Phosphorus in a solution of sodium phosphate

[bmlevac]

1. Homework Statement

I have a solution containing both mono basic (480mg/ml) and dibasic (180mg/ml) sodium phosphate. How do I determine the total mass of phosphorus per ml of the entire solution?

2. Homework Equations

?

3. The Attempt at a Solution

Monobasic sodium phosphate (MSP):
(480mg/mL)/(119.98mg/mmol)=4 mmol/mL

Phosphorus in MSP: (30.974 mg/mmol)(4 mmol/mL)=123.90 mg/mL

Dibasic sodium phosphate (DSP)
(180 mg/mL)/(141.96mg/mmol)=1.268 mmol/mL

Phosphorus in DSP: (30.97 mg/mmol)(1.268 mmol/mL)=39.28 mg/mL

Total elemental phosphorus = 123.90+39.28=163.18 mg/mL

However, this answer is not correct. Apparently, the correct answer is 124.36 mg/mL

 

[Borek]

163 mg/mL looks OK to me.

Are you sure about concentrations given? I have no solubility tables at hand, but 480 mg/mL looks high. Not necessarily impossible, just worth checking.

 

[bmlevac]

It is dissolved in water and glycerin, which likely improves the solubility.

I've found an alternative solution to the problem, but now I don't know how to justify one over the other. Can someone explain why the following answer is the correct answer versus the one above?

Here is the alternate solution (using some of the calculations made above):

[MSP]=4 mmol/ml (see above)
[DSP]=1.268 mmol/ml (see above)
Molar mass phosphate ion: 94.97 mg/mmol
Molar mass MSP: 119.98 mg/mmol
Molar mass DSP: 141.96 mg/mmol

Phosphate ion concentration:
[(94.97/119.98)x4 mmol/ml]+[(94.97/141/96)x1.268 mmol/ml]=3.1667+0.8483=4.015 mmol/ml

Elemental phosphorus in phosphate ions:
(30.974 mg/mmol)x(4.015 mmol/ml)=124.36 mg/ml

 

[Borek]

Solution that 4 mmol/mL in MSP is also 4 mmol/mL in phosphate (and sodium).

Your previous answer was correct, now you are just juggling numbers.