A 20.0 gram sample is a mixture of sodium phosphate ,sodium mono-hydrogen phosphate,sodium dihydrogen phosphate and sodium chloride. The sample is dissolved in 100.0 ml of deionized water and titrated with 1.5 M hydrochloric acid. The initial pH of the solution is pH= 12.9. The first equivalence point occurs at 16.0 ml of acid ( pH= 10.5). The second equivalence occurs after the addition of an additional 44.0 ml of acid( pH= 8.05). The third equivalence occurs after the addition of an additional 11.1 ml of acid( pH= 1.22). Calculate the mass percent of each component in the mixture.
See my response to your earlier post of this problem.
it isn't showing your response in the earlier post!
I must have hit the wrong button when I tried to post. Here are my partial thoughts. I said something like,
Bill, we can't draw diagrams on the board and I don't know how to explain a problem like this without better aids than are available. I can try to get you started with some info and you can re-post with very specific questions if you have trouble. This really is a long and complicated problem.
The first thing you need to know is/are the equation(s).
PO4^3- is titrated first, HPO4^2- is second, and H2PO4^- is last.
PO4^3- + H^+ ==> HPO4^2-
HPO4^2- + H^+ ==> H2PO4^-
H2PO4^- + H^+ ==> H3PO4.
The first equivalence point is straight forward. mL x M = 16.0 x 1.5M = ? millimoles HCl = same mmols PO4^3-. Then you convert that to grams and you have the first component.
The problem gets more complicated from here.
You have mL for the second equivalence point BUT that is the volume to titrate the original HPO4^2- in the sample PLUS the HPO4^2- formed in getting to the first equivalence point. You will need to subtract an equivalent amount to find HPO4^2- in the original sample. I would calculate total millimoles - millimoles for the first amount = millimoles for the second amount (in the initial 20g sample) Then the third one as twice as many problems as this. The third equivalence point is the volume to titrate the original H2PO4^- + H2PO4^- formed from the first stage + H2PO4^- from the second stage.
Good luck. Post your work if you get stuck but better yet be VERY explicit about what you don't understand.
To calculate the mass percent of each component in the mixture, we need to determine the moles of each compound.
Step 1: Calculate the moles of HCl used at each equivalence point.
- At the first equivalence point: 16.0 mL of 1.5 M HCl.
Moles of HCl = volume (L) x concentration (M) = 0.016 L x 1.5 M = 0.024 moles HCl.
- At the second equivalence point: 44.0 mL of additional HCl.
Moles of HCl = total volume (L) x concentration (M) = (0.016 L + 0.044 L) x 1.5 M = 0.090 moles HCl.
- At the third equivalence point: 11.1 mL of additional HCl.
Moles of HCl = total volume (L) x concentration (M) = (0.016 L + 0.044 L + 0.0111 L) x 1.5 M = 0.104 moles HCl.
Step 2: Construct the balanced chemical equation for each equivalence point reaction.
We know that sodium phosphate (Na3PO4) is a triprotic acid, and by determining the moles of HCl, we can calculate the moles of sodium phosphate reacted in each equivalence point reaction.
1st equivalence point:
Na3PO4 (s) + 3 HCl (aq) → NaCl (aq) + H3PO4 (aq)
For every mole of HCl, we have 1/3 mole of Na3PO4 (or 3 moles of HCl react with 1 mole of Na3PO4).
2nd equivalence point:
Na3PO4 (s) + 2 HCl (aq) → NaCl (aq) + NaH2PO4 (aq)
For every mole of HCl, we have 1/2 mole of Na3PO4 (or 2 moles of HCl react with 1 mole of Na3PO4).
3rd equivalence point:
Na3PO4 (s) + HCl (aq) → NaCl (aq) + Na2HPO4 (aq)
For every mole of HCl, we have 1 mole of Na3PO4 (or 1 mole of HCl reacts with 1 mole of Na3PO4).
Step 3: Calculate the moles of each compound in the mixture.
Using the stoichiometry from the balanced chemical equations, we can determine the moles of each component reacted at each equivalence point.
At the first equivalence point:
Moles of Na3PO4 = 0.024 moles HCl x (1/3) moles Na3PO4/mole HCl = 0.008 moles Na3PO4.
At the second equivalence point:
Moles of Na3PO4 = (0.090 moles HCl - 0.024 moles HCl) x (1/2) moles Na3PO4/mole HCl = 0.033 moles Na3PO4.
At the third equivalence point:
Moles of Na3PO4 = (0.104 moles HCl - 0.090 moles HCl) x 1 mole Na3PO4/mole HCl = 0.014 moles Na3PO4.
Step 4: Calculate the mass of each compound in the mixture.
Now, using the moles of each compound, we can determine their corresponding masses.
Mass of Na3PO4 = moles of Na3PO4 x molar mass of Na3PO4.
Molar mass of Na3PO4 = (3 x atomic mass of Na) + (1 x atomic mass of P) + (4 x atomic mass of O) = (3 x 22.99) + 31.00 + (4 x 16.00) = 163.99 g/mol.
Mass of Na3PO4 at the first equivalence point = 0.008 moles x 163.99 g/mol = 1.312 g.
Mass of Na3PO4 at the second equivalence point = 0.033 moles x 163.99 g/mol = 5.407 g.
Mass of Na3PO4 at the third equivalence point = 0.014 moles x 163.99 g/mol = 2.296 g.
From the information given in the question, the initial sample is 20.0 grams. Therefore, the mass of any other compound can be calculated by subtracting the mass of Na3PO4 at each equivalence point from the total sample mass.
Mass of Na3PO4 = 20.0 g - mass of Na3PO4 at each equivalence point.
Step 5: Calculate the mass percent of each compound.
Mass percent = (mass of compound / total mass of sample) x 100
Mass percent of Na3PO4 at the first equivalence point = (1.312 g / 20.0 g) x 100 = 6.56%
Mass percent of Na3PO4 at the second equivalence point = (5.407 g / 20.0 g) x 100 = 27.04%
Mass percent of Na3PO4 at the third equivalence point = (2.296 g / 20.0 g) x 100 = 11.48%
Finally, to calculate the mass percent of the other components (sodium mono-hydrogen phosphate, sodium dihydrogen phosphate, and sodium chloride), you can repeat the same steps by substituting the corresponding compound in the calculations.