Question

Toluene (C6H5CH3 ), an organic compound often used as a solvent in paints, is mixed with a similar organic compound, benzene (C6H6 ). Calculate the molarity, molality, mass percent, and mole fraction of toluene in 200. mL of solution that contains 75.8 g of toluene and 95.6 g of benzene. The density of the solution is 0.857 g/cm3.

Answer 1

Explanation:

The given data is as follows.

 Weight of solute = 75.8 g,   Molecular weight of solute (toulene) = 92.13 g/mol,    volume = 200 ml

• Therefore, molarity of toulene is calculated as follows.

      Molarity = $\frac{\text{weight of solute}}{\text{molecular weight of solute}} \times \frac{1000}{\text{volume of solution in ml}}$

                    = $\frac{75.8 g}{92.13 g/mol} \times \frac{1000}{200 ml}$

                    = 4.11 M

Hence, molarity of toulene is 4.11 M.

• As molality is the number of moles of solute present in kg of solvent.

So, we will calculate the molality of toulene as follows.

   Molality = $\frac{\text{given weight of solute}}{\text{given molecular weight of solute}} \times \frac{1000}{\text{weight of solvent in grams}}$

             = $\frac{75.8 g}{92.13 g/mol} \times \frac{1000}{95.6 g}$

             = 8.6 m

Hence, molality of given toulene solution is 8.6 m.

• Now, calculate the number of moles of toulene as follows.

       No. of moles = $\frac{mass}{\text{molar mass}}$

                             = $\frac{75.8 g}{92.13 g/mol}$

                             = 0.8227 mol

Now, no. of moles of benzene will be as follows.

     No. of moles = $\frac{mass}{\text{molar mass}}$

                             = $\frac{95.6 g}{78.11 g/mol}$

                             = 1.2239 mol

Hence, the mole fraction of toulene is as follows.

         Mole fraction = $\frac{\text{moles of toulene}}{\text{total moles}}$

                             = $\frac{0.8227 mol}{(0.8227 + 1.2239) mol}$

                             = 0.402

Hence, mole fraction of toulene is 0.402.

• As density of given solution is 0.857 $g/cm^{3}$ so, we will calculate the mass of solution as follows.

         Density = $\frac{mass}{volume}$

     0.857 $g/cm^{3}$ = $\frac{mass}{200 ml}$      (As 1 $cm^{3}$ = 1 g)

                      mass = 171.4 g

Therefore, calculate the mass percent of toulene as follows.

      Mass % = $\frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

                   = $\frac{75.8 g}{171.4 g} \times 100$

                   = 44.22%

Therefore, mass percent of toulene is 44.22%.