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Chapter 13: Problem 48

Ascorbic acid (vitamin \(\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6} )\) 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, ( \(\mathbf{d}\) ) the molarity of ascorbic acid in this solution.

Short Answer

Expert verified
The ascorbic acid solution has: (a) Mass percentage = 27.71% (b) Mole fraction = 0.0377 (c) Molality = 2.18 mol/kg (d) Molarity = 1.92 M

Step by step solution

01

Calculate the mass of the solution

To find the mass percentage, mole fraction, molality, and molarity of the solute (ascorbic acid) in the solution, we first need to calculate the total mass of the solution. We are given the mass of ascorbic acid (80.5 g) and the mass of water (210 g). We can find the total mass by adding these two values: Total mass of solution = Mass of ascorbic acid + Mass of water Total mass of solution = 80.5 g + 210 g = 290.5 g
02

Calculate the mass percentage

Mass percentage is calculated by dividing the mass of the solute by the mass of the solution, and then multiplying by 100. In this case, the solute is ascorbic acid: Mass percentage = (Mass of ascorbic acid / Total mass of solution) * 100 Mass percentage = (80.5 g / 290.5 g) * 100 = 27.71% The mass percentage of ascorbic acid in the solution is 27.71%.
03

Calculate the mole fraction

To calculate the mole fraction, we need to find the moles of ascorbic acid and the moles of water in the solution. The molar mass of ascorbic acid (C6H8O6) is 176.12 g/mol, and the molar mass of water (H2O) is 18.01 g/mol: Moles of ascorbic acid = Mass of ascorbic acid / Molar mass of ascorbic acid Moles of ascorbic acid = 80.5 g / 176.12 g/mol = 0.457 mol Moles of water = Mass of water / Molar mass of water Moles of water = 210 g / 18.01 g/mol = 11.66 mol Now, calculate the mole fraction: Mole fraction = Moles of ascorbic acid / (Moles of ascorbic acid + Moles of water) Mole fraction = 0.457 mol / (0.457 mol + 11.66 mol) = 0.0377 The mole fraction of ascorbic acid in the solution is 0.0377.
04

Calculate the molality

Molality is calculated by dividing the moles of solute by the mass of solvent in kilograms. In this case, the solute is ascorbic acid, and the solvent is water: Molality = Moles of ascorbic acid / Mass of water (in kg) Molality = 0.457 mol / (210 g / 1000) = 2.18 mol/kg The molality of ascorbic acid in the solution is 2.18 mol/kg.
05

Calculate the molarity

To calculate the molarity, we need the volume of the solution. We can find this by using the density and the mass of the solution: Volume of solution = Total mass of solution / Density Volume of solution = 290.5 g / (1.22 g/mL) = 238.1 mL Now, convert the volume to liters: Volume of solution (in L) = 238.1 mL / 1000 = 0.2381 L Molarity = Moles of ascorbic acid / Volume of solution (in L) Molarity = 0.457 mol / 0.2381 L = 1.92 M The molarity of ascorbic acid in the solution is 1.92 M. In summary, the ascorbic acid solution has: (a) Mass percentage = 27.71% (b) Mole fraction = 0.0377 (c) Molality = 2.18 mol/kg (d) Molarity = 1.92 M

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Most popular questions from this chapter

Arrange the following aqueous solutions, each 10\(\%\) by mass in solute, in order of increasing boiling point: glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),\) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),\) sodium nitrate (\textrm{NaNO} _ { 3 } ) .

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