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To determine the empirical formula of a compound composed of 32.4% sodium (Na), 22.5% sulfur (S), and 45.1% oxygen (O) by mass, we can follow these steps:

1. Convert the given percentages to grams: Assume we have 100 grams of the compound. This means we have:
- 32.4 grams of Na
- 22.5 grams of S
- 45.1 grams of O

2. Convert the masses to moles:
- The molar mass of Na (sodium) is approximately 22.99 g/mol.
- The molar mass of S (sulfur) is approximately 32.07 g/mol.
- The molar mass of O (oxygen) is approximately 16.00 g/mol.

Using these molar masses, we can convert grams to moles:
- Moles of Na = 32.4 g Na / 22.99 g/mol ≈ 1.409 moles
- Moles of S = 22.5 g S / 32.07 g/mol ≈ 0.702 moles
- Moles of O = 45.1 g O / 16.00 g/mol ≈ 2.819 moles

3. Determine the smallest number of moles:
The smallest number of moles among Na, S, and O is approximately 0.702 (moles of S).

4. Divide all the mole amounts by the smallest number of moles to get the simplest whole number ratio:
- Ratio of Na = 1.409 moles / 0.702 moles ≈ 2
- Ratio of S = 0.702 moles / 0.702 moles ≈ 1
- Ratio of O = 2.819 moles / 0.702 moles ≈ 4

5. Write the empirical formula:
The simplest whole number ratio of Na:S:O is 2:1:4. Therefore, the empirical formula of the compound is [tex]\( \text{Na}_2\text{SO}_4 \)[/tex].

The empirical formula of the compound is [tex]\( \text{Na}_2\text{SO}_4 \)[/tex].

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