To determine which molecular formulas correspond to a molecular ion with a mass-to-charge ratio (m/z) of 100, we need to calculate the molecular weight of each given compound. We consider the atomic weights of the elements involved:
- Carbon (C) = 12
- Hydrogen (H) = 1
- Nitrogen (N) = 14
- Oxygen (O) = 16
Let's calculate the molecular weight for each formula:
1. [tex]\( \text{C}_7\text{H}_{16} \)[/tex]
- [tex]\( 7 \times 12 + 16 \times 1 \)[/tex]
- [tex]\( 84 + 16 = 100 \)[/tex]
2. [tex]\( \text{C}_8\text{H}_4 \)[/tex]
- [tex]\( 8 \times 12 + 4 \times 1 \)[/tex]
- [tex]\( 96 + 4 = 100 \)[/tex]
3. [tex]\( \text{C}_6\text{H}_{12}\text{N} \)[/tex]
- [tex]\( 6 \times 12 + 12 \times 1 + 14 \)[/tex]
- [tex]\( 72 + 12 + 14 = 98 \)[/tex]
4. [tex]\( \text{C}_8\text{H}_5 \)[/tex]
- [tex]\( 8 \times 12 + 5 \times 1 \)[/tex]
- [tex]\( 96 + 5 = 101 \)[/tex]
5. [tex]\( \text{C}_4\text{H}_{12}\text{O}\text{N} \)[/tex]
- [tex]\( 4 \times 12 + 12 \times 1 + 16 + 14 \)[/tex]
- [tex]\( 48 + 12 + 16 + 14 = 90 \)[/tex]
6. [tex]\( \text{C}_7\text{H}_{15} \)[/tex]
- [tex]\( 7 \times 12 + 15 \times 1 \)[/tex]
- [tex]\( 84 + 15 = 99 \)[/tex]
From our calculations, the molecular formulas that result in a molecular weight of 100 are:
- [tex]\( \text{C}_7\text{H}_{16} \)[/tex]
- [tex]\( \text{C}_8\text{H}_4 \)[/tex]
Thus, the correct molecular formulas that sum to a molecular ion at m/z = 100 are [tex]\( \text{C}_7\text{H}_{16} \)[/tex] and [tex]\( \text{C}_8\text{H}_4 \)[/tex].
