Question

a solution if phosphoric acid was made by dissolving 10g of H3PO4 in 100mL of water. the resulting volume was 104mL. calculate the density, mole fraction, molarity, and molality of the solution. assume water has a density of 1g/cm3

Answer 1

Mass of H3PO4 =10 g
Molar Mass of H3PO4 = 98 g/mol
number of moles of H3PO4 = mass / molar mass
                                                        = 10/98
                                                        = 0.102 mol

volume of water = 100 mL
density = 1 g/mL
mass of water = density * volume = 100 * 1 = 100 g
Molar mass of water = 18 g/mol
number of moles of water = mass / molar mass
                                                       = 100/18
                                                       = 5.56 mol

Total volume of solution = 104 mL = 0.104 L

A)
density = total mass aadded / total volume
                = (10 g + 100 g) / 104 mL
                = 110 g / 104 mL
                = 1.06 g/mL

B)
mole fraction of H3PO4 = number of H3PO4 / Total number of moles
                      = 0.102 / (0.102 + 5.56)
                      = 0.018

mole fraction of water = number of water / Total number of moles
                      = 5.56 / (0.102 + 5.56)
                      = 0.982

C)
Molarity = number of moles of H3PO4/ Volume of solution in L
                   = 0.102 mol/ 0.104 L
                   = 0.981 M

D)
Molality = number of moles of H3PO4/ mass of water in Kg
                   = 0.102 mol/ 0.1 Kg (since 100 g = 0.1 Kg)
                   = 1.02 m