Toluene (C7H8, molar mass = 92.13 g/mol) an organic compound often used as a solvent in paints is mixed with a similar organic compound benzene (C6H6, molar mass 78.11 g/mol). Calculate the molarity, molality, mass percent, and mole fraction of toluenein 2.00 x 103mL of solution that contains 75.8 g of toluene and 95.6 g of benzene. The density of solution is 0.857 g/cm3.

The answers to the question are as follows

In the solution

The molarity of toluene is 0.4114 M

The molality of toluene is 0.48 molal

The mass percent of toluene is 4.4224 %

The mole fraction of toluene is 0.402.

Explanation:

The molar mass of toluene = 92.13 g/mol

The molar mass of benzene = 78.11 g/mol

The mass of toluene in the sample = 75.8 g

The mass of benzene in the sample = 95.6 g

(i) The number of moles, n of each, toluene an benzene is given by

n = Mass/(Molar Mass) = n_Toluene = 75.8 g/(92.13 g/mol) = 0.823 moles

n_benzene = 95.6 g/(78.11 g/mol) = 1.224 moles

Volume of solution = 2.00 x 10³ mL = 2 liters

Therefore 2 liters of solution contains 0.823 moles of toluene

1 liter of solution will contain (0.823 moles)/(2.L) = 0.4114 moles

and the molarity of toluene in the solution is 0.4114 M.

(ii) The molality is the number of moles per kilogram of solvent given by

molality = (Number of moles of solute)/(1 kg of solvent)

Mass of solvent = Density × Volume

Where;

Density = Density of the solution = 0.857 g/cm³

Volume  = Volume of the solution = 2.00 x 10³ mL = 2 liters = 2000 cm³

Therefore mass of solvent = 0.857 g/cm³ × 2000 cm³ = 1714 g

1 kg = 1000 g ∴ 1714 g = 1.714 kg

Number of moles of toluene in 1.714 kg of solvent = 0.823 moles

We divide both sides by 1.714 kg to arrive at

The number of moles of toluene in 1.0 kg of solvent = (0.823 moles)/1.714 = 0.48 molal.

(iii) The mass percent is given by

(Mass of component/ (total mass of the mixture) ) × 100 %

The total mass of the solution ±was found as 1714 g

The mass of toluene is given as 75.8 g

The mass percent therefore is

(75.8 g/(1714 g)) × 100 % = 4.4224 %.

(iv) The mole fraction can be found as

Mole fraction = (Number of moles of a component)/(Total number o moles in the solution)

Number of moles of toluene in the solution = 0.823 moles

Total number of moles in the solution = n_Toluene + n_benzene

= 0.823 moles + 1.224 moles = 2.05 moles

Mole fraction = 0.823 moles/(2.05 moles) = 0.402.