A mixture is prepared by adding 25.0 mL of 0.185 M Na3PO4 to 34.0 mL of 0.140 M Ca(NO3)2.
(a) What mass, in grams, of calcium phosphate will be formed?
What will be the concentration of each of the ions in the mixture after the reaction?
(b) [Ca2+]
(c) [PO43-]
(d) [Na+]
(e) [NO3-]
To answer the given questions, we need to utilize the principles of stoichiometry and calculate the number of moles, masses, and concentrations of different substances involved in the reaction.
(a) To determine the mass of calcium phosphate formed, we first need to determine the limiting reagent, i.e., the reactant that is completely consumed in the reaction. The balanced chemical equation for the reaction between Na3PO4 and Ca(NO3)2 is:
3Na3PO4 + 2Ca(NO3)2 → Ca3(PO4)2 + 6NaNO3
The molar ratio between Na3PO4 and Ca3(PO4)2 is 3:1. We can start by calculating the moles of Na3PO4 and Ca(NO3)2 involved in the reaction:
Moles of Na3PO4 = volume (in liters) × molarity = (25.0 mL ÷ 1000 mL/L) × 0.185 mol/L
Moles of Ca(NO3)2 = volume (in liters) × molarity = (34.0 mL ÷ 1000 mL/L) × 0.140 mol/L
The molar mass of Ca3(PO4)2 is:
3(40.1 g/mol) + 2(31.0 g/mol) + 8(16.0 g/mol) = 310.18 g/mol
Now, we compare the moles of Na3PO4 and Ca(NO3)2 to find the limiting reagent. Since the stoichiometric ratio is 3:1, we divide the moles of Ca(NO3)2 by 2 and compare it with the moles of Na3PO4. The smaller value will be the limiting reagent.
Moles of Ca(NO3)2 ÷ 2 = (34.0 mL ÷ 1000 mL/L) × 0.140 mol/L ÷ 2
Moles of Na3PO4 = (25.0 mL ÷ 1000 mL/L) × 0.185 mol/L
Compare the above values to determine the limiting reagent. If the moles of Ca(NO3)2 ÷ 2 are smaller, it is the limiting reagent. Otherwise, Na3PO4 is the limiting reagent.
Once you have identified the limiting reagent, use its moles to calculate the moles of Ca3(PO4)2 formed. Since the stoichiometric ratio is 2:1, we multiply the moles of the limiting reagent by 1/2 to find the moles of Ca3(PO4)2 formed.
Moles of Ca3(PO4)2 = moles of limiting reagent × (1 mole of Ca3(PO4)2 ÷ 2 moles of limiting reagent)
Finally, we can calculate the mass of calcium phosphate formed using the moles of Ca3(PO4)2 and its molar mass:
Mass of Ca3(PO4)2 = moles of Ca3(PO4)2 × molar mass of Ca3(PO4)2
(b) To determine the concentration of [Ca2+] in the mixture after the reaction, divide the moles of Ca3(PO4)2 by the total volume of the mixture:
[Ca2+] = moles of Ca3(PO4)2 ÷ total volume (in liters) of the mixture
(c) To determine the concentration of [PO43-], divide the moles of Ca3(PO4)2 by the total volume of the mixture:
[PO43-] = moles of Ca3(PO4)2 ÷ total volume (in liters) of the mixture
(d) To determine the concentration of [Na+], divide the moles of Na3PO4 by the total volume of the mixture:
[Na+] = moles of Na3PO4 ÷ total volume (in liters) of the mixture
(e) To determine the concentration of [NO3-], divide the moles of Ca(NO3)2 by the total volume of the mixture:
[NO3-] = moles of Ca(NO3)2 ÷ total volume (in liters) of the mixture