College

A sample of a substance is analyzed and found to contain 36.5 grams of sodium, 25.4 grams of sulfur, and 38.1 grams of oxygen. If the molar mass of the compound is [tex]126.0 \, \text{g/mole}[/tex], determine the molecular formula.

What is the name of this compound?

Answer :

To determine the molecular formula of the compound and its name, we'll follow these steps:

1. Calculate the Moles of Each Element:
- For Sodium (Na):
[tex]\[
\text{Moles of Na} = \frac{36.5 \text{ grams}}{22.99 \text{ g/mole}} = 1.5876 \text{ moles}
\][/tex]
- For Sulfur (S):
[tex]\[
\text{Moles of S} = \frac{25.4 \text{ grams}}{32.06 \text{ g/mole}} = 0.7923 \text{ moles}
\][/tex]
- For Oxygen (O):
[tex]\[
\text{Moles of O} = \frac{38.1 \text{ grams}}{16.00 \text{ g/mole}} = 2.3813 \text{ moles}
\][/tex]

2. Determine the Simplest Ratio:
- Identify the smallest number of moles, which is 0.7923 moles of Sulfur.
- Divide the moles of each element by the smallest number to find the ratio:
- Sodium:
[tex]\[
\frac{1.5876}{0.7923} \approx 2
\][/tex]
- Sulfur:
[tex]\[
\frac{0.7923}{0.7923} = 1
\][/tex]
- Oxygen:
[tex]\[
\frac{2.3813}{0.7923} \approx 3
\][/tex]

3. Write the Empirical Formula:
- Based on the mole ratios, the empirical formula is [tex]\( \text{Na}_2\text{SO}_3 \)[/tex].

4. Given the Molar Mass:
- The empirical formula weight for [tex]\( \text{Na}_2\text{SO}_3 \)[/tex] matches the given molar mass of 126.0 g/mole. Therefore, the empirical formula is the same as the molecular formula.

5. Name the Compound:
- The compound with the formula [tex]\( \text{Na}_2\text{SO}_3 \)[/tex] is called Sodium Sulfite.

Thus, the molecular formula is [tex]\( \text{Na}_2\text{SO}_3 \)[/tex] and the name of the compound is Sodium Sulfite.

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