A hard water sample contains 121 mg of CaCO3 per liter of water. Calculate the mass of Na3Po4 needed to remove all Ca^2+ ions from 2.50 L of the water sample?
Please help! This question is already on here, but I don't understand the part where it says substitute expression into ksp & solve for PO4^3 & the rest?
You have (Ca^2+) from 0.121/molar mass CaCO3.
You know Ksp, plug in Ca^2+ and solve for PO4^3- from the Ksp expression of
Ksp = (Ca^2+)^3(PO4^3-)^2.
That will give you PO4^- in mols/L, convert that to 2.5L, and convert mols to grams by g = mols x molar mass Na3PO4.
To solve this problem, we need to use the solubility product constant (Ksp) of calcium phosphate (Ca3(PO4)2) in water.
First, we need to determine the number of moles of Ca^2+ ions in the water sample. We can do this using the given information that the water sample contains 121 mg of CaCO3 per liter of water.
Step 1: Convert the mass of CaCO3 to moles
To convert the mass of CaCO3 to moles, we need to know the molar mass of CaCO3. The molar mass of CaCO3 is calculated as follows:
1 atom of Ca = 40.08 g/mol
1 atom of C = 12.01 g/mol
3 atoms of O = 3 x 16.00 g/mol = 48.00 g/mol
Adding these masses together, we get:
Molar mass of CaCO3 = 40.08 g/mol + 12.01 g/mol + 48.00 g/mol = 100.09 g/mol
Now we can calculate the number of moles of CaCO3 in the water sample:
Number of moles of CaCO3 = mass of CaCO3 / molar mass of CaCO3
= 121 mg / 100.09 g/mol
= 1.209 x 10^-3 mol
Since CaCO3 contains one mole of Ca^2+ ions, the number of moles of Ca^2+ ions in the water sample is also 1.209 x 10^-3 mol.
Step 2: Use Ksp and stoichiometry to find the number of moles of PO4^3- ions
The solubility product constant (Ksp) of calcium phosphate (Ca3(PO4)2) is the equilibrium constant for the dissolution of the solid substance in water. It is given by the expression:
Ksp = [Ca^2+]^3 * [PO4^3-]^2
Since we want to remove all the Ca^2+ ions, we are looking for the number of moles of PO4^3- ions.
Substituting the known values into the Ksp expression:
Ksp = (1.209 x 10^-3 mol/L)^3 * [PO4^3-]^2
Rearranging the equation to solve for [PO4^3-]:
[PO4^3-]^2 = Ksp / [(1.209 x 10^-3 mol/L)^3]
Taking the square root of both sides:
[PO4^3-] = sqrt(Ksp / [(1.209 x 10^-3 mol/L)^3])
Step 3: Calculate the number of moles of PO4^3-
Now, we can substitute the values into the equation to find the concentration of PO4^3- ions in mol/L:
[PO4^3-] = sqrt(Ksp / [(1.209 x 10^-3 mol/L)^3])
= sqrt(Ksp / 1.460 x 10^-9 mol^3 / L^3)
Finally, we can multiply the concentration of PO4^3- ions by the volume of the water sample to find the number of moles of PO4^3- ions needed to remove all the Ca^2+ ions:
Number of moles of PO4^3- = [PO4^3-] x volume of water sample
In this case, the volume of water sample is given as 2.50 L. So, we can substitute this value into the equation above to find the number of moles of PO4^3- ions needed.