Answer:
(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 <u>mole fraction of C₄H₄S</u> 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 <u>molarity of C₄H₄S</u> 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) <u>Assuming that the volumes of solute and solvent are additive</u>, 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 <u>molarity of C₄H₄S</u>:
M(C₄H₄S)= moles C₄H₄S/ total volume = 0.096 moles/0.2576 L = 0.373 M
