a solution is prepared by mixing 50.0 mL toluene (C6H5CH3 d=0.867 g/mL) with 125 mL Benzene (C6H6 d=0.874 g/mL). assuming that the volumes add upon mixing, calculate the mass percent, mole fraction, molality, and molarity of the toluene.
A long drawn out problem. How much do you know how to do and exactly what do you not understand about the problem.
To calculate the mass percent, mole fraction, molality, and molarity of toluene in the solution, we can follow these steps:
Step 1: Calculate the total mass of the solution:
Mass of toluene = Volume of toluene × Density of toluene
Mass of toluene = 50.0 mL × 0.867 g/mL = 43.35 g
Mass of benzene = Volume of benzene × Density of benzene
Mass of benzene = 125 mL × 0.874 g/mL = 109.25 g
Total mass of the solution = Mass of toluene + Mass of benzene
Total mass of the solution = 43.35 g + 109.25 g = 152.6 g
Step 2: Calculate the mass percent of toluene in the solution:
Mass percent = (Mass of toluene / Total mass of the solution) × 100
Mass percent = (43.35 g / 152.6 g) × 100
Mass percent = 28.41%
Step 3: Calculate the mole fraction of toluene in the solution:
Moles of toluene = Mass of toluene / Molar mass of toluene
Molar mass of toluene = 92.14 g/mol
Moles of toluene = 43.35 g / 92.14 g/mol = 0.470 mol
Moles of benzene = Mass of benzene / Molar mass of benzene
Molar mass of benzene = 78.11 g/mol
Moles of benzene = 109.25 g / 78.11 g/mol = 1.399 mol
Total moles of the solution = Moles of toluene + Moles of benzene
Total moles of the solution = 0.470 mol + 1.399 mol = 1.869 mol
Mole fraction of toluene = Moles of toluene / Total moles of the solution
Mole fraction of toluene = 0.470 mol / 1.869 mol = 0.251
Step 4: Calculate the molality of toluene in the solution:
Molality (m) = Moles of toluene / Mass of solvent (in kg)
Mass of solvent = Mass of benzene = 109.25 g = 0.10925 kg
Molality (m) = 0.470 mol / 0.10925 kg = 4.30 mol/kg
Step 5: Calculate the molarity of toluene in the solution:
Molarity (M) = Moles of toluene / Volume of solution (in L)
Volume of solution = Volume of toluene + Volume of benzene = 50.0 mL + 125 mL = 175 mL = 0.175 L
Molarity (M) = 0.470 mol / 0.175 L = 2.69 M
So, the mass percent of toluene in the solution is 28.41%, the mole fraction is 0.251, the molality is 4.30 mol/kg, and the molarity is 2.69 M.
To calculate the mass percent, mole fraction, molality, and molarity of toluene in the solution, we'll need to determine the mass and moles of toluene.
1. Mass of Toluene:
The mass of toluene can be calculated by multiplying its volume (50.0 mL) by its density (0.867 g/mL).
Mass of toluene = Volume × Density = 50.0 mL × 0.867 g/mL = 43.35 g
2. Moles of Toluene:
The moles of toluene can be calculated using its mass and molar mass. The molar mass of toluene (C6H5CH3) can be found by summing the atomic masses of its constituent elements from the periodic table.
Molar mass of toluene = 6 × atomic mass of carbon + 5 × atomic mass of hydrogen + atomic mass of methyl group (CH3)
= (6 × 12.01 g/mol) + (5 × 1.01 g/mol) + 15.03 g/mol
= 92.14 g/mol
Moles of toluene = Mass of toluene / Molar mass of toluene
= 43.35 g / 92.14 g/mol
= 0.470 mol
Now, we can proceed to calculate the requested parameters:
1. Mass Percent of Toluene:
Mass percent of toluene = (Mass of toluene / Mass of solution) × 100%
= (43.35 g / (43.35 g + 125 mL × 0.874 g/mL)) × 100%
2. Mole Fraction of Toluene:
Mole fraction of toluene = (Moles of toluene / Moles of toluene + Moles of benzene)
3. Molality of Toluene:
Molality is defined as the moles of solute per kilogram of solvent. Since the volume of the solution is given and not the mass of the solvent, we first need to calculate the mass of benzene.
Mass of benzene = Volume × Density = 125 mL × 0.874 g/mL = 109.25 g
Molality of toluene = (Moles of toluene / Mass of benzene (in kg))
4. Molarity of Toluene:
Molarity is defined as the moles of solute per liter of solution. We need to convert the volume of the solution into liters before calculating molarity.
Volume of solution = Volume of toluene + Volume of benzene
= 50.0 mL + 125 mL
= 175 mL = 0.175 L
Molarity of toluene = (Moles of toluene / Volume of solution)
Plug in the calculated values into the respective formulas to find the final answers.