Understanding the Concept

When determining molecular weight using depression in freezing point, the formula used is:

$\mathrm{\Delta T}f=i\times Kf\times m$

where $\mathrm{\Delta T}f$ is the depression in freezing point, $i$ is the van't Hoff factor, $Kf$ is the cryoscopic constant, and $m$ is the molality.

The molecular weight (M) is calculated from the formula:

$M=\frac{i\times Kf\times w\times 1000}{\mathrm{\Delta T}f\times W}$

where $w$ is the mass of solute and $W$ is the mass of solvent.

For CaCl₂, which is an electrolyte, dissociation occurs in aqueous solution:

$\mathrm{CaCl}2(\mathrm{aq})\to \mathrm{Ca}{}^{\mathrm{2+}}(\mathrm{aq})+2\mathrm{Cl}{}^{-}(\mathrm{aq})$

The van't Hoff factor (i) for CaCl₂ is ideally 3 because it dissociates into 3 ions. However, in real solutions, due to ion pairing or incomplete dissociation, the observed value of i is often less than 3.

Step-by-Step Reasoning

Step 1: Note the theoretical molecular weight of CaCl₂.

Atomic mass of Ca = 40 g/mol, Cl = 35.5 g/mol. So, M_theoretical = 40 + 2×35.5 = 111 g/mol.

Step 2: Understand the effect of dissociation on molecular weight determination.

The experimental molecular weight (M_exp) is calculated using the formula M = (i × K_f × w × 1000) / (ΔT_f × W).

Since i is used in the numerator, a lower than ideal i (i.e., i < 3) would result in a lower calculated M.

Step 3: Relate van't Hoff factor to the result.

For CaCl₂, the ideal i is 3, but experimentally i is often less than 3 due to incomplete dissociation. Therefore, the experimental molecular weight will be higher than the theoretical value because M_exp is inversely related to i (since i is in the numerator).

If i (actual) < i (ideal), then M_exp > M_theoretical.

Final Answer: The molecular weight determined experimentally will be greater than 111. So, the correct option is > 111.

Related Topics

• Colligative Properties
• Freezing Point Depression
• Van't Hoff Factor
• Dissociation of Electrolytes
• Ion Pairing

Key Formulae and Theory

Freezing Point Depression: $\mathrm{\Delta T}f=i\times Kf\times m$

Molecular Weight Calculation: $M=\frac{i\times Kf\times w\times 1000}{\mathrm{\Delta T}f\times W}$

Van't Hoff Factor (i): i = (observed colligative property) / (colligative property for non-electrolyte)

For electrolytes, i is greater than 1 but often less than the ideal value due to incomplete dissociation.