Question

Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the atoms in the molecule. The mass spectrum of \(\mathrm{H}_{2}\) is taken under conditions that prevent decomposition into \(\mathrm{H}\) atoms. The two naturally occurring isotopes of hydrogen are \({ }^{1} \mathrm{H}\) (atomic mass \(=1.00783 \mathrm{amu}\) abundance \(99.9885 \%\) ) and \({ }^{2} \mathrm{H}\) (atomic mass \(=2.01410 \mathrm{amu}\) abundance \(0.0115 \%\) ). (a) How many peaks will the mass spectrum have? (b) Give the relative atomic masses of each of these peaks. (c) Which peak will be the largest, and which the smallest?

Short answer

(a) The mass spectrum of \(\mathrm{H}_{2}\) has three peaks. (b) The relative atomic masses are 2.01566 amu, 3.02193 amu, and 4.02820 amu. (c) The largest peak is \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}\) (99.977%) and the smallest peak is \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}\) (0.000132%).

Step-by-step solution

Identify the possible combinations of hydrogen isotopes forming H2

There are two naturally occurring isotopes of hydrogen: \({}^{1}\mathrm{H}\) and \({}^{2}\mathrm{H}\). Therefore, there are different combinations of these isotopes that can form \(\mathrm{H}_{2}\): 1. \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}\) 2. \({ }^{1} \mathrm{H} - { }^{2} \mathrm{H}\) 3. \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}\)

Calculate the relative atomic masses of each peak

We need to calculate the mass of each combination of isotopes to find the relative atomic mass for each peak: 1. \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}: 1.00783 \mathrm{amu} + 1.00783 \mathrm{amu} = 2.01566 \mathrm{amu}\) 2. \({ }^{1} \mathrm{H} - { }^{2} \mathrm{H}: 1.00783 \mathrm{amu} + 2.01410 \mathrm{amu} = 3.02193 \mathrm{amu}\) 3. \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}: 2.01410 \mathrm{amu}+2.01410\mathrm{amu}=4.02820\mathrm{amu}\)

Determine the number of peaks in the mass spectrum

Since there are three different combinations of hydrogen isotopes forming \(\mathrm{H}_{2}\), there will be three peaks in the mass spectrum.

Calculate the abundance of each peak

Now, we need to calculate the abundance of each combination (peak) by multiplying the abundances of the individual isotopes: 1. \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}: 99.9885\% \times 99.9885\% = 99.977\%\) 2. \({ }^{1} \mathrm{H} - { }^{2} \mathrm{H}: 99.9885\% \times 0.0115\% = 1.149\%\) 3. \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}: 0.0115\% \times 0.0115\% = 0.000132\%\)

Identify the largest and smallest peaks

Compare the abundances of each peak to determine the largest and smallest peaks: 1. \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}\): largest peak (99.977%) 3. \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}\): smallest peak (0.000132%) #Summary#: (a) The mass spectrum of \(\mathrm{H}_{2}\) will have three peaks. (b) The relative atomic masses of these peaks are 2.01566 amu, 3.02193 amu, and 4.02820 amu. (c) The largest peak is \({ }^{1} \mathrm{H} - { }^{1} \mathrm{H}\) and the smallest peak is \({ }^{2} \mathrm{H} - { }^{2} \mathrm{H}\).

Key concepts

Molecular Weight

Understanding molecular weight is fundamental in the study of mass spectrometry. The molecular weight, sometimes referred to as the molecular mass, of a molecule is the sum of the atomic weights of all the atoms in the molecule. It's important to note that molecular weight is typically reported in atomic mass units (amu), where one atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom.

For example, the molecular weight of a water molecule, which consists of two hydrogen atoms and one oxygen atom, is the sum of twice the atomic weight of hydrogen (approximately 1.00783 amu each) plus the atomic weight of oxygen (approximately 15.999 amu), resulting in about 18.015 amu. The precision in analyzing molecular weight is crucial for interpreting mass spectra accurately and understanding the composition of a molecule.

Atomic Weight

When we discuss atomic weight in relation to mass spectrometry, we are referring to the average weight of an element's atoms, taking into account the different isotopes and their abundance. This average is weighted by the abundance of each isotope in the natural world. The atomic weight is what you see listed on the periodic table for each element.

For instance, the atomic weight of carbon is approximately 12.011 amu, which accounts for the fact that carbon exists mainly as two isotopes: Carbon-12 (about 98.93% abundant) and Carbon-13 (about 1.07% abundant). In mass spectrometry, knowing the atomic weight of each element involved is essential for predicting and interpreting the mass spectrum of a molecule.

Isotopes

Isotopes are variants of the same chemical element that have the same number of protons but different numbers of neutrons, thus differing in mass. Each isotope of an element has its own unique mass, which is a key concept in mass spectrometry. Take hydrogen, for example, which has two isotopes relevant to mass spectrometry: protium (¹H) with no neutrons, and deuterium (²H) with one neutron.

The different masses of isotopes cause them to behave slightly differently under mass spectrometry, which allows us to distinguish between them based on their mass-to-charge ratio and consequently create a mass spectrum with distinct peaks representing each isotope or combinations thereof.

Abundance of Isotopes

The abundance of isotopes plays a critical role in determining the relative intensity of peaks in a mass spectrum. The term 'abundance' refers to how common an isotope is compared to other isotopes of the same element. Since the abundance of isotopes varies significantly, so can the intensity of each peak corresponding to each isotope in a mass spectrum.

For example, because ¹H is much more abundant than ²H, the mass spectrum of hydrogen will show a much larger peak for the former. This is why the abundance of each isotope must be taken into account when analyzing mass spectra. It's the relative abundance of the isotopes that allows us to quantify the presence of different isotopic species in a sample.

Mass Spectrum Peaks

In mass spectrometry, peaks on a mass spectrum represent the distinct masses of particles that have been ionized and detected. The location, or m/z (mass-to-charge ratio) value of a peak, indicates the mass of the ion, while the height or area of the peak is proportional to the abundance of that ion. Complex molecules can produce a variety of peaks due to the presence of different isotopes, as well as fragments of the molecule.

Understanding how to read these peaks is key to interpreting a mass spectrum. For example, in the mass spectrum of ¹H₂, the peaks correspond to the different isotopic combinations of hydrogen, resulting in three distinct peaks with varying heights based on the isotopes' natural abundance. The ability to decipher these peaks leads to an understanding of the molecular composition of the sample being analyzed.