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Chapter 13: Problem 45

Calculate the molality of each of the following solutions: (a) \(8.66 \mathrm{~g}\) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) dissolved in \(23.6 \mathrm{~g}\) carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\) (b) \(4.80 \mathrm{~g} \mathrm{NaCl}\) dissolved in \(0.350 \mathrm{~L}\) of water.

Short Answer

Expert verified
The molality of the benzene solution is 4.6949 mol/kg and the molality of the sodium chloride solution is 0.2349 mol/kg.

Step by step solution

01

(a) Calculate the moles of benzene in the solution)

First, determine the molar mass of benzene: C6H6 \(C_{6}H_{6}\): (6 * 12.01 g/mol) + (6 * 1.008 g/mol) = 72.06 + 6.048 = 78.108 g/mol Now, we can calculate the moles of benzene in the solution: Moles of benzene = mass/molar_mass = \( \frac{8.66~g}{78.108~g/mol} \) = 0.1108 mol
02

(a) Calculate the molality of the benzene solution)

To calculate the molality of the solution, we need the mass of carbon tetrachloride (solvent) in kilograms. Given the mass of solvent is 23.6 g, we can convert it to kilograms: Mass of solvent = \( \frac{23.6~g}{1000~g/kg} \) = 0.0236 kg Now, the molality of the solution can be calculated as: Molality = moles_of_solute / mass_of_solvent = \( \frac{0.1108~mol}{0.0236~kg} \) = 4.6949 mol/kg The molality of the benzene solution is 4.6949 mol/kg.
03

(b) Calculate the moles of sodium chloride in the solution)

First, determine the molar mass of sodium chloride: NaCl \(NaCl\): (1 * 22.99 g/mol) + (1 * 35.45 g/mol) = 22.99 + 35.45 = 58.44 g/mol Now, we can calculate the moles of sodium chloride in the solution: Moles of sodium chloride = mass/molar_mass = \( \frac{4.80~g}{58.44~g/mol} \) = 0.0822 mol
04

(b) Calculate the mass of water in the solution)

We are given the volume of water in the solution: 0.350 L. To convert this to mass, we need to use the density of water: Density of water = 1 g/mL or 1000 g/L Mass of water = volume * density = 0.350 L * 1000 g/L = 350 g Now, we convert it to kg: Mass of water = \( \frac{350~g}{1000~g/kg} \) = 0.35 kg
05

(b) Calculate the molality of the sodium chloride solution)

Now, the molality of the solution can be calculated as: Molality = moles_of_solute / mass_of_solvent = \( \frac{0.0822~mol}{0.35~kg} \) = 0.2349 mol/kg The molality of the sodium chloride solution is 0.2349 mol/kg.

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Most popular questions from this chapter

List four properties of a solution that depend on the total concentration but not the type of particle or particles present as solute. Write the mathematical expression that describes how each of these properties depends on concentration.

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