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Chapter 11: Problem 66

A \(2.00-\mathrm{g}\) sample of a large biomolecule was dissolved in \(15.0 \mathrm{~g}\) carbon tetrachloride. The boiling point of this solution was determined to be \(77.85^{\circ} \mathrm{C}\). Calculate the molar mass of the biomolecule. For carbon tetrachloride, the boiling-point constant is \(5.03^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\), and the boiling point of pure carbon tetrachloride is \(76.50^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The molar mass of the biomolecule is approximately 492.95 g/mol.

Step by step solution

01

Calculate the change in boiling point

First, we need to calculate the change in boiling point of the solution compared to pure carbon tetrachloride. The difference can be obtained by subtracting the boiling point of pure carbon tetrachloride from the boiling point of the solution: ΔT = T_solution - T_pure ΔT = \(77.85^{\circ} \mathrm{C}\) - \(76.50^{\circ} \mathrm{C}\) ΔT = \(1.35^{\circ} \mathrm{C}\)
02

Calculate the molality

Next, we need to calculate the molality of the solution. We can do this using the formula: molality = ΔT / Kb Where molality is the molality of the solution, ΔT is the change in boiling point, and Kb is the boiling-point constant given for carbon tetrachloride. Now, substituting the values we have: molality = \(1.35^{\circ} \mathrm{C}\) / \(5.03^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\) molality = 0.26839 mol/kg
03

Calculate the molar mass of the biomolecule

Finally, we can find the molar mass of the biomolecule by using the molality and the mass of the biomolecule in grams. The formula for molar mass (MM) is: MM = (mass of biomolecule) / (molality × mass of solvent in kg) First, let's convert the mass of carbon tetrachloride solvent from grams to kilograms: mass of solvent = 15.0 g = 0.015 kg Now, plug in the values to find the molar mass of the biomolecule: MM = (2.00 g) / (0.26839 mol/kg × 0.015 kg) MM = 492.95 g/mol So,the molar mass of the biomolecule is approximately 492.95 g/mol.

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Most popular questions from this chapter

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