What is the percent by mass of sodium in [tex]Na_2SO_4[/tex]?

Use [tex]\% \text{ Element} = \frac{\text{total mass of element in compound}}{\text{molar mass of compound}} \times 100[/tex]

A. [tex]16.18\%[/tex]
B. [tex]22.58\%[/tex]
C. [tex]32.37\%[/tex]
D. [tex]45.98\%[/tex]



Answer :

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]