The density of acetonitrile (CH3CN) is 0.786 g/mL, and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.0 mL CH3OH in 98.4 mL CH3CN. Part A What is the mole fraction of methanol in the solution?

The answer to your question is  0.22

Explanation:

Data

Acetonitrile (CH₃CN) density = 0.786 g/ml

Methanol (CH₃OH) density = 0.791 g/ml

Volume of CH₃OH = 22 ml

Volume of CH₃CN = 98.4 ml

Process

1.- Calculate the mass of Acetonitrile and the mass of Methanol

density = mass/ volume

mass = density x volume

Acetonitrile

        mass = 0.786 x 98.4

                  = 77.34 g

Methanol

        mass = 0.791 x 22

                  = 17.40 g

2.- Calculate the moles of the reactants

Acetonitrile molar mass = (12 x 2) + (14 x 1) + (3 x 1)

                                        = 24 + 14 + 3

                                        = 41 g

Methanol molar mass = (12 x 1) + (4 x 1) + (16 x 1)

                                      = 12 + 4 + 16

                                      = 32 g

Moles of Acetonitrile

                     41 g 1 mol

                      77.34g  x

                      x = (77.34 x 1) / 41

                      x = 1.89 moles

Moles of Methanol

                      32 g 1 mol

                       17.40 g  x

                       x = (17.40 x 1)/32

                       x = 0.54 moles

3.- Calculate the mole fraction of Methanol

Total number of moles = 1.89 + 0.54

                                       = 2.43

Mole fraction = moles of Methanol / total number of moles

Mole fraction = 0.54/ 2.43

Mole fraction = 0.22