A sample of aluminum sulfate 18-hydrate, Al2(SO4)3 · 18 H2O, containing 157.0 mg is dissolved in 1.000 L of solution. Calculate
(a) molarity of Al2(SO4)3
(b) molarity of SO42-
(c) molality of Al2(SO4)3, assuming that the density of the solution is 1.00 g/mL
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To calculate the molarity of Al2(SO4)3 and SO42-, we need to determine the number of moles of the solute and the volume of the solution.
(a) Molarity of Al2(SO4)3:
Step 1: Calculate the molar mass of Al2(SO4)3
Molar mass of Al2(SO4)3 = (2 * molar mass of Al) + (3 * molar mass of S) + (12 * molar mass of O)
= (2 * 26.98 g/mol) + (3 * 32.07 g/mol) + (12 * 16.00 g/mol)
= 342.12 g/mol
Step 2: Convert the given mass of Al2(SO4)3 to moles
Mass of Al2(SO4)3 = 157.0 mg = 0.157 g
Number of moles = mass / molar mass = 0.157 g / 342.12 g/mol = 0.000458 mol
Step 3: Calculate the molarity of Al2(SO4)3
Molarity = number of moles / volume of solution
Since the volume of solution is given as 1.000 L, the molarity of Al2(SO4)3 is 0.000458 M.
(b) Molarity of SO42-:
Since each formula unit of Al2(SO4)3 contains 3 sulfate ions (SO42-), the molarity of Al2(SO4)3 is equal to the molarity of SO42-.
Therefore, the molarity of SO42- is also 0.000458 M.
(c) Molality of Al2(SO4)3:
Molality is defined as the number of moles of solute per kilogram of solvent.
Step 1: Calculate the mass of the solvent
Given density of the solution = 1.00 g/mL
Volume of solution = 1.000 L = 1000 mL
Mass of the solution = density * volume = 1.00 g/mL * 1000 mL = 1000 g
Step 2: Convert the mass of the solute to moles
Number of moles of Al2(SO4)3 = 0.000458 mol (from part a)
Step 3: Calculate the molality of Al2(SO4)3
Molality = number of moles / mass of the solvent (in kg)
= 0.000458 mol / 1.000 kg
= 0.000458 mol/kg
Therefore, the molality of Al2(SO4)3 is 0.000458 mol/kg.