The boiling point of \(\mathrm{CHCl}_{3}\) was raised by \(0.323^{\circ} \mathrm{C}\) when \(0.37 \mathrm{~g}\) of naphthalene was dissolved in \(35 \mathrm{~g} \mathrm{CHCl}_{3} .\) Calculate the molecular weight of naphthalene. \(K_{\mathrm{b}}^{\prime}\) for \(\mathrm{CHCl}_{3}=3.9 \mathrm{~K} \mathrm{~mol}^{-1} \mathrm{~kg}\).

Colligative properties are characteristics of solutions that depend solely on the number of solute particles, regardless of their nature. This is a fundamental concept in chemistry, especially when studying solutions. There are four main colligative properties: vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.

For our discussion, the boiling point elevation of a solvent upon addition of a non-volatile solute is most relevant. The principle behind this phenomenon is that the added solute particles obstruct the solvent's molecules from evaporating, which in turn requires more thermal energy – or a higher temperature – to achieve the boiling state.

When solving problems involving colligative properties, students should remember that these calculations typically assume the solute does not dissociate or ionize; hence, for non-electrolytes like naphthalene, the calculations are more straightforward.

Boiling point elevation is a specific type of colligative property where the boiling point of a solvent increases when a solute is dissolved in it. This effect occurs because the solute particles disrupt the solvent's ability to transition into a gaseous state.

The magnitude of boiling point elevation can be determined using the formula:
\(\triangle T_b = i \cdot K_b \cdot m\)
where \(\triangle T_b\) is the boiling point elevation, \(K_b\) is the solvent's ebullioscopic constant, \(i\) is the Van't Hoff factor (which accounts for the number of particles the solute breaks into, if any), and \(m\) is the molality of the solution. Considering the exercise, we noticed that the solution's boiling point was raised by a specific temperature increment, which directly ties into calculating the molecular weight of naphthalene.

The ebullioscopic constant, denoted as \(K_b\), is a key parameter regarding boiling point elevation. It's unique to each solvent and reflects the solvent's susceptibility to changes in boiling point per unit of molal concentration of the solute.

In more technical terms, \(K_b\) represents the boiling point elevation observed when one mole of a non-volatile solute is dissolved in one kilogram of solvent. The constant has units of degrees Celsius per molal (°C/m) or Kelvins per molal (K/m).

In our problem involving naphthalene and chloroform, \(K_b\) for chloroform is provided as 3.9 K·mol^-1·kg, which we use to calculate the molality of the solution.

Molality is a measure of the concentration of a solution. Unlike molarity, which is the number of moles of solute per liter of solution, molality measures the number of moles of solute per kilogram of solvent. The formula for molality is expressed as:
\(m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}\)

This measure doesn't change with temperature, making it particularly useful in colligative property calculations, where temperature can play a role. Understanding how to calculate molality is an essential step, as it's part of the equation for boiling point elevation.

In the provided exercise, we would use the mass of chloroform and the mass of naphthalene to compute the molality, which then helps determine the molecular weight of naphthalene.

The Van't Hoff factor, represented by the symbol \(i\), indicates the number of particles a solute splits into when it dissolves in a solvent. For compounds that do not dissociate in solution, such as most non-electrolytes, the Van't Hoff factor is 1.

However, for electrolytes which dissociate into ions, the factor can be greater than 1. For example, sodium chloride (NaCl) separates into two ions (Na⁺ and Cl^-), giving it a Van't Hoff factor of 2. This factor is crucial because it directly affects calculations relating to boiling point elevation and other colligative properties.

In the context of our naphthalene example, since naphthalene is a non-electrolyte and does not dissociate in solution, the Van't Hoff factor is 1. This simplifies our calculations since we don’t have to account for ionization.