The mass balance equations for 0.1 M Na₂HPO₄ system can be expressed as follows:

For sodium ions (Na⁺):

[ [Na^+] = 2 \times [Na_2HPO_4] ]

For phosphate species:

The total concentration of the phosphate species, as given, is 0.1 M. Thus: [ 0.1 , M = [H_3PO_4] + [H_2PO_4^-] + [HPO_4^{2-}] + [PO_4^{3-}] ]

For the saturated solution of MgCO₃:

Mass balance for Mg²⁺:

[ [Mg^{+2}] = \text{{Blank 1:}} , [CO_3^{2-}] + [HCO_3^-] + [H_2CO_3] ]

So, for the saturated MgCO₃ solution: [ [Mg^{+2}] = [CO_3^{2-}] + [HCO_3^-] + [H_2CO_3] ]

Corresponding blanks:

• Blank 1: [CO₃²⁻]
• Blank 2: [CO₃²⁻]
• Blank 3: [HCO₃⁻]
• Blank 4: [H₂CO₃]

Would you like further details or have any questions?

Here are five follow-up questions that might help deepen your understanding:

1. What are the dissociation constants for the different phosphate species?
2. How do pH changes affect the concentration of different phosphate species?
3. What assumptions are made in constructing mass balance equations for this system?
4. How would the presence of additional salts affect the sodium ion balance?
5. Can you calculate the equilibrium concentrations of each species in a buffer solution?

Tip: When performing mass balance calculations, always ensure that all species derived from the same compound are accounted for, especially in multi-step equilibria like the phosphate system.