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Chapter 13: Problem 110

A solution contains \(750 \mathrm{g}\) of ethanol and \(85.0 \mathrm{g}\) of sucrose \(\left(180 \mathrm{g} \mathrm{mol}^{-1}\right) .\) The volume of the solution is \(810.0 \mathrm{mL} .\) Determine (a) the density of the solution (b) the percent of sucrose in the solution (c) the mole fraction of sucrose (d) the molality of the solution (e) the molarity of the solution

Short Answer

Expert verified
The detailed calculations are needed to give precise results. However, the density would be roughly \(1.03 g/mL\), the percent of sucrose around \(10.18%\), and the molarity around \(0.583 M\). The mole fraction and molality cannot be calculated without additional information about the moles or mass of ethanol.

Step by step solution

01

Calculation of density

The density of a solution is defined as its mass divided by its volume. The total mass of the solution is the sum of the masses of ethanol and sucrose, which is \(750 g + 85 g = 835 g = 0.835 kg\). The volume of the solution is given as \(810.0 mL = 0.810 L\). Thus, the density of the solution can be calculated using the formula: \[ Density = \frac{mass}{volume} \]
02

Calculation of percent of sucrose

Percentage of sucrose in the solution is calculated as the ratio of the mass of sucrose to the total mass of the solution, multiplied by 100. So, \[ Percentage = \frac{mass_{sucrose}}{mass_{total}} \times 100\%\]
03

Calculation of mole fraction of sucrose

The mole fraction of sucrose is calculated as the ratio of the number of moles of sucrose to the total number of moles (sucrose + ethanol). The number of moles of a compound is given by the ratio of its mass to its molar mass. For sucrose, the molar mass is given as \(180 g/mol\). Thus, the number of moles of sucrose is \(85 g / 180 g/mol = 0.4722 mol\). Unfortunately, the number of moles of ethanol is not given, so it is not possible to calculate the mole fraction of sucrose.
04

Calculation of molality of the solution

Molality is defined as the number of moles of the solute per kilogram of the solvent. In this case, the solute is sucrose and the solvent is ethanol. It can be calculated using the formula: \[ Molality = \frac{moles_{sucrose}}{mass_{ethanol}} \]
05

Calculation of molarity of the solution

Molarity is defined as the number of moles of the solute per liter of the solution. It is calculated using the formula: \[ Molarity = \frac{moles_{sucrose}}{volume_{solution}} \]

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