Question
Elemental analysis is performed on an unknown organic substance which is found to contain 12 grams of hydrogen and 72 grams of carbon. Subsequent analysis with a mass spectrometer yields a molar mass of 84 g/mole. What is the molecular formula of the unknown?
Group of answer choices
C7H14
C6H12
C5H12
C6H6
Group of answer choices
C7H14
C6H12
C5H12
C6H6
Answers
GPT-4o mini
To determine the molecular formula of the unknown substance, we first need to identify the empirical formula based on the elemental analysis provided.
1. **Convert grams to moles**:
- For Carbon (C):
\( \text{Moles of C} = \frac{\text{mass}}{\text{molar mass}} = \frac{72 \text{ g}}{12 \text{ g/mol}} = 6 \text{ moles of C} \)
- For Hydrogen (H):
\( \text{Moles of H} = \frac{\text{mass}}{\text{molar mass}} = \frac{12 \text{ g}}{1 \text{ g/mol}} = 12 \text{ moles of H} \)
2. **Determine the mole ratio**:
- The mole ratio of C to H is \( \frac{6}{6} : \frac{12}{6} = 1 : 2 \).
- Hence, the empirical formula is \( \text{CH}_2 \).
3. **Calculate the molar mass of the empirical formula**:
- For \( \text{CH}_2 \):
\( \text{Molar mass} = 12 \text{ g/mol} + 2 \times 1 \text{ g/mol} = 14 \text{ g/mol} \).
4. **Determine the ratio of the molecular mass to the empirical formula mass**:
- The molar mass of the substance found from mass spectrometry is 84 g/mol, and the empirical formula mass is 14 g/mol.
- The ratio is:
\( \frac{84}{14} = 6 \).
5. **Calculate the molecular formula**:
- Therefore, the molecular formula is obtained by multiplying the subscripts in the empirical formula by 6:
- \( \text{C}_{1 \times 6}\text{H}_{2 \times 6} = \text{C}_6\text{H}_{12} \).
Thus, the molecular formula of the unknown substance is **C6H12**.
1. **Convert grams to moles**:
- For Carbon (C):
\( \text{Moles of C} = \frac{\text{mass}}{\text{molar mass}} = \frac{72 \text{ g}}{12 \text{ g/mol}} = 6 \text{ moles of C} \)
- For Hydrogen (H):
\( \text{Moles of H} = \frac{\text{mass}}{\text{molar mass}} = \frac{12 \text{ g}}{1 \text{ g/mol}} = 12 \text{ moles of H} \)
2. **Determine the mole ratio**:
- The mole ratio of C to H is \( \frac{6}{6} : \frac{12}{6} = 1 : 2 \).
- Hence, the empirical formula is \( \text{CH}_2 \).
3. **Calculate the molar mass of the empirical formula**:
- For \( \text{CH}_2 \):
\( \text{Molar mass} = 12 \text{ g/mol} + 2 \times 1 \text{ g/mol} = 14 \text{ g/mol} \).
4. **Determine the ratio of the molecular mass to the empirical formula mass**:
- The molar mass of the substance found from mass spectrometry is 84 g/mol, and the empirical formula mass is 14 g/mol.
- The ratio is:
\( \frac{84}{14} = 6 \).
5. **Calculate the molecular formula**:
- Therefore, the molecular formula is obtained by multiplying the subscripts in the empirical formula by 6:
- \( \text{C}_{1 \times 6}\text{H}_{2 \times 6} = \text{C}_6\text{H}_{12} \).
Thus, the molecular formula of the unknown substance is **C6H12**.