Question

Write molecular formulas for the five possible molecular ions of \(\mathrm{m} / z 100\) containing only the elements \(\mathrm{C}, \mathrm{H}, \mathrm{N}\), and \(\mathrm{O}\).

Short answer

Question: List the five possible molecular ions of m/z 100 containing only the elements carbon (C), hydrogen (H), nitrogen (N), and oxygen (O). Answer: The five possible molecular ions are: 1. \(\mathrm{C}_5 \mathrm{H}_4 \mathrm{N}_2\) 2. \(\mathrm{C}_5 \mathrm{H}_8 \mathrm{O}_2\) 3. \(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}_1 \mathrm{N}_1\) 4. \(\mathrm{C}_6 \mathrm{H}_4 \mathrm{O}_3\) 5. \(\mathrm{C}_7 \mathrm{H}_{16}\)

Step-by-step solution

Determine the atomic masses of elements involved

The atomic masses for the elements are as follows: C = 12, H = 1, N = 14, and O = 16. These values will be used in the next step to find out the possible combinations.

Generate possible combinations

Since the molar mass of the resulting molecules must be 100 amu, we can create equations that represent the sum of the elements' atomic masses multiplied by the number of atoms of each element in the molecule. The equations will have the form: 12 * C + 1 * H + 14 * N + 16 * O = 100. Now, we systematically try different amounts of each element until we reach the solutions that are equal to 100 amu.

List the potential molecular formulas

By trying various combinations of amounts of atoms, we find the following five molecular formulas with an m/z of 100 amu: 1. \(\mathrm{C}_5 \mathrm{H}_4 \mathrm{N}_2\): (5 * 12) + (4 * 1) + (2 * 14) = 60 + 4 + 28 = 100 2. \(\mathrm{C}_5 \mathrm{H}_8 \mathrm{O}_2\): (5 * 12) + (8 * 1) + (2 * 16) = 60 + 8 + 32 = 100 3. \(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}_1 \mathrm{N}_1\): (5 * 12) + (12 * 1) + (1 * 16) + (1 * 14) = 60 + 12 + 16 + 14 = 100 4. \(\mathrm{C}_6 \mathrm{H}_4 \mathrm{O}_3\): (6 * 12) + (4 * 1) + (3 * 16) = 72 + 4 + 48 = 100 5. \(\mathrm{C}_7 \mathrm{H}_{16}\): (7 * 12) + (16 * 1) = 84 + 16 = 100 These are the five possible molecular ions of m/z 100 containing only the elements C, H, N, and O.