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Chapter 11: Problem 113

Consider an aqueous solution containing sodium chloride that has a density of 1.01 \(\mathrm{g} / \mathrm{mL}\) . Assume the solution behaves ideally. The freezing point of this solution at 1.0 \(\mathrm{atm}\) is $-1.28^{\circ} \mathrm{C}$ . Calculate the percent composition of this solution (by mass).

Short Answer

Expert verified
The percent composition of the sodium chloride solution (by mass) is approximately 21.2%.

Step by step solution

01

Calculate the molality of the solution using freezing point depression formula

We are given the freezing point depression of the solution (ΔTf = 1.28°C). Using the freezing point depression formula, we can calculate the molality (m) of the solution: ΔTf = Kf × m where Kf is the cryoscopic constant, which is 1.86°C kg/mol for water. Now, we can calculate the molality: 1.28°C = 1.86°C kg/mol × m m = \( \frac{1.28}{1.86} \) mol/kg
02

Calculate the mass of solute using molality and density

Now that we have the molality, we can use the given density of the solution to find the mass of solute in 1 liter (or 1,000mL) of the solution: Density = \( \frac{mass_{solution}}{volume_{solution}} \) 1.01 g/mL = \( \frac{mass_{solution}}{1000\,\mathrm{mL}} \) mass_solution = 1010 g We know that molality (m) = \( \frac{moles_{solute}}{mass_{solvent_{(kg)}}} \) Rearranging this formula, we get: mass_solute = moles_solute × molar_mass_solute mass_solvent = mass_solution - mass_solute We now have a system of two equations with two variables (mass_solute and mass_solvent): \( \frac{mass_{solute}}{mass_{solvent}/1000} \) = \(\frac{1.28}{1.86}\) mass_solution = mass_solute + mass_solvent
03

Solve for mass_solute and mass_solvent

By solving the two equations, we can find the mass_solute and mass_solvent: mass_solute = \( \frac{mass_{solution}}{1 + \frac{molar\_mass_{solute} \times 1.86}{1.28 \times 1000}} \) For sodium chloride (NaCl), the molar_mass_solute = 58.44 g/mol. Plugging the values: mass_solute = \( \frac{1010}{1 + \frac{58.44 \times 1.86}{1.28 \times 1000}} \) = 214.16 g (approximately) mass_solvent = mass_solution - mass_solute = 1010 - 214.16 = 795.84 g (approximately)
04

Calculate the percent composition by mass

Now we can calculate the mass percent of sodium chloride in the solution: Percent composition (NaCl) = \( \frac{mass_{solute}}{mass_{solution}} \times 100\% \) Percent composition (NaCl) = \( \frac{214.16}{1010} \times 100\% \) ≈ 21.2% The percent composition of the sodium chloride solution (by mass) is approximately 21.2%.

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Most popular questions from this chapter

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