The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene. (a) Calculate the mole fraction of thiophene in the solution.
(b) Calculate the molality of thiophene in the solution.
(c) Assuming that the volumes of the solute and solvent are additive, what is the molarity of thiophene in the solution?

(a) 0.039

(b) 0.384 M

(c) 0.373 M

Explanation:

We have the following data:

d(C₇H₈) = 0.867 g/mL

d(C₄H₄S) = 1.065 g/mL

V(C₇H₈) = 250.0 mL

mass(C₄H₄S) = 8.10 g

(a) The mole fraction of C₄H₄S in the solution is the number of moles of C₄H₄S divided into the total moles of the solution:

X(C₄H₄S) = moles C₄H₄S/ total moles

To calculate the moles, we need the molecular weight (MW) of each compound:

MW(C₄H₄S) = (4 x 12 g/mol) + (4 x 1 g/mol) + 32 g/mol = 84 g/mol

MW(C₇H₈) =  (7 x 12 g/mol) + (8 x 1 g/mol) = 92 g/mol

Thus, we calculate the moles of C₄H₄S by dividing the mass into the MW(C₄H₄S):

moles C₄H₄S = mass(C₄H₄S)/MW(C₄H₄S)= 8.10 g/(84 g/mol) = 0.096 moles

Then, we have to calculate the moles of C₇H₈. First, we need the mass, obtained from the product of the density by the volume:

mass(C₇H₈)= d(C₇H₈) x V(C₇H₈) = 0.867 g/mL x 250.0 mL = 216.75 g

Thus, we divide the mass of C₇H₈ into the MW to calculate the moles of C₇H₈:

moles C₇H₈ = mass(C₇H₈)/MW(C₇H₈) = 216.75 g/(92 g/mol) = 2.35 moles

The total moles is obtained from the addition of the moles of the solute (C₄H₄S) and the solvent (C₇H₈):

total moles = moles C₄H₄S + moles C₇H₈ = 0.096 moles + 2.35 moles = 2.45 moles

Finally, we calculate the mole fraction of C₄H₄S:

X(C₄H₄S) = moles C₄H₄S/ total moles = 0.096 moles/2.45 moles = 0.039

(b) The molarity of C₄H₄S is calculated as follows:

M(C₄H₄S) = moles C₄H₄S/1 liter solution

Assuming that the total volume of the solution is the volume of solvent (C₇H₈), we calculate the molarity of C₄H₄S by dividing the moles into the volume of solvent in liters:

V(C₇H₈) = 250.0 mL = 0.250 L

M(C₄H₄S) = 0.096 moles/(0.250 L) = 0.384 mol/M = 0.384 M

(c) Assuming that the volumes of solute and solvent are additive, we can add the volumes of C₄H₄S and C₇H₈. First, we need the volume of C₄H₄S, which can be calculated from the mass and density:

V(C₄H₄S) = mass(C₄H₄S)/ d(C₄H₄S) = 8.10 g/(1.065 g/mL) = 7.606 mL = 0.0076 L

Now, we add the volumes:

total volume = V(C₇H₈) + V(C₄H₄S) = 0.250 L + 0.0076 L = 0.2576 L

Finally, we recalculate the molarity of C₄H₄S:

M(C₄H₄S)= moles C₄H₄S/ total volume = 0.096 moles/0.2576 L = 0.373 M