Problem 32 - Chemistry: The Central Science in SI Units, Global Edition

Question

One way in which Earth's evolution as a planet can be understood is by measuring the amounts of certain isotopes in rocks. One quantity recently measured is the ratio of \({ }^{129} \mathrm{Xe}\) to \({ }^{130}\) Xe in some minerals. In what way do these two isotopes differ from one another? In what respects are they the same?

Step-by-Step Solution

Answer

The isotopes \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) differ in the number of neutrons in their nuclei, having 75 and 76 neutrons, respectively. This results in slightly different atomic masses and physical properties. However, they share the same number of protons (54) and electrons (54), which makes them chemically indistinguishable, with identical chemical properties and electron configurations.

Step 1: 1. Define isotopes

Isotopes are different forms of a single chemical element, having the same number of protons but differing in the number of neutrons present in their atomic nucleus.

Step 2: 2. Identify the atomic structure of \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) isotopes

Xenon is element number 54 in the periodic table, which means that it has 54 protons in its nucleus. For \({ }^{129}\mathrm{Xe}\) isotope: - Number of protons (Z) = 54 - Mass number (A) = 129 - Number of neutrons (N) = A - Z = 129 - 54 = 75 For \({ }^{130}\mathrm{Xe}\) isotope: - Number of protons (Z) = 54 - Mass number (A) = 130 - Number of neutrons (N) = A - Z = 130 - 54 = 76

Step 3: 3. Describe the differences between \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) isotopes

The main difference between \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) is the difference in the number of neutrons present in their nuclei. \({ }^{129}\mathrm{Xe}\) has 75 neutrons, while \({ }^{130}\mathrm{Xe}\) has 76 neutrons. This difference in the number of neutrons results in slightly different atomic masses and physical properties.

Step 4: 4. Describe the similarities between \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) isotopes

The isotopes \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) have the same number of protons (54) and therefore the same chemical properties. Both isotopes belong to the same element, Xenon, and have the same electron configuration, as the number of electrons is also the same (54). This means that both isotopes exhibit similar chemical behavior and reactivity. In conclusion, \({ }^{129}\mathrm{Xe}\) and \({ }^{130}\mathrm{Xe}\) isotopes differ in the number of neutrons present in their nuclei, resulting in slightly different atomic masses and physical properties. However, they have the same number of protons and electrons, and therefore share the same chemical properties and electron configuration, which makes them chemically indistinguishable.

Key Concepts

Xenon

Xenon is a noble gas, represented by the symbol Xe, and is located in Group 18 of the periodic table. As a noble gas, it is characterized by its lack of reactivity under normal conditions. This makes xenon quite unique compared to many other elements that often readily participate in chemical reactions.

Xenon was discovered in 1898 by the Scottish chemist William Ramsay and the English chemist Morris Travers, who realized its presence in residues left over from evaporating components of liquid air.

Key features of xenon include:

• Atomic number: 54, indicating it has 54 protons.
• Stable and unreactive due to its complete outer electron shell.
• Colorless, dense, and odorless at room temperature.

Despite being inert, under extreme conditions such as in laboratories, xenon can form compounds with very active elements like fluorine and even oxygen. These discoveries of xenon's chemical activity have advanced the understanding of noble gases.

Atomic Structure

The atomic structure of an element defines how its atoms are organized and consists of three primary components: protons, neutrons, and electrons. Protons and neutrons form the nucleus, while electrons orbit this nucleus in various energy levels. The number of protons in the nucleus is called the atomic number, and it determines the element's identity on the periodic table.

For example, in xenon:

• The atomic number is 54, meaning there are 54 protons.
• The number of electrons is usually equal to the protons, maintaining a neutral charge.
• Neutrons vary among isotopes, allowing for diversity within the same element.

The concept of isotopes is significant here, as isotopes are variants of a particular chemical element that differ in neutron number. This results in different mass numbers but does not affect the chemical behavior due to the same number of protons and electrons.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom alongside protons. They have no electrical charge, which distinguishes them from positively charged protons and negatively charged electrons. Neutrons play a crucial role in the stability and mass of atoms.

Isotopes are particularly defined by the number of neutrons in their nuclei. For instance, the isotopes

• \( {}^{129} \text{Xe} \): Contains 75 neutrons.
• \( {}^{130} \text{Xe} \): Contains 76 neutrons.

The difference in neutron count among isotopes causes slight variations in their mass and physical properties. However, their chemical properties remain unchanged as they have the same number of protons and electrons. Understanding neutrons further aids in comprehending nuclear reactions, atomic mass calculations, and the binding energy of nuclei.