1) Identify the ions and their charges
The name sodium hexametaphosphate indicates a salt of:
- Cation: sodium, \(\mathrm{Na^+}\).
- Anion: hexametaphosphate, commonly written \(\mathrm{P_6O_{18}^{6-}}\).
The anion charge \(-6\) matches the “hexa-” (six phosphate units in the metaphosphate ring) and the metaphosphate repeating unit idea \((\mathrm{PO_3^-})\), giving \((\mathrm{PO_3})_6\) overall \(-6\).
2) Write the neutral formula by charge balance
Electrical neutrality requires total positive charge \(=\) total negative charge. With \(\mathrm{P_6O_{18}^{6-}}\), six \(\mathrm{Na^+}\) ions are needed:
\[ 6(+1) + (-6) = 0 \]
Therefore, the commonly used formula is:
\[ (\mathrm{NaPO_3})_6 = \mathrm{Na_6P_6O_{18}} \]
3) Ionic dissociation in water (idealized)
Treated as a soluble ionic compound, the stoichiometric dissociation is:
\[ \mathrm{Na_6P_6O_{18}(s) \rightarrow 6\,Na^+(aq) + P_6O_{18}^{6-}(aq)} \]
For each formula unit dissolved, the ion-count ratio is: Na+ : P6O186− = 6 : 1.
4) Molar mass of sodium hexametaphosphate
Using the formula \(\mathrm{Na_6P_6O_{18}}\), the molar mass is:
\[ M = 6M_{\mathrm{Na}} + 6M_{\mathrm{P}} + 18M_{\mathrm{O}} \]
With \(M_{\mathrm{Na}}=22.98977\), \(M_{\mathrm{P}}=30.97376\), \(M_{\mathrm{O}}=15.999\ \mathrm{g\cdot mol^{-1}}\):
\[ \begin{aligned} M &\approx 6(22.98977) + 6(30.97376) + 18(15.999) \\ &\approx 137.93862 + 185.84256 + 287.982 \\ &\approx 611.76318\ \mathrm{g\cdot mol^{-1}} \end{aligned} \]
Rounded appropriately: \(\boxed{M \approx 611.77\ \mathrm{g\cdot mol^{-1}}}\).
5) Check the arithmetic with an HTML table
| Element | Count in \(\mathrm{Na_6P_6O_{18}}\) | Atomic mass \((\mathrm{g\cdot mol^{-1}})\) | Contribution \((\mathrm{g\cdot mol^{-1}})\) |
|---|---|---|---|
| Sodium (Na) | 6 | 22.98977 | \(6 \cdot 22.98977 = 137.93862\) |
| Phosphorus (P) | 6 | 30.97376 | \(6 \cdot 30.97376 = 185.84256\) |
| Oxygen (O) | 18 | 15.999 | \(18 \cdot 15.999 = 287.982\) |
| Total | \(611.76318\) |
6) Visualization: charge balance for sodium hexametaphosphate
7) Final results
- Formula: \(\boxed{(\mathrm{NaPO_3})_6 = \mathrm{Na_6P_6O_{18}}}\).
- Ions in water (stoichiometric): \(\boxed{6\,\mathrm{Na^+} \text{ and } \mathrm{P_6O_{18}^{6-}}}\).
- Molar mass: \(\boxed{M \approx 611.77\ \mathrm{g\cdot mol^{-1}}}\).