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To determine which molecular formulas correspond to a molecular ion with a mass-to-charge ratio (m/z) of 73, we need to calculate the molecular masses of each given formula and compare them to 73.
### Molecular Mass Calculations:
1. [tex]\( \text{C}_4 \text{H}_{11} \text{O} \)[/tex]
- Carbon (C): 4 atoms × 12 = 48
- Hydrogen (H): 11 atoms × 1 = 11
- Oxygen (O): 1 atom × 16 = 16
Total = 48 + 11 + 16 = 75
2. [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 7 atoms × 1 = 7
- Nitrogen (N): 3 atoms × 14 = 42
Total = 24 + 7 + 42 = 73
3. [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex]
- Carbon (C): 4 atoms × 12 = 48
- Hydrogen (H): 11 atoms × 1 = 11
- Nitrogen (N): 1 atom × 14 = 14
Total = 48 + 11 + 14 = 73
4. [tex]\( \text{C}_2 \text{H}_5 \text{N}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 5 atoms × 1 = 5
- Nitrogen (N): 3 atoms × 14 = 42
Total = 24 + 5 + 42 = 71
5. [tex]\( \text{C}_5 \text{H}_{13} \)[/tex]
- Carbon (C): 5 atoms × 12 = 60
- Hydrogen (H): 13 atoms × 1 = 13
Total = 60 + 13 = 73
6. [tex]\( \text{C}_2 \text{H}_7 \text{O}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 7 atoms × 1 = 7
- Oxygen (O): 3 atoms × 16 = 48
Total = 24 + 7 + 48 = 79
### Comparison to Target Mass (73):
1. [tex]\( \text{C}_4 \text{H}_{11} \text{O} \)[/tex] = 75 (does not match)
2. [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex] = 73 (matches)
3. [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex] = 73 (matches)
4. [tex]\( \text{C}_2 \text{H}_5 \text{N}_3 \)[/tex] = 71 (does not match)
5. [tex]\( \text{C}_5 \text{H}_{13} \)[/tex] = 73 (matches)
6. [tex]\( \text{C}_2 \text{H}_7 \text{O}_3 \)[/tex] = 79 (does not match)
### Conclusion:
The molecular formulas [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex], [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex], and [tex]\( \text{C}_5 \text{H}_{13} \)[/tex] correspond to a molecular ion with an m/z of 73.
Since the question asks to select two of them, any two from these three will be correct. For example:
- [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex]
- [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex]
### Molecular Mass Calculations:
1. [tex]\( \text{C}_4 \text{H}_{11} \text{O} \)[/tex]
- Carbon (C): 4 atoms × 12 = 48
- Hydrogen (H): 11 atoms × 1 = 11
- Oxygen (O): 1 atom × 16 = 16
Total = 48 + 11 + 16 = 75
2. [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 7 atoms × 1 = 7
- Nitrogen (N): 3 atoms × 14 = 42
Total = 24 + 7 + 42 = 73
3. [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex]
- Carbon (C): 4 atoms × 12 = 48
- Hydrogen (H): 11 atoms × 1 = 11
- Nitrogen (N): 1 atom × 14 = 14
Total = 48 + 11 + 14 = 73
4. [tex]\( \text{C}_2 \text{H}_5 \text{N}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 5 atoms × 1 = 5
- Nitrogen (N): 3 atoms × 14 = 42
Total = 24 + 5 + 42 = 71
5. [tex]\( \text{C}_5 \text{H}_{13} \)[/tex]
- Carbon (C): 5 atoms × 12 = 60
- Hydrogen (H): 13 atoms × 1 = 13
Total = 60 + 13 = 73
6. [tex]\( \text{C}_2 \text{H}_7 \text{O}_3 \)[/tex]
- Carbon (C): 2 atoms × 12 = 24
- Hydrogen (H): 7 atoms × 1 = 7
- Oxygen (O): 3 atoms × 16 = 48
Total = 24 + 7 + 48 = 79
### Comparison to Target Mass (73):
1. [tex]\( \text{C}_4 \text{H}_{11} \text{O} \)[/tex] = 75 (does not match)
2. [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex] = 73 (matches)
3. [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex] = 73 (matches)
4. [tex]\( \text{C}_2 \text{H}_5 \text{N}_3 \)[/tex] = 71 (does not match)
5. [tex]\( \text{C}_5 \text{H}_{13} \)[/tex] = 73 (matches)
6. [tex]\( \text{C}_2 \text{H}_7 \text{O}_3 \)[/tex] = 79 (does not match)
### Conclusion:
The molecular formulas [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex], [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex], and [tex]\( \text{C}_5 \text{H}_{13} \)[/tex] correspond to a molecular ion with an m/z of 73.
Since the question asks to select two of them, any two from these three will be correct. For example:
- [tex]\( \text{C}_2 \text{H}_7 \text{N}_3 \)[/tex]
- [tex]\( \text{C}_4 \text{H}_{11} \text{N} \)[/tex]
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