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 \(=1.00783 \mathrm{u}\); abundance \(\left.99.9885 \%\right)\) and \({ }^{2} \mathrm{H}\) (atomic mass \(=2.01410 \mathrm{u}\); abundance \(\left.0.0115 \%\right)\). (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

The mass spectrum of \(\mathrm{H}_{2}\) has three peaks corresponding to the following combinations of hydrogen isotopes: \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\) with a relative atomic mass of \(2.01566 \mathrm{u}\), \({ }^{1} \mathrm{H}-{ }^{2} \mathrm{H}\) with a relative atomic mass of \(3.02193 \mathrm{u}\), and \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\) with a relative atomic mass of \(4.02820 \mathrm{u}\). The largest peak corresponds to \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\) and the smallest peak corresponds to \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\).

Step-by-step solution

(a) Identifying peaks in the mass spectrum)

To identify the number of peaks in the mass spectrum, we need to consider all possible combinations of hydrogen isotopes that may form \(\mathrm{H}_{2}\) molecules. There are two hydrogen isotopes, so we could have three possible combinations: \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\), \({ }^{1} \mathrm{H}-{ }^{2} \mathrm{H}\), or \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\). These three combinations would give rise to three diferent mass peaks in the mass spectrum.

(b) Calculating the relative atomic masses for each peak)

For each peak, we can find the relative atomic mass by summing the atomic masses of the isotopes forming the \(\mathrm{H}_{2}\) molecule in each combination: 1. For \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\): \(1.00783 \mathrm{u} + 1.00783 \mathrm{u} = 2.01566 \mathrm{u}\) 2. For \({ }^{1} \mathrm{H}-{ }^{2} \mathrm{H}\): \(1.00783 \mathrm{u} + 2.01410 \mathrm{u} = 3.02193 \mathrm{u}\) 3. For \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\): \(2.01410 \mathrm{u} + 2.01410 \mathrm{u} = 4.02820 \mathrm{u}\)

(c) Identifying the largest and smallest peaks)

In order to find the largest and smallest peaks, we must consider the abundance of each isotope combination. The abundance for a specific combination of isotopes can be calculated by multiplying the individual isotope abundances: 1. For \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\): abundance = \(0.999885 \times 0.999885 = 0.999770\) 2. For \({ }^{1} \mathrm{H}-{ }^{2} \mathrm{H}\): abundance = \(0.999885 \times 0.000115 = 0.000115\) 3. For \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\): abundance = \(0.000115 \times 0.000115 = 0.000000013\) From these abundances, we can observe that the largest peak corresponds to \({ }^{1} \mathrm{H}-{ }^{1} \mathrm{H}\) (abundance = \(0.999770\)) with a relative atomic mass of \(2.01566 \mathrm{u}\), while the smallest peak corresponds to \({ }^{2} \mathrm{H}-{ }^{2} \mathrm{H}\) (abundance = \(0.000000013\)) with a relative atomic mass of \(4.02820 \mathrm{u}\).

Key concepts

Molecular Weight

Molecular weight is a crucial concept in chemistry, and it refers to the total weight of all the atoms in a molecule.
To calculate the molecular weight, you need to sum up the atomic weights of every atom present in a molecule.
For example, in the case of the hydrogen molecule often represented as two hydrogen atoms bonded together, we find its molecular weight by adding the atomic weights of the isotopes involved.
This is especially important because different isotopes of hydrogen have slightly varying atomic masses.
Molecular weight comes into play in mass spectrometry; a process frequently used to analyze molecules rather than individual atoms.
Understanding molecular weight helps us determine the different peaks formed on a mass spectrum when studying molecules.
Thus, the idea of molecular weight gives insight into the composition and properties of molecules, paving the way for deeper analysis through techniques such as mass spectrometry.

Isotopes

Isotopes are variations of a particular chemical element that have the same number of protons but different numbers of neutrons.
This difference in neutron count results in different atomic masses for the isotopes of the same element.
Hydrogen, for instance, has two naturally occurring isotopes:

• each with specific atomic masses and abundances.
  The most common of these isotopes is protium ( ^{ } ^{1} H), which has one proton and no neutrons, giving it an atomic mass of about 1.00783 u.
• Deuterium ( ^{ } ^{2} H), on the other hand, has an additional neutron, resulting in a higher atomic mass of about 2.01410 u.

In mass spectrometry, understanding isotopes is crucial since their unique atomic masses will exhibit distinct peaks in the spectrum.
By analyzing the isotopic composition, chemists can investigate the structure and behavior of molecules at a fundamental level.

Atomic Mass

Atomic mass is a fundamental property of an isotope, which is defined as the mass of an individual atom of a particular isotope.
It is usually expressed in atomic mass units (u), where one u is equivalent to one-twelfth of the mass of a carbon-12 atom.
To determine the atomic mass of an isotope, scientists consider the number of protons and neutrons present in the nucleus.
In the context of hydrogen, the atomic masses of its isotopes are pivotal for creating accurate predictions and measurements.

• Protium ( ^{ } ^{1} H) with one proton has an atomic mass of 1.00783 u.
• Deuterium ( ^{ } ^{2} H) with one proton and one neutron totals an atomic mass of 2.01410 u.

These atomic masses directly impact the process and outcome in mass spectrometry by determining the distinct peaks that arise from different molecular combinations.
Understanding atomic mass not only allows scientists to characterize molecules but also aids in deciphering the intricate details of atomic and subatomic structures.

Abundance

Abundance in chemistry refers to the relative amount of each isotope of an element found in a natural sample.
It is typically expressed as a percentage that indicates how common each isotope is.
For instance, when we look at hydrogen, the abundance figures tell us how often we find each of its isotopes:

• Protium ( ^{ } ^{1} H) is extremely abundant, making up about 99.9885% of natural hydrogen.
• Deuterium ( ^{ } ^{2} H) is far less common, representing roughly 0.0115%.

In mass spectrometry, abundance helps predict the size of the peaks corresponding to different isotopic combinations in a molecule.
The greater the abundance of an isotope, the more intense its peak will be in the mass spectrum.
Understanding abundance not only aids in interpreting mass spectrometry data but also provides insight into the natural distribution of elements on Earth, key for fields ranging from geochemistry to cosmochemistry.