCl.

Step-by-step solution

Identify Freezing Points

From the information provided, the freezing point of solution A is \(-1.15^{\circ}C\) and the freezing point of solution B is \(-4.10^{\circ}C\).

Compare Freezing Points

Using the principle that a lower freezing point indicates a higher concentration of solute, and comparing the freezing points of the two solutions, solution A freezes at a higher temperature than solution B.

Determine Solution with Higher Concentration

Because solution B freezes at a lower temperature than solution A, solution B has the higher concentration of NaCl.

Key concepts

Freezing Point Depression

Understanding the phenomenon of freezing point depression is critical when studying colligative properties in chemistry. This is the process by which the freezing point of a solvent is lowered when a non-volatile solute, such as salt, is added. Water, for instance, normally freezes at 0°C. However, when a substance like NaCl (table salt) is dissolved in it, the freezing point is reduced. This effect is directly related to the number of particles of solute in the solution.

In technical terms, freezing point depression happens because the solute particles disrupt the formation of the crystalline lattice structure that is needed for a liquid to turn into a solid (freeze). As more particles are introduced, it becomes increasingly difficult for the solvent to form a solid structure, hence requiring a lower temperature to freeze. The magnitude of freezing point depression can be calculated using the formula: \[ \text{Freezing point depression} = i \times K_f \times m \] where 'i' is the van 't Hoff factor, 'K_f' is the cryoscopic constant of the solvent, and 'm' is the molality of the solute. For non-electrolytes, 'i' is typically 1. However, for ionic compounds like NaCl, which dissociate into ions, 'i' is generally equal to the number of particles the compound dissociates into in solution.

Solute Concentration

The concept of solute concentration in a solution is another key aspect in understanding colligative properties. It implies the proportion of solute to solvent present in a solution. There are various ways to express concentration such as molarity, molality, and percent composition. For colligative properties, molality (moles of solute per kilogram of solvent) is often used because it remains constant with temperature changes.

An important thing to remember is that colligative properties, like freezing point depression, depend on the number of solute particles in the solution and not on their identity. Hence, the more concentrated the solution, the more pronounced the effects on properties such as freezing point, boiling point elevation, and osmotic pressure will be. In our exercise, solution B, with a lower freezing point, indicates a higher concentration of NaCl because the presence of more solute particles disturbs the solvent's ability to freeze at a higher temperature.

NaCl Solutions

When discussing NaCl solutions, it is essential to consider the unique properties of NaCl, commonly known as table salt. NaCl is an ionic compound composed of sodium (Na+) and chloride (Cl-) ions. When dissolved in water, NaCl dissociates into its ions, increasing the solution's particle concentration significantly.

For every mole of NaCl dissolved, we essentially get two moles of particles (one mole of Na+ and one mole of Cl-), assuming complete dissociation. This means the colligative properties will be more pronounced for NaCl solutions compared to non-ionic solutes that don't dissociate. Consequently, in the context of the provided exercise, we can infer that solution B, having the lower freezing point, contains more dissolved NaCl, thus more sodium and chloride ions, which significantly contributes to the process of freezing point depression.