Answer:
a) Based on the given information, the volume of the solvent given is 999 ml and the density of water given is 0.9982 gram per ml.
The mass of solvent can be calculated by the formula mass = density * volume
mass = 0.9982 * 999 = 0.997 Kg
The molarity of the solution given is 2.300 * 10^-2 M
Molality of the glycerol solution can be calculated by using the formula,
Molality = molarity/solvent (kg) = 2.300 * 10^-2 / 0.997 = 0.023 m
b) Molarity or the moles of the solute given is 2.300 * 10^-2 moles
The moles of solvent can be determined by using the formula, n = mass of solvent/mol.wt = 997/18 (mol.wt of solvent is 18 g/mol), now putting the values we get,
n = 997/18 = 55.4
The mole fraction of the glycerol will be = 2.300 * 10^-2 M/(2.300 * 10^-2)+55.40
= 4.15 * 10^-4
c) The mass percent of glycerol can be determined by using the formula,
mass of solute/mass of solution * 100% ----- (i)
The mass of solute can be determined by using the formula,
n = mass of solute/mol.wt of solute
The n or the no. of moles is 2.300 * 10^-2 and the molecular weight of glycerol is 92.09 g/mol. Now putting the values we get,
mass = 2.300 * 10^-2 * 92.09 = 2.12 grams
Now putting the values in equation (i) we get,
mass percent = 2.12 / 997 * 100% = 0.21%
d) Based on the above calculation, the mass of solute (glycerol) is 2.12 g or 2.12 * 1000 mg
The volume of water is 999 ml or 999 * 10^-3 L
The concentration of the glycerol solution will be,
Concentration = 2.12 * 10^3 mg/999 * 10^-3 L
= 2.12/999 * 10^6 mg/L
= 2122.1 ppm