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Chapter 11: Problem 42

A solution is prepared by mixing 50.0 \(\mathrm{mL}\) toluene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\right.\) $d=0.867 \mathrm{g} / \mathrm{cm}^{3} )\( with 125 \)\mathrm{mL}$ benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}, d=0.874 \mathrm{g} / \mathrm{cm}^{3}\right)$ Assuming that the volumes add on mixing, calculate the mass percent, mole fraction, molality, and molarity of the toluene.

Short Answer

Expert verified
The mass percent of toluene in the solution is 28.4%, the mole fraction is 0.252, the molality is 4.30 mol/kg, and the molarity is 2.69 mol/L.

Step by step solution

01

Calculate the mass of toluene and benzene

Given, volume of toluene (V1) = 50.0 mL, density of toluene (d1) = 0.867 g/cm³ Given, volume of benzene (V2) = 125 mL, density of benzene (d2) = 0.874 g/cm³ To find the mass, we can use the formula: mass = volume × density Mass of toluene (m1) = V1 × d1 = 50.0 mL × 0.867 g/cm³ = 43.35 g Mass of benzene (m2) = V2 × d2 = 125 mL × 0.874 g/cm³ = 109.25 g
02

Calculate the moles of toluene and benzene

Next, we need to calculate the moles of toluene and benzene using their molar masses. Molar mass of toluene (M1) = 92.14 g/mol (C₆H₅CH₃) Molar mass of benzene (M2) = 78.11 g/mol (C₆H₆) To find the moles, we can use the formula: moles = mass ÷ molar mass Moles of toluene (n1) = m1 ÷ M1 = 43.35 g ÷ 92.14 g/mol = 0.470 mol Moles of benzene (n2) = m2 ÷ M2 = 109.25 g ÷ 78.11 g/mol = 1.398 mol
03

Calculate the mass percent of toluene

To find the mass percent of toluene, we can use the formula: mass percent = (mass of solute ÷ mass of solution) × 100 Mass of solution = m1 + m2 = 43.35 g + 109.25 g = 152.60 g Mass percent of toluene = (m1 ÷ (m1 + m2)) × 100 = (43.35 g ÷ 152.60 g) × 100 = 28.4%
04

Calculate the mole fraction of toluene

To find the mole fraction of toluene, we can use the formula: mole fraction = moles of solute ÷ total moles Total moles = n1 + n2 = 0.470 mol + 1.398 mol = 1.868 mol Mole fraction of toluene = n1 ÷ (n1 + n2) = 0.470 mol ÷ 1.868 mol = 0.252
05

Calculate the molality of toluene

To find the molality of toluene, we can use the formula: molality = moles of solute ÷ mass of solvent (in kg) The mass of benzene, m2, is the mass of the solvent in this case. Molality of toluene = n1 ÷ (m2 ÷ 1000) = 0.470 mol ÷ (109.25 g ÷ 1000) = 0.470 mol ÷ 0.10925 kg = 4.30 mol/kg
06

Calculate the molarity of toluene

To find the molarity of toluene, we can use the formula: molarity = moles of solute ÷ volume of solution (in L) Total volume of the solution (in L) = (V1 + V2) ÷ 1000 = (50.0 mL + 125 mL) ÷ 1000 = 0.175 L Molarity of toluene = n1 ÷ total volume = 0.470 mol ÷ 0.175 L = 2.69 mol/L The mass percent of toluene is 28.4%, the mole fraction is 0.252, the molality is 4.30 mol/kg, and the molarity is 2.69 mol/L.

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