Question

Hydrogen and chlorine atoms react to form simple diatomic molecules in a 1: 1 ratio, that is, \(\mathrm{HCl}\). The natural abundances of the chlorine isotopes are \(75.77 \%^{35} \mathrm{Cl}\) and \(24.23 \%^{37} \mathrm{Cl} .\) The natural abundances of \(^{2} \mathrm{H}\) and \(^{3} \mathrm{H}\) are \(0.015 \%\) and less than \(0.001 \%,\) respectively. (a) How many different HCl molecules are possible, and what are their mass numbers (that is, the sum of the mass numbers of the H and Cl atoms)? (b) Which is the most abundant of the possible HCl molecules? Which is the second most abundant?

Short answer

The six different HCl molecules are \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 36, \(^1\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 38, \(^2\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 37, \(^2\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 39, \(^3\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 38 and \(^3\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 40. The most abundant molecule is \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) and the second most abundant molecule is \(^1\mathrm{H}\,^{37}\mathrm{Cl}\).

Step-by-step solution

Determining Possible Molecules and their Mass Numbers

First, identify the distinct isotopes for both Hydrogen and Chlorine. Hydrogen has two, namely \(^{1}\mathrm{H}\), \(^{2}\mathrm{H}\) and \(^{3}\mathrm{H}\), and Chlorine has two as well, namely \(^{35}\mathrm{Cl}\) and \(^{37}\mathrm{Cl}\). By pairing each Hydrogen isotope with each Chlorine isotope, you will be able to determine the number of different HCl molecules. Using the isotopic mass, sum the mass numbers of the Hydrogen and Chlorine atoms to get the mass number for each molecule.

Number of Different Molecules and their Mass Numbers

There are six different molecules possible: \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 36, \(^1\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 38, \(^2\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 37, \(^2\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 39, \(^3\mathrm{H}\,^{35}\mathrm{Cl}\) with mass 38 and \(^3\mathrm{H}\,^{37}\mathrm{Cl}\) with mass 40.

Determining the Most and Second Most Abundant Molecules

Use the natural abundances to determine the most common molecules. Multiply the abundance of each Hydrogen isotope by the abundance of each Chlorine isotope for each possible pair. The molecule whose isotopes have the highest product of abundances is the most abundant, and the molecule with the second highest product is the second most abundant.

The Most and Second Most Abundant Molecules

The most abundant HCl molecule is \(^1\mathrm{H}\,^{35}\mathrm{Cl}\) as both the isotopes \(^1\mathrm{H}\) and \(^{35}\mathrm{Cl}\) are the most abundant isotopes of their respective elements. The second most abundant HCl molecule is \(^1\mathrm{H}\,^{37}\mathrm{Cl}\), since \(^1\mathrm{H}\) is the most common isotope of hydrogen and \(^{37}\mathrm{Cl}\) is the second most common isotope of chlorine.

Key concepts

Understanding Hydrogen Isotopes

Isotopes are varieties of the same chemical element that have the same number of protons but different numbers of neutrons, leading to different mass numbers. Hydrogen is a unique element with three isotopes that are structurally simple. It includes

• Protium ( ^{1}H), which has one proton and zero neutrons.
• Deuterium ( ^{2}H), with one proton and one neutron.
• Tritium ( ^{3}H), possessing one proton and two neutrons.

The abundances of these isotopes vary greatly in nature. Protium is by far the most common, making up approximately 99.98% of naturally occurring hydrogen. Deuterium is present in a much smaller amount, about 0.02%. Tritium is extremely rare, with its abundance being less than 0.001%. Due to these differences, the presence of each isotope significantly affects the properties and behavior of hydrogen compounds, including their mass and stability. Understanding isotopic abundance is crucial in determining the molecular mass and the type of hydrogen compound formed.

Chlorine Isotopes and Their Abundance

Chlorine, an essential element found in various chemical compounds, also has isotopes that influence the molecular mass of chlorine compounds. These isotopes are:

• Chlorine-35 ( ^{35}Cl), which consists of 17 protons and 18 neutrons.
• Chlorine-37 ( ^{37}Cl), containing 17 protons and 20 neutrons.

Just like hydrogen, the isotope abundance of chlorine influences the formation and characteristics of its compounds. In natural chlorine, approximately 75.77% is ^{35}Cl, while about 24.23% is ^{37}Cl. This variation in abundance results in the formation of different isotopic combinations in compounds like hydrochloric acid (HCl). Knowing these abundances helps us predict which isotopic form of a chlorine compound is more prominent, allowing for a better understanding of the molecular mass and distribution of chlorine isotopic compounds in nature.

Molecular Mass Determination for HCl

When determining the molecular mass of a compound like hydrochloric acid ( HCl), it's essential to consider the isotopic compositions of the elements involved. This process involves calculating the mass numbers by adding the mass number of each hydrogen isotope with the one of each chlorine isotope they combine with. The possible HCl combinations result from these pairings:

• ^{1}H with ^{35}Cl results in a mass of 36.
• ^{1}H with ^{37}Cl gives a mass of 38.
• ^{2}H with ^{35}Cl results in a mass of 37.
• ^{2}H with ^{37}Cl gives a mass of 39.
• ^{3}H with ^{35}Cl results in a mass of 38.
• ^{3}H with ^{37}Cl gives a mass of 40.

Each of these combinations has a probability of occurrence based on the natural isotopic abundance of hydrogen and chlorine. The most abundant HCl molecule is the one made of the most prevalent isotopes: ^{1}H and ^{35}Cl. This pairing forms the molecule ^{1}H^{35}Cl, which is also the most commonly found in nature due to the high percent abundance of these isotopes. The second most abundant molecule involves ^{1}H with ^{37}Cl. Understanding this isotopic makeup allows us to accurately determine and predict the physical properties of HCl and its behavior in various chemical reactions.