Melting Ice CaCl2 is used to melt ice on sidewalks. Could CaCl2 melt ice at -20^∘ C ? Assume tha

step 1 So in this question, we're considering the freezing point depression, so delta TF, that will res

Melting Ice CaCl2 is used to melt ice on sidewalks. Could...

Melting Ice $\mathrm{CaCl}_{2}$ is used to melt ice on sidewalks. Could $\mathrm{CaCl}_{2}$ melt ice at $-20^{\circ} \mathrm{C} ?$ Assume that the solubility of $\mathrm{CaCl}_{2}$ at this temperature is $70.1 \mathrm{g} \mathrm{CaCl}_{2} / 100.0 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$ and that the van 't Hoff factor for a saturated solution of $\mathrm{CaCl}_{2}$ is 2.5.

Melting Ice $\mathrm{CaCl}_{2}$ is used to melt ice on sidewalks. Could $\mathrm{CaCl}_{2}$ melt ice at $-20^{\circ} \mathrm{C} ?$ Assume that the solubility of $\mathrm{CaCl}_{2}$ at this temperature is $70.1 \mathrm{g} \mathrm{CaCl}_{2} / 100.0 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$
and that the van 't Hoff factor for a saturated solution of $\mathrm{CaCl}_{2}$ is 2.5.

Key Concepts

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is used in calculations of colligative properties because it remains unaffected by temperature changes. In freezing point depression calculations, molality directly influences the magnitude of the temperature decrease in the solvent.

Solubility

Solubility refers to the maximum amount of a substance that can dissolve in a solvent at a given temperature and pressure. It is an important factor in determining the concentration of a solution available for producing colligative effects such as freezing point depression. In this context, the given solubility of CaCl? at a low temperature limits the maximum concentration that can be achieved in the solution.

Van 't Hoff Factor

The van 't Hoff factor is a measure of the degree of dissociation of a solute in a solution. It indicates the number of particles the solute produces when dissolved. For electrolytes like CaCl?, which dissociate into ions, the factor amplifies the effect on the freezing point depression because more particles are introduced into the solution than the original formula unit.

Freezing Point Depression

This concept describes the phenomenon where the freezing point of a liquid (typically a solvent such as water) is lowered by the addition of a solute. It is a colligative property that depends on the number of solute particles in the solution and is quantitatively given by the equation ?Tf = i · Kf · m, where ?Tf is the freezing point depression, i is the van’t Hoff factor, Kf is the freezing point depression constant, and m is the molality of the solution.

Colligative Properties

Colligative properties are solution properties that depend only on the number of solute particles present in the solution and not on their identity. These include freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure. Their reliance on the concentration of particles makes them essential for understanding how solutes like salts affect phase change temperatures.

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