Question

If \(1 \mathrm{~m}\) solution of benzoic acid in benzene has a freezing point depression of \(2.4^{\circ} \mathrm{C}\). \(\left(K_{f}=5.12^{\circ} \mathrm{C} \mathrm{mol}^{-1} \mathrm{~kg}\right)\) and boiling point elevation of \(2.53^{\circ} \mathrm{C}\left(K_{b}=2.53^{\circ} \mathrm{C} \mathrm{mol}^{-1} \mathrm{~kg}\right)\) then select the correct statement/s : Statement I : there is dimer formation when undergoing freezing Statement II : there is no change when undergoing boiling Statement III : reverse of I and II Statement IV : dimer formation in freezing and boiling state (a) I, II (b) II, III (c) III, I (d) only I

Short answer

Statements I and II are correct as there is dimer formation during freezing but not during boiling.

Step-by-step solution

Determine Molality from Freezing Point Depression

Using the formula for freezing point depression \( \Delta T_f = K_f \cdot m \) where \(\Delta T_f = 2.4^\circ C\) and \(K_f = 5.12^\circ C \cdot kg / mol\), solve for molality (m).

Calculate the Number of Moles of Benzoic Acid

With the calculated molality, use the definition of molality \( m = \frac{moles \; of \; solute}{kg \; of \; solvent} \) to find the moles of benzoic acid assuming 1 kg of the solvent since the solution is 1 molal.

Determine Molality from Boiling Point Elevation

Use the formula for boiling point elevation \( \Delta T_b = K_b \cdot m \) where \(\Delta T_b = 2.53^\circ C\) and \(K_b = 2.53^\circ C \cdot kg / mol\) to solve for molality (m) again.

Compare the Calculated Molalities

If molality from freezing point depression is different than the molality from boiling point elevation, this indicates dimer formation in freezing. Statement I is true as dimerization would result in fewer particles to affect the boiling point as compared to the freezing point.

Assess Statement II for Boiling Point Change

The fact that the boiling point elevation constant \(K_b\) is equal to the observed \(\Delta T_b\) implies that no dimerization occurs during boiling, hence Statement II is also true.

Determine the Correct Statements

As dimerization occurs during the freezing and not during boiling, Statement I is true. Since boiling point change correctly indicates no dimer formation, Statement II is also true. Hence, Statements III and IV are incorrect.

Key concepts

Freezing Point Depression

Freezing point depression is a phenomenon where the freezing point of a solvent decreases when a solute is dissolved in it. This colligative property is relevant when identifying chemical behaviors in solutions. The formula for calculating the degree of freezing point depression is centered:

centered:
centered: centered: . Here, centered: is the change in freezing point, centered: is the molality of the solution, and centered: is the freezing point depression constant, unique to each solvent. In the given exercise, we see a decrease of centered: in the freezing point which indicates the presence of a dissolved substance. Using the given values, one can infer information about the solute, including phenomena like dimer formation which would affect the number of particles in the solution and alter the expected freezing point depression.

In the exercise, the depression in freezing point for a 1 molal solution indicates that some sort of association (like dimerization) is causing fewer particles to be present than initially assumed, as pure benzoic acid would generate more depression and the occurrence of fewer freezing point depression than expected confirms the formation of dimers.

Boiling Point Elevation

Boiling point elevation describes the increase in the boiling point of a solvent when a solute is dissolved in it. This too is a colligative property, which means it depends on the number of solute particles in the solvent and not the nature of the particles. The formula for boiling point elevation is similar to freezing point depression but uses the boiling point elevation constant centered: : centered: . This parameter, centered: , is specific to the solvent being used. In the context of the textbook exercise that we are discussing, the boiling point of benzene is elevated by centered: when benzoic acid is dissolved in it.

Interestingly, the constant centered: is exactly equal to the observed change in temperature, indicating that no dimerization takes place during the boiling process. In other words, the solvent is acting upon all the benzoic acid molecules equally and individual particles are affecting the boiling point according to expectations. Thus, this suggests that all the benzoic acid exists as monomers in the boiling state.

Molality

Molality is an important concentration measure used in the context of colligative properties. It is defined as the number of moles of solute per kilogram of solvent, expressed as centered: . Unlike molarity, which measures concentration based on the volume of solution, molality is based on the mass of the solvent, making it temperature-independent. In the classroom problem we're examining, molality plays a crucial role because colligative property formulas centered: and centered: require the value of molality to calculate the changes in freezing and boiling points.

Once we ascertain the molality from the observed freezing or boiling point change, we can use it to infer the actual number of solute particles in the solution. If the molality values do not match the expected values (assuming no dimerization), it suggests that the solute particles are not behaving as individual entities, which can indicate molecular associations such as dimer formation.

Dimer Formation

Dimer formation refers to the chemical phenomenon where two identical molecules (monomers) bond together to form a dimer. This process can significantly alter the properties of a solution because it effectively reduces the number of solute particles. Dimers can influence colligative properties such as freezing point depression and boiling point elevation because these properties depend on the number of particles in a solution.

In the solution from the exercise, dimerization occurred during freezing but not boiling. We deduced this from the discrepancies between the expected and measured boiling points and freezing points. Essentially, dimerization during freezing would halve the number of particles impacting the freezing point, resulting in less depression than predicted for monomeric particles. During boiling, however, the lack of dimer formation ensures that each benzoic acid molecule contributes to the elevation of boiling point separately. Recognizing dimer formation is important in various fields, such as polymer chemistry and biochemistry, where it can have considerable effects on the physical properties of substances.