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Chapter 13: Problem 48

Ascorbic acid (vitamin \(\left.\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\right)\) is a water-soluble vitamin. A solution containing \(80.5 \mathrm{~g}\) of ascorbic acid dissolved in \(210 \mathrm{~g}\) of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.

Short Answer

Expert verified
The mass percentage, mole fraction, molality, and molarity of ascorbic acid in this solution are: (a) Mass percentage = \(27.71\%\) (b) Mole fraction = \(0.0377\) (c) Molality = \(2.18 \: \text{mol/kg}\) (d) Molarity = \(1.92 \: \text{mol/L}\)

Step by step solution

01

Calculate the molar mass of ascorbic acid

To calculate the molar mass of ascorbic acid (C6H8O6), we need to consider the molar mass of each element present in ascorbic acid and add them all together: Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of ascorbic acid = 6 * (12.01) + 8 * (1.01) + 6 * (16.00) = 72.06 + 8.08 + 96.00 = 176.14 g/mol
02

Calculate the mass percentage

Mass percentage is calculated by dividing the mass of the solute (ascorbic acid) by the total mass of the solution (ascorbic acid and water), then multiplied by 100 to express it as a percentage: Mass percentage = (mass of ascorbic acid / total mass) * 100 Mass percentage = (80.5 g / (80.5 g + 210 g)) * 100 = (80.5 g / 290.5 g) * 100 = 27.71%
03

Calculate the mole fraction

To determine the mole fraction, we need to find the moles of each component in the solution: - Moles of ascorbic acid = mass / molar mass = 80.5 g / 176.14 g/mol = 0.457 moles - Moles of water = 210 g / 18.02 g/mol (molar mass of water) = 11.65 moles Mole fraction of ascorbic acid = moles of ascorbic acid / total moles Mole fraction = 0.457 moles / (0.457 moles + 11.65 moles) = 0.457 moles / 12.107 moles = 0.0377
04

Calculate the molality

Molality is the number of moles of solute (ascorbic acid) divided by the mass of the solvent (water) in kilograms: Molality = (moles of ascorbic acid) / (mass of water in kg) Molality = (0.457 moles) / (210 g / 1000) = 0.457 moles / 0.210 kg = 2.18 mol/kg
05

Calculate the molarity

First, we need to find the volume of the solution. We are given the density (1.22 g/mL) and the total mass (290.5 g), so we can calculate the volume: Volume = mass /density = 290.5 g / (1.22 g/mL) = 238.1 mL Now we can calculate the molarity. Molarity is the number of moles of solute (ascorbic acid) divided by the volume of the solution in liters: Molarity = (moles of ascorbic acid) / (volume of solution in L) Molarity = 0.457 moles / (238.1 mL / 1000) = 0.457 moles / 0.2381 L = 1.92 mol/L In summary, the mass percentage, mole fraction, molality, and molarity of ascorbic acid in this solution are: (a) Mass percentage = 27.71% (b) Mole fraction = 0.0377 (c) Molality = 2.18 mol/kg (d) Molarity = 1.92 mol/L

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Most popular questions from this chapter

A "canned heat" product used to warm chafing dishes consists of a homogeneous mixture of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and paraffin that has an average formula of \(\mathrm{C}_{24} \mathrm{H}_{50}\). What mass of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) should be added to \(620 \mathrm{~kg}\) of the paraffin in formulating the mixture if the vapor pressure of ethanol at \(35^{\circ} \mathrm{C}\) over the mixture is to be 8 torr? The vapor pressure of pure ethanol at \(35^{\circ} \mathrm{C}\) is 100 torr.

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