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Arenes are a special type of compound consisting of only carbon and hydrogen. If 6.000 g of a specific arene with a molar mass of approximately 155 g/mol g/mol yields 20.548g of CO 2​ upon combustion in a purely oxygen atmosphere, determine the a) empirical, and b) molecular formulas, for the compound.

User Kohlerm
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1 Answer

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To determine the empirical and molecular formulas, follow these steps:

### a) Empirical Formula:

1. **Convert grams to moles:**
\[ \text{moles of } \ce{CO2} = \frac{20.548 \, \text{g}}{44.01 \, \text{g/mol}} \]

This gives you the moles of carbon because each mole of \ce{CO2} has one mole of carbon.

2. **Determine moles of carbon:**
Since the empirical formula of the arene only contains carbon and hydrogen, the moles of carbon are equal to the moles of \ce{CO2}.

3. **Calculate moles of hydrogen:**
\[ \text{moles of hydrogen} = \text{total moles} - \text{moles of carbon} \]

4. **Determine the simplest whole number ratio:**
Divide both moles of carbon and moles of hydrogen by the smaller value among them.

5. **Write the empirical formula:**
Use the ratio to write the empirical formula.

### b) Molecular Formula:

6. **Determine the molecular mass of the empirical formula:**
\[ \text{Molecular mass} = \text{Empirical formula mass} \times n \]

where \( n \) is the factor by which the molecular formula is greater than the empirical formula.

7. **Calculate \( n \):**
\[ n = \frac{\text{Molar mass given}}{\text{Empirical formula mass}} \]

8. **Write the molecular formula:**
Multiply the subscripts in the empirical formula by \( n \).

This process will give you both the empirical and molecular formulas for the arene compound.
User Animir
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