Potassium sulfate: formula and molar mass
Potassium sulfate is an ionic compound made from potassium ions and the sulfate polyatomic ion. The chemical formula is obtained by balancing charges so the overall compound is electrically neutral.
Step 1: Identify the ions and their charges
- Potassium ion: \( \mathrm{K^+} \) (Group 1 metals form \(+1\) cations)
- Sulfate ion: \( \mathrm{SO_4^{2-}} \) (a common polyatomic anion with charge \(-2\))
Step 2: Balance charges to write the formula
One sulfate ion contributes \(-2\). Each potassium ion contributes \(+1\). Therefore, two potassium ions are required to balance one sulfate ion:
\[ 2(\mathrm{K^+}) + 1(\mathrm{SO_4^{2-}}) \rightarrow \mathrm{K_2SO_4} \]
\[ 2 \times (+1) + 1 \times (-2) = 0 \]
The chemical formula of potassium sulfate is \(\mathrm{K_2SO_4}\).
Step 3: Calculate the molar mass of potassium sulfate
The molar mass is the sum of each element’s atomic mass multiplied by its subscript in \( \mathrm{K_2SO_4} \). Using common periodic-table values: \(M(\mathrm{K}) \approx 39.10\), \(M(\mathrm{S}) \approx 32.06\), \(M(\mathrm{O}) \approx 16.00\) (in g/mol).
| Element | Count in \( \mathrm{K_2SO_4} \) | Atomic mass (g/mol) | Contribution (g/mol) |
|---|---|---|---|
| K | 2 | 39.10 | \(2 \times 39.10 = 78.20\) |
| S | 1 | 32.06 | \(1 \times 32.06 = 32.06\) |
| O | 4 | 16.00 | \(4 \times 16.00 = 64.00\) |
\[ M(\mathrm{K_2SO_4}) = 78.20 + 32.06 + 64.00 = 174.26\ \text{g/mol} \]
Potassium sulfate has formula \( \mathrm{K_2SO_4} \) and molar mass \( \mathrm{174.26\ g/mol} \) (to the shown precision).
Optional extension: percent composition (mass percent)
Mass percent of each element is computed by dividing that element’s total mass contribution by the molar mass:
\[ \%\ \text{element} = \frac{\text{element contribution}}{M(\mathrm{K_2SO_4})} \times 100 \]
\[ \%\mathrm{K}=\frac{78.20}{174.26}\times 100 \approx 44.87,\quad \%\mathrm{S}=\frac{32.06}{174.26}\times 100 \approx 18.40,\quad \%\mathrm{O}=\frac{64.00}{174.26}\times 100 \approx 36.73 \]