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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 \(497.04 \thinspace \mathrm{g/mol}\).

Step by step solution

01

Determine the change in boiling point

Use the boiling point of the solution and the boiling point of pure carbon tetrachloride to calculate the change in boiling point (∆Tb): ∆Tb = Tb (solution) - Tb (pure carbon tetrachloride) ∆Tb = \(77.85^{\circ} \mathrm{C}\) - \(76.50^{\circ} \mathrm{C}\) ∆Tb = \(1.35^{\circ} \mathrm{C}\)
02

Calculate molality of the solution

Use the boiling point elevation formula and the boiling-point constant (Kb) to calculate the molality (m) of the solution: ∆Tb = Kb * m m = ∆Tb / Kb m = \(1.35^{\circ} \mathrm{C}\) / \(5.03^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\) m = 0.2684 mol/kg
03

Convert the solvent mass to kg

Convert the mass of carbon tetrachloride from grams to kilograms: mass (carbon tetrachloride) = 15.0 g * (1 kg / 1000 g) mass (carbon tetrachloride) = 0.015 kg
04

Calculate moles of biomolecule

Use the molality and the mass of the solvent to calculate the moles of biomolecule present in the solution: moles (biomolecule) = molality * mass (solvent) moles (biomolecule) = 0.2684 mol/kg * 0.015 kg moles (biomolecule) = 0.004026 mol
05

Calculate the molar mass of the biomolecule

Use the moles and mass of the biomolecule to determine the molar mass: molar mass (biomolecule) = mass (biomolecule) / moles (biomolecule) molar mass (biomolecule) = 2.00 g / 0.004026 mol molar mass (biomolecule) = 497.04 g/mol The molar mass of the biomolecule is 497.04 g/mol.

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Most popular questions from this chapter

A solution of sodium chloride in water has a vapor pressure of \(19.6\) torr at \(25^{\circ} \mathrm{C}\). What is the mole fraction of solute particles in this solution? What would be the vapor pressure of this solution at \(45^{\circ} \mathrm{C} ?\) The vapor pressure of pure water is \(23.8\) torr at \(25^{\circ} \mathrm{C}\) and \(71.9\) torr at \(45^{\circ} \mathrm{C}\) and assume sodium chloride exists as \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions in solution.

Plants that thrive in salt water must have internal solutions (inside the plant cells) that are isotonic with (have the same osmotic pressure as) the surrounding solution. A leaf of a saltwater plant is able to thrive in an aqueous salt solution (at \(\left.25^{\circ} \mathrm{C}\right)\) that has a freezing point equal to \(-0.621^{\circ} \mathrm{C}\). You would like to use this information to calculate the osmotic pressure of the solution in the cell. a. In order to use the freezing-point depression to calculate osmotic pressure, what assumption must you make (in addition to ideal behavior of the solutions, which we will assume)? b. Under what conditions is the assumption (in part a) reasonable? c. Solve for the osmotic pressure (at \(25^{\circ} \mathrm{C}\) ) of the solution in the plant cell. d. The plant leaf is placed in an aqueous salt solution (at \(\left.25^{\circ} \mathrm{C}\right)\) that has a boiling point of \(102.0^{\circ} \mathrm{C}\). What will happen to the plant cells in the leaf?

An aqueous antifreeze solution is \(40.0 \%\) ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) by mass. The density of the solution is \(1.05 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the molality, molarity, and mole fraction of the ethylene glycol.

In some regions of the southwest United States, the water is very hard. For example, in Las Cruces, New Mexico, the tap water contains about \(560 \mu \mathrm{g}\) of dissolved solids per milliliter. Reverse osmosis units are marketed in this area to soften water. A typical unit exerts a pressure of \(8.0 \mathrm{~atm}\) and can produce \(45 \mathrm{~L}\) water per day. a. Assuming all of the dissolved solids are \(\mathrm{MgCO}_{3}\) and assuming a temperature of \(27^{\circ} \mathrm{C}\), what total volume of water must be processed to produce \(45 \mathrm{~L}\) pure water? b. Would the same system work for purifying seawater? (Assume seawater is \(0.60 \mathrm{M} \mathrm{NaCl}\).)

A solution is prepared by mixing \(25 \mathrm{~mL}\) pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}, d=\right.\) \(\left.0.63 \mathrm{~g} / \mathrm{cm}^{3}\right)\) with \(45 \mathrm{~mL}\) hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}, d=0.66 \mathrm{~g} / \mathrm{cm}^{3}\right)\). Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the pentane.
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