Question

A solution of \(5.0 \mathrm{~g}\) of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) in \(100.0 \mathrm{~g}\) of carbon tetrachloride has a boiling point of \(77.5^{\circ} \mathrm{C}\). (a) Calculate the molar mass of benzoic acid in the solution. (b) Suggest a reason for the difference between the molar mass based on the formula and that found in part (a). (Hint: Consider intermolecular forces in this compound.)

Short answer

The calculated molar mass is roughly 154.0 g/mol. The discrepancy arises due to dimer formation via hydrogen bonding in non-polar solvents.

Step-by-step solution

- Calculate the molality of the solution

First, determine the molality (m) of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. Here, we have 5.0 g of benzoic acid (solute) in 100.0 g (0.100 kg) of carbon tetrachloride (CCl4, solvent). Calculate the number of moles of benzoic acid using its given mass and molar mass (122.12 g/mol, for calculation purposes). Molality (m) is then calculated as follows:\[\text{ Molality } (m) = \frac{\text{ moles of solute }}{\text{ kilograms of solvent }} = \frac{\frac{5.0 \text{ g}}{122.12 \text{ g/mol}}}{0.100 \text{ kg}}\text{ Molality } (m) = 0.409 \text{ mol/kg}.\]

- Determine the boiling point elevation constant (ΔTb)

Next, use the boiling point elevation equation: ΔTb = i * Kb * m to determine the boiling point elevation. For Carbon tetrachloride, the boiling point elevation constant (Kb) is approximately 5.03 °C/m. Assuming i (van't Hoff factor) for benzoic acid is 1:\[ΔTb = i * Kb * m = 1 * 5.03 \text{°C/m} * 0.409 \text{ mol/kg} = 2.06°C\]

- Calculate the observed molar mass

To find the observed molar mass of benzoic acid in solution, use the experimental boiling point elevation ΔTb. Measure the observed boiling point elevation:\[ΔTb (\text{observed}) = 77.5°C - 76.7°C = 0.8°C\] (Where 76.7°C is the normal boiling point of CCl4)Use the boiling point elevation equation to solve for molarity (m) and the molar mass (M) of benzoic acid:\[\begin{aligned}\ &ΔTb (\text{observed}) = Kb * m\, 0.8°C = 5.03 \text{°C/m} * m\,m (\text{observed}) = \frac{0.8°C}{5.03 \text{°C/m}} \& 0.159 \text{ mol/kg}\text{(observed})\,\& \text{ Number of moles of benzoic acid)}\ = 0.159 \text{ mol/kg} * 0.1 \text{ kg = 0.0159 mol(M)}\, = \frac{5.0g}{0.0159}).\ \&Observed \text mend(benzoic acid)}\154.0 \text{ g/mol}umber(encough report}.\]

- Suggest a reason for the discrepancy

Explain the discrepancy between the calculated molar mass and the molar mass derived from the formula weight. Benzoic acid can form dimers in non-polar solvents like carbon tetrachloride due to hydrogen bonding, which effectively doubles the molar mass when in solution.

Key concepts

boiling point elevation

Boiling point elevation is a colligative property, which means it depends on the number of solute particles in a solution and not their nature. When a non-volatile solute dissolves in a solvent, it raises the boiling point of the solvent. This happens because the solute particles disrupt the solvent molecules, making it harder for them to evaporate.
The general equation to calculate the boiling point elevation is: \[ \Delta T_{b} = i \cdot K_{b} \cdot m \] where \(\Delta T_{b}\) is the boiling point elevation, \(i\) is the van't Hoff factor, \(K_{b}\) is the ebullioscopic constant of the solvent, and \(m\) is the molality of the solution. In our example with benzoic acid in carbon tetrachloride, the boiling point elevation observed was 0.8°C, which is lower than calculated, suggesting that fewer particles are in solution than expected.

molality

Molality is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent.
The formula to calculate molality is: \[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \] In this case, we have 5.0 g of benzoic acid dissolved in 100.0 g of carbon tetrachloride. Converting the mass of benzoic acid to moles using its molar mass (122.12 g/mol): \[ \text{Moles of benzoic acid} = \frac{5.0 \text{ g}}{122.12 \text{ g/mol}} = 0.041 mol \] Then, calculating the molality: \[ m = \frac{0.041 \text{ mol}}{0.1 \text{ kg}} = 0.41 \text{ mol/kg} \] This value is crucial as it is used to determine the extent of boiling point elevation.

intermolecular forces

Intermolecular forces are the forces that act between molecules, influencing the physical properties of substances. There are several types of intermolecular forces, including:

• Van der Waals forces
• Dipole-dipole interactions
• Hydrogen bonding

In the instance of benzoic acid in carbon tetrachloride, hydrogen bonding is significant. Benzoic acid can form dimers due to hydrogen bonds between two benzoic acid molecules. This dimerization in a non-polar solvent like carbon tetrachloride means fewer individual particles are present in the solution.
This behavior results in an effectively higher molar mass, reconciling the observed discrepancy between the calculated and experimental molar masses.

van't Hoff factor

The van't Hoff factor \(i\) represents the number of particles a solute produces in solution. For non-electrolytes like benzoic acid in carbon tetrachloride, \(i\) is typically 1 because they do not dissociate into ions. However, due to dimerization in this case, the actual effective particles in the solution decrease. The equation for boiling point elevation, factoring in the van't Hoff factor, goes: \[ \Delta T_{b} = i \cdot K_{b} \cdot m \] where \(i\) adjusts for the number of effective particles in solution. Since benzoic acid forms dimers, \(i\) is closer to 0.5 (indicating dimer formation), which aligns with the experimental observations.