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.

answer: the rate of diffusion increases with increase in temperature.

increase in temperature, increases the molecular/particles speed (kinetic energy. diffusion means movement of particles through the material.

generally, the heavier the particle the more it interacts with the environment and more the temperature matters. so higher temperature results in higher diffusion.

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