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Chapter 11: Problem 72

A 2.00 -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 497 g/mol.

Step by step solution

01

Understand the Boiling-Point Elevation formula

Boiling-point elevation is the phenomenon that occurs when a non-volatile solute is dissolved in a solvent, resulting in an increase in the boiling point of the solvent. The relationship is described by the following formula: ΔT = Kₘ ⋅ molality where ΔT is the boiling point elevation, Kₘ is the boiling-point constant for the solvent, and the molality is the concentration of the solute in the solution.
02

Calculate the boiling point elevation

First, let's calculate the boiling point elevation (ΔT). We are given the boiling point of the pure solvent (carbon tetrachloride) and the boiling point of the solution: ΔT = Boiling point of the solution - Boiling point of pure solvent ΔT = \(77.85^{\circ} \mathrm{C}\ - 76.50^{\circ} \mathrm{C}\) ΔT = 1.35 °C
03

Rearrange the formula to calculate molality

Now we can rearrange the boiling-point elevation formula to solve for the molality of the biomolecule in the solution: molality = ΔT / Kₘ
04

Calculate the molality of the biomolecule

The boiling-point constant for carbon tetrachloride \(Kₘ = 5.03^{\circ}\mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\) and ΔT = 1.35 °C. So, let's plug the values: molality = (1.35 °C) / \(5.03^{\circ}\mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\) molality = 0.2684 mol / kg
05

Calculate the amount of moles of the biomolecule

Molality is defined as the number of moles of solute per kilogram of solvent. We know the mass of the solvent and the molality of the biomolecule. Using this information, we can calculate the number of moles of the biomolecule present in the solution: moles = molality × mass of solvent in kg moles = (0.2684 mol / kg) × (15.0 g CCl₄ × (1 kg / 1000 g)) moles = 0.004026 mol
06

Calculate the molar mass of the biomolecule

We are given the mass of the biomolecule (2.00 g) and we have calculated the number of moles present in the solution. We can now calculate the molar mass of the biomolecule: molar mass = mass of biomolecule / moles of biomolecule molar mass = (2.00 g) / (0.004026 mol) molar mass ≈ 497 g/mol The molar mass of the biomolecule is approximately 497 g/mol.

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Most popular questions from this chapter

The lattice energy of \(\mathrm{NaCl}\) is \(-786 \mathrm{kJ} / \mathrm{mol},\) and the enthalpy of hydration of 1 mole of gaseous Na' and 1 mole of gaseous \(\mathrm{Cl}^{-}\) ions is \(-783 \mathrm{kJ} / \mathrm{mol}\) . Calculate the enthalpy of solution per mole of solid NaCl.

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