If 100.0 mL of 0.0025 M Na2SO4
(aq)is saturated with CaSO4
how many grams of CaSO4 would be present
in the solution? [Hint: Does the usual simplifying assumption hold?]
To find the number of grams of CaSO4 present in the solution, we need to use the principles of solubility and stoichiometry.
First, let's consider the solubility of CaSO4. If a substance is said to be "saturated" with another substance, it means that the maximum amount of the second substance has dissolved in the first substance at a given temperature. In this case, the Na2SO4 solution is saturated with CaSO4, which means no more CaSO4 can dissolve in the solution. This is useful because it allows us to assume that all the CaSO4 that could have dissolved has indeed dissolved.
The usual simplifying assumption in this case is that the concentration of the dissolved species Na+ derived from Na2SO4 is negligible compared to the concentration of Ca2+ from CaSO4. This assumption holds true as the concentration of CaSO4 is extremely low.
Now, let's move on to the stoichiometry. From the balanced equation of CaSO4 dissolving in water, we know that 1 mole of CaSO4 produces 1 mole of Ca2+. Therefore, the moles of CaSO4 and Ca2+ present in the solution are the same.
To calculate the moles of CaSO4, we need to multiply the molarity (0.0025 M) by the volume (100.0 mL = 0.100 L) of the Na2SO4 solution:
moles of CaSO4 = molarity x volume
= 0.0025 M x 0.100 L
= 0.00025 moles
Since 1 mole of CaSO4 is equal to its molar mass in grams, we can determine the number of grams of CaSO4 by multiplying the moles by the molar mass. The molar mass of CaSO4 is the sum of the atomic masses of calcium (Ca), sulfur (S), and oxygen (O):
molar mass of CaSO4 = (1 x atomic mass of Ca) + (1 x atomic mass of S) + (4 x atomic mass of O)
Using the periodic table, we find the atomic masses: Ca = 40.08 g/mol, S = 32.07 g/mol, O = 16.00 g/mol.
molar mass of CaSO4 = (1 x 40.08 g/mol) + (1 x 32.07 g/mol) + (4 x 16.00 g/mol)
= 40.08 g/mol + 32.07 g/mol + 64.00 g/mol
= 136.15 g/mol
Now, we can calculate the mass of CaSO4:
mass of CaSO4 = moles of CaSO4 x molar mass of CaSO4
= 0.00025 moles x 136.15 g/mol
= 0.034 g
Therefore, the mass of CaSO4 present in the solution is approximately 0.034 grams.