Question

Chloroform, \(\mathrm{CHCl}_{3}\), boils at \(61.7^{\circ} \mathrm{C}\). If the \(K_{b}\) for chloroform is \(3.63^{\circ} \mathrm{C} / \mathrm{molal}\), what is the boiling point of a solution of \(15.0 \mathrm{~kg}\) of \(\mathrm{CHCl}_{3}\) and \(0.616 \mathrm{~kg}\) of acenaphthalene, \(\mathrm{C}_{12} \mathrm{H}_{10} ?\) (a) \(61.9\) (b) \(62.0\) (c) \(52.2\) (d) \(62.67\)

Short answer

The new boiling point of the solution is approximately \(62.67^\circ \mathrm{C}\).

Step-by-step solution

Calculate the molality of the solution

Use the formula for molality: molality (m) = moles of solute / kilograms of solvent. First, calculate the molar mass of acenaphthalene, which is \(C_{12}H_{10}\). This is the sum of the atomic masses of carbon (12 atoms at 12.01 g/mol) and hydrogen (10 atoms at 1.01 g/mol). Then, use the mass of acenaphthalene to find the moles of acenaphthalene. Finally, divide by the mass of the solvent, chloroform, in kilograms to find molality.

Calculate the boiling point elevation

Apply the boiling point elevation formula: \( \Delta T_b = K_b \times m \), where \( \Delta T_b \) is the boiling point elevation, \( K_b \) is the ebullioscopic constant for chloroform, and \( m \) is the molality of the solution from Step 1.

Calculate the new boiling point

Add the boiling point elevation from Step 2 to the normal boiling point of chloroform to find the new boiling point of the solution.

Key concepts

Molality

Molality, often represented by the symbol 'm', is a measure of the concentration of a solute in a solution. Unlike molarity, which is based on the volume of the solution, molality is defined as the number of moles of solute per kilogram of solvent. This makes it a more reliable unit of concentration in physical chemistry, particularly when dealing with temperature changes since it's not affected by changes in volume.

To calculate molality, you need to know two things: the number of moles of the solute being dissolved and the mass of the solvent in kilograms. The formula is expressed as:

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Ebullioscopic Constant

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Colligative Properties

Colligative properties are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the type of chemical species present. These include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

The significant aspect is that these properties are not affected by the identity of the solute, which means whether you dissolve salt, sugar, or any other non-volatile solute in a liquid, the effect on the colligative properties for the same number of solute particles will be similar.

In the context of boiling point elevation, a non-volatile solute will cause the boiling point of the solvent to rise. This occurs because the solute particles interfere with the formation of vapor above the liquid. As a result, more heat energy is required for the liquid to boil, which leads to an increase in its boiling point.

Physical Chemistry for JEE

Physical Chemistry is an integral part of the JEE syllabus, which is the Joint Entrance Examination for engineering in India. Understanding colligative properties and concepts such as molality and the ebullioscopic constant is crucial for JEE aspirants. Particularly in the field of solutions and their colligative properties, questions often arise that test the application of formulas and the understanding of how these properties are influenced by the presence of different solutes.

JEE problems require a solid grasp of principles and the ability to apply them to various scenarios. For instance, calculating the boiling point elevation of a solution requires an understanding of molality and how it relates to the boiling point elevation through the ebullioscopic constant. These consistent patterns in problem-solving, learned through exercises and step-by-step solutions, build the foundational knowledge that is imperative for JEE candidates to excel in the chemistry portion of the exam.