Question

The molecular ion region in the mass spectrum of a large molecule, such as a protein, consists of a cluster of peaks differing by 1 Da. This pattern occurs because a molecule with many atoms has a high probability of containing one or several atoms of ${{}^{\mathbf{13}}\mathbf{C}}^{\mathbf{15}}\mathbf{N}{\mathbf{,}}^{\mathbf{18}}\mathbf{O}\mathbf{,}{\mathbf{}}^{\mathbf{2}}\mathbf{H}$and ${\mathbf{}}^{\mathbf{32}}\mathbf{S}$. In fact, the probability of finding a molecule with only ${{}^{\mathbf{12}}\mathbf{C}}^{\mathbf{14}}\mathbf{N}{\mathbf{,}}^{\mathbf{16}}\mathbf{O}\mathbf{,}{\mathbf{}}^1\mathbf{H}$and ${\mathbf{}}^{\mathbf{32}}\mathbf{S}$ may be so small that the nominal molecular ion is not observed. The electrospray mass spectrum of the rat protein interleukin-8 consists of a series of clusters of peaks arising from intact molecular ions with different charge. One cluster has peaks at m/z 1 961.12, 1 961.35, 1 961.63, 1 961.88, 1 962.12 (tallest peak), 1 962.36, 1 962.60, 1 962.87, 1 963.10, 1 963.34, 1 963.59, 1 963.85, and 1 964.09. These peaks correspond to isotopic ions differing by 1 Da. From the observed peak separation, fi nd the charge of the ions in this cluster. From m/z of the tallest peak, estimate the molecular mass of the protein.

Short answer

The charge is 4, and molecular mass: 7848.48Da

Step-by-step solution

solving for charge:

To determine the charge of ions, we simply get the average of the different between the m/z of the 13 peaks give, then we get the average of the computed value:

m/z	m/z
1961.12	-
1961.35	0.23
1961.63	0.28
1961.88	0.25
1962.12	0.25

1992.36	0.24
1962.60	0.24
1962.87	0.17
1963.10	0.23
1963.34	0.24
1963.59	0.25
1963.85	0.26
1963.09	0.24
Average m/z	0.25

computing further:

The computed m/z average represents the m/z of the ions in the cluster, trough this, the charge, z, will be determined:

$$\begin{gathered} 0.25=\frac{\mathrm{m}}{\mathrm{z}} \\ 0.25=\frac{1\mathrm{Da}}{\mathrm{z}} \\ \mathrm{z}=\frac{1\mathrm{Da}}{0.25} \\ \mathrm{z}=4 \end{gathered}$$

The charge of ions in the clusture is 4

Protein molecular mass:

The molecular mass of protein from the tallest peak reading can be estimated:

$$\begin{gathered} \frac{\mathrm{m}}{\mathrm{z}}=1962.12 \\ \mathrm{m}=1962.12\left(\mathrm{z}\right) \\ =1962.12\left(4\right) \\ =7848.48\mathrm{Da} \end{gathered}$$

Hence, the charge is 4, and molecular mass: 7848.48Da