To determine the percent by mass of sodium in sodium sulfate (Na₂SO₄), we will follow a series of steps considering the molecular masses of the elements involved. Here is a detailed, step-by-step solution:
1. Determine the Atomic Masses:
- The atomic mass of Sodium (Na): 22.99 g/mol
- The atomic mass of Sulfur (S): 32.07 g/mol
- The atomic mass of Oxygen (O): 16.00 g/mol
2. Calculate the Molar Mass of Na₂SO₄:
- Sodium sulfate has the chemical formula Na₂SO₄, which means it contains:
- 2 Sodium (Na) atoms
- 1 Sulfur (S) atom
- 4 Oxygen (O) atoms
- The molar mass of Na₂SO₄ is computed as follows:
[tex]\[
\text{Molar mass of Na₂SO₄} = (2 \times \text{Atomic mass of Na}) + (\text{Atomic mass of S}) + (4 \times \text{Atomic mass of O})
\][/tex]
[tex]\[
\text{Molar mass of Na₂SO₄} = (2 \times 22.99\, \text{g/mol}) + (32.07\, \text{g/mol}) + (4 \times 16.00\, \text{g/mol})
\][/tex]
[tex]\[
\text{Molar mass of Na₂SO₄} = 45.98\, \text{g/mol} + 32.07\, \text{g/mol} + 64.00\, \text{g/mol}
\][/tex]
[tex]\[
\text{Molar mass of Na₂SO₄} = 142.05\, \text{g/mol}
\][/tex]
3. Calculate the Total Mass of Sodium in Na₂SO₄:
- The total mass of Sodium in Na₂SO₄ is given by:
[tex]\[
\text{Mass of Sodium} = 2 \times \text{Atomic mass of Na}
\][/tex]
[tex]\[
\text{Mass of Sodium} = 2 \times 22.99\, \text{g/mol}
\][/tex]
[tex]\[
\text{Mass of Sodium} = 45.98\, \text{g/mol}
\][/tex]
4. Calculate the Percent by Mass of Sodium in Na₂SO₄:
- The percent by mass of Sodium in sodium sulfate can be calculated using the formula:
[tex]\[
\% \text{Element} = \left( \frac{\text{Total mass of element in compound}}{\text{Molar mass of compound}} \right) \times 100
\][/tex]
[tex]\[
\% \text{Na} = \left( \frac{45.98\, \text{g/mol}}{142.05\, \text{g/mol}} \right) \times 100
\][/tex]
[tex]\[
\% \text{Na} \approx 32.37\%
\][/tex]
Therefore, the percent by mass of sodium in Na₂SO₄ is approximately 32.37%. The correct answer is:
[tex]\[
\boxed{32.37\%}
\][/tex]
