Q1) A solution of ascorbic acid (C6H8O6, Formula mass = 176 g/mol) is made up by dissolving 80.5 g of ascorbic acid in 210 g of water, and has a density of 1.22 g/mL at 55 oC. Calculate the following:
a) the mass percentage of ascorbic acid
b) the mole fraction of ascorbic acid
c) the molality of the solution
d) the molarity of ascorbic acid in this solution
You do most of this the same way I worked the first problem for you. Just remember the de4finitions.
mass% = (mass X/total mass)*100 = ?
X = (moles X/total moles)
molality = m = moles X/kg solvent.
M = molarity = moles/L soln.
ewfg
a) To calculate the mass percentage of ascorbic acid, we need to find the ratio of the mass of ascorbic acid to the total mass of the solution and multiply it by 100.
Mass percentage = (Mass of ascorbic acid / Total mass of solution) × 100
Given:
Mass of ascorbic acid = 80.5 g
Mass of water = 210 g
Total mass of solution = Mass of ascorbic acid + Mass of water
Total mass of solution = 80.5 g + 210 g = 290.5 g
Mass percentage = (80.5 g / 290.5 g) × 100 = 27.7%
Therefore, the mass percentage of ascorbic acid in the solution is 27.7%.
b) To calculate the mole fraction of ascorbic acid, we need to find the moles of ascorbic acid and the moles of water.
First, let's calculate the moles of ascorbic acid using the formula:
Moles = Mass / Molar mass
Moles of ascorbic acid = 80.5 g / 176 g/mol = 0.457 moles
Next, let's calculate the moles of water using the formula:
Moles of water = Mass / Molar mass
Moles of water = 210 g / 18 g/mol = 11.67 moles
The mole fraction of ascorbic acid is given by:
Mole fraction = Moles of ascorbic acid / (Moles of ascorbic acid + Moles of water)
Mole fraction = 0.457 moles / (0.457 moles + 11.67 moles)
Mole fraction = 0.0377
Therefore, the mole fraction of ascorbic acid in the solution is approximately 0.0377.
c) To calculate the molality of the solution, we need to find the moles of solute (ascorbic acid) and the mass of the solvent (water).
Molality is given by the formula:
Molality = Moles of solute / Mass of solvent (in kg)
Given:
Moles of solute (ascorbic acid) = 0.457 moles
Mass of solvent (water) = 210 g = 0.210 kg
Molality = 0.457 moles / 0.210 kg = 2.18 mol/kg
Therefore, the molality of the solution is approximately 2.18 mol/kg.
d) To calculate the molarity of ascorbic acid in this solution, we need to find the moles of ascorbic acid and the volume of the solution.
Molarity is given by the formula:
Molarity = Moles of solute / Volume of solution (in L)
Given:
Moles of solute (ascorbic acid) = 0.457 moles
Density of the solution = 1.22 g/mL = 1.22 g/cm³
Volume of solution = Total mass of solution / Density
Total mass of solution = 290.5 g
Volume of solution = 290.5 g / (1.22 g/cm³) = 238.11 cm³ = 0.23811 L
Molarity = 0.457 moles / 0.23811 L = 1.92 mol/L
Therefore, the molarity of ascorbic acid in this solution is approximately 1.92 mol/L.
To calculate the different values, we need to understand the concepts of mass percentage, mole fraction, molality, and molarity.
a) Mass percentage of ascorbic acid:
Mass percentage is calculated by dividing the mass of the solute (ascorbic acid) by the mass of the solution and then multiplying by 100.
Mass of the ascorbic acid = 80.5 g
Mass of the solution = 80.5 g (ascorbic acid) + 210 g (water) = 290.5 g
Mass percentage = (80.5 g / 290.5 g) * 100 = 27.7%
b) Mole fraction of ascorbic acid:
Mole fraction is the ratio of the moles of one component to the total moles of all components in the mixture.
For this, we need to convert the mass of ascorbic acid and water into moles and then calculate the mole fraction.
Moles of ascorbic acid = Mass / Molar mass
Moles of water = Mass / Molar mass
Molar mass of ascorbic acid (C6H8O6) = (6 * 12.01 g/mol) + (8 * 1.01 g/mol) + (6 * 16.00 g/mol) = 176 g/mol
Moles of ascorbic acid = 80.5 g / 176 g/mol = 0.457 mol
Moles of water = 210 g / 18.02 g/mol = 11.63 mol
Mole fraction of ascorbic acid = Moles of ascorbic acid / (Moles of ascorbic acid + Moles of water)
Mole fraction of ascorbic acid = 0.457 mol / (0.457 mol + 11.63 mol) = 0.037
c) Molality of the solution:
Molality is the ratio of the moles of solute to the mass of the solvent (in kilograms).
Molality = Moles of ascorbic acid / Mass of water (in kg)
Mass of water = 210 g = 210 g / 1000 g/kg = 0.21 kg
Molality = 0.457 mol / 0.21 kg = 2.18 mol/kg
d) Molarity of ascorbic acid in the solution:
Molarity is the ratio of the moles of solute to the volume of the solution (in liters).
To calculate the volume, we need to use the density of the solution.
Density = Mass of the solution / Volume of the solution
Volume of the solution = Mass of the solution / Density
Volume of the solution = 290.5 g / (1.22 g/mL) = 238.11 mL = 0.23811 L
Molarity = Moles of ascorbic acid / Volume of the solution (in L)
Molarity = 0.457 mol / 0.23811 L = 1.92 mol/L
So, the answers are:
a) Mass percentage of ascorbic acid = 27.7%
b) Mole fraction of ascorbic acid = 0.037
c) Molality of the solution = 2.18 mol/kg
d) Molarity of ascorbic acid in the solution = 1.92 mol/L