A solution contains an unknown amount of dissolved calcium . Addition of 0.112 mole of K3PO4 causes complete precipitation of all the calcium. How many moles of calcium were dissolved in the solution?
1) use the M method to solve the following linear programming problem:
Minimize C+ -5x+10x+15x
Subject to 2x+3x+x <(or equal to) 24
x-2x-2x >(or equal to) 1
x,,x,x>(and equal to) 0
3Ca^2+ + 2PO4^3- ==> Ca3(PO4)2(s)
If you added 0.112 moles K3PO4, (and none of the K3PO4 remains unreacted, then use the coefficients in the balanced equation to determine the amount of Ca.
0.112 mole K3PO4 x (3 moles Ca^2+/2 moles PO4^3-) = ??moles Ca^2+.
To determine the moles of calcium dissolved in the solution, we need to consider the reaction between calcium and potassium phosphate.
The balanced chemical equation for the reaction is as follows:
3 Ca2+ + 2 PO4^3- → Ca3(PO4)2
From the balanced equation, we can see that it takes 3 moles of calcium ions (Ca2+) to react with 2 moles of phosphate ions (PO4^3-) to form 1 mole of calcium phosphate (Ca3(PO4)2).
Given that we have added 0.112 moles of potassium phosphate (K3PO4), which is equivalent to 0.112 moles of phosphate ions (PO4^3-), we can set up a ratio to calculate the moles of calcium ions (Ca2+) that were dissolved:
2 moles PO4^3- : 3 moles Ca2+
0.112 moles PO4^3- : x moles Ca2+
Using the ratio, we can calculate:
x = (0.112 moles Ca2+ × 3 moles Ca2+) / 2 moles PO4^3-
x = 0.168 moles Ca2+
Therefore, 0.168 moles of calcium were dissolved in the solution.
To determine the number of moles of calcium dissolved in the solution, we need to use stoichiometry and the balanced chemical equation between calcium and K3PO4.
The balanced chemical equation for the reaction between calcium ions (Ca^2+) and phosphate ions (PO4^3-) is:
3Ca^2+ + 2PO4^3- → Ca3(PO4)2 (s)
According to the equation, for every 3 moles of calcium ions, we require 2 moles of phosphate ions to form 1 mole of calcium phosphate precipitate.
Given that 0.112 moles of K3PO4 causes complete precipitation, we can see from the equation that it must contain 3/2 of the moles of calcium ions that will react with it. So, we can calculate the number of moles of calcium as follows:
Moles of calcium = (0.112 moles K3PO4) × (3/2) = 0.168 moles
Therefore, there were 0.168 moles of calcium dissolved in the solution.