Problem 135 - Chemistry The Molecular Science

Question

The diatomic compound \(\mathrm{BrCl}\) is a reddish-brown gas. Consider the naturally occurring isotopes of each element: $$ \begin{array}{lc} \hline \text { Isotope } & \text { Natural Abundance, \% } \\ \hline \text { Br-79 } & 50.69 \\ \text { Br-81 } & 49.31 \\ \text { Cl-35 } & 75.77 \\ \text { Cl-37 } & 24.23 \\ \hline \end{array} $$ (a) Name the compound. (b) Determine how many different types of \(\mathrm{BrCl}\) molecules are possible by using the sum of mass numbers as the criterion for type. (c) Determine which is the most abundant type in (b). (d) Determine which is the second most abundant type.

Step-by-Step Solution

Answer

(a) Bromine Chloride (b) 3 unique types (c) The most abundant type is a sum of mass number 116. (d) The second most abundant type is a sum of mass number 114.

Step 1: Name the Compound

The compound is a diatomic molecule made of bromine and chlorine. The proper nomenclature for such a compound is bromine chloride. Therefore, the name of the compound is Bromine Chloride.

Step 2: Determine Possible Types of Molecules

To find the different types of \(\mathrm{BrCl}\) molecules, consider the possible combinations of isotopes. Bromine has isotopes \(\text{Br-79}\) and \(\text{Br-81}\), while chlorine has isotopes \(\text{Cl-35}\) and \(\text{Cl-37}\). This results in the following combinations: \(\text{Br-79Cl-35}\), \(\text{Br-79Cl-37}\), \(\text{Br-81Cl-35}\), and \(\text{Br-81Cl-37}\). Each combination has a unique sum of mass numbers.

Step 3: Calculate Sum of Mass Numbers

Compute the sum of mass numbers for each molecule: - \(\text{Br-79Cl-35}\) has a sum of \(79 + 35 = 114\).- \(\text{Br-79Cl-37}\) has a sum of \(79 + 37 = 116\).- \(\text{Br-81Cl-35}\) has a sum of \(81 + 35 = 116\).- \(\text{Br-81Cl-37}\) has a sum of \(81 + 37 = 118\).There are three unique mass numbers: 114, 116, and 118.

Step 4: Determine Abundances

Calculate the abundance of each type of molecule. - \(\text{Br-79Cl-35}\): \(0.5069 \times 0.7577 = 0.384\) - \(\text{Br-79Cl-37}\): \(0.5069 \times 0.2423 = 0.1227\) - \(\text{Br-81Cl-35}\): \(0.4931 \times 0.7577 = 0.3736\) - \(\text{Br-81Cl-37}\): \(0.4931 \times 0.2423 = 0.1194\) Combine abundances for the same sum of mass numbers:- Mass number 114 (Br-79Cl-35): 38.4%- Mass number 116 (Br-79Cl-37 and Br-81Cl-35): Combined 49.6%- Mass number 118 (Br-81Cl-37): 11.94%

Step 5: Identify Most and Second Most Abundant Types

From the calculated abundances, the most abundant type is the one with mass number 116, having an abundance of 49.6%. The second most abundant is the type with mass number 114, having an abundance of 38.4%.

Key Concepts

Isotopic Composition

Isotopic composition refers to the natural occurrence of isotopes of an element. Isotopes are atoms of the same element, which have the same number of protons but different numbers of neutrons, giving them different mass numbers. In the case of bromine (\( \text{Br} \)) and chlorine (\( \text{Cl} \)), they each have two naturally occurring isotopes.

• Bromine: \( \text{Br-79} \) (with 50.69% abundance) and \( \text{Br-81} \) (with 49.31% abundance).
• Chlorine: \( \text{Cl-35} \) (with 75.77% abundance) and \( \text{Cl-37} \) (with 24.23% abundance).

These isotopic proportions affect the types of molecules that can be formed, influencing the physical and chemical properties of the compound. Understanding isotopic composition is crucial in fields such as chemistry, physics, and environmental science.

Mass Number

The mass number of an isotope is the sum of protons and neutrons in its nucleus, and it is an important property that distinguishes different isotopes. In the \( \text{BrCl} \) compound, there are specific mass numbers for the isotopes:

• For bromine isotopes: \( \text{Br-79} \) and \( \text{Br-81} \) with mass numbers 79 and 81 respectively.
• For chlorine isotopes: \( \text{Cl-35} \) and \( \text{Cl-37} \) with mass numbers 35 and 37 respectively.

Mass number is used as a criterion to classify different \( \text{BrCl} \) molecules. When combining different isotopes of bromine and chlorine, the sum of their mass numbers results in various unique values like 114, 116, and 118. These combinations are helpful for calculating molecular abundances and determining molecular mass in experimental settings.

Abundance Calculation

Abundance calculation involves determining the relative proportion of each type of molecule resulting from different isotopic combinations. It gives insight into which molecular forms are most common or rare:- For \( \text{BrCl} \)al molecules, use the product of the natural abundances of each isotope.- For example, the combination \( \text{Br-79Cl-35} \)is calculated as: \( 0.5069 \times 0.7577 = 0.384 \)or 38.4%.- Similar calculations yield: \( \text{Br-79Cl-37} \) at 12.27%, \( \text{Br-81Cl-35} \) at 37.36%, \( \text{Br-81Cl-37} \) at 11.94%.By summing up the contributions of Br-79Cl-37 and Br-81Cl-35 (both with a mass number 116), it results in a mass abundance of 49.6%. This process allows us to identify which isotopic molecule is the most abundant and to understand the distribution pattern of \( \text{BrCl} \)molecules in nature.

Diatomic Molecules

Diatomic molecules consist of two atoms, which may be the same or different elements. In this case, \( \text{BrCl} \) is a diatomic molecule formed by bromine and chlorine. The concept of diatomic molecules is crucial in chemistry because they represent the simplest form of a molecule.- Diatomic molecules can be homonuclear, like \( \text{O}_2 \)or heteronuclear, like \( \text{BrCl} \).- They are formed through covalent bonding where electrons are shared between the two atoms.Understanding diatomic molecules helps in the study of molecular bonding and chemical reactions, especially in how molecules absorb and interact with light or other energy forms in processes like spectroscopy.
The ability to predict the different types of \( \text{BrCl} \)diatomic molecules based on isotopic composition gives insights into their physical properties and reactivity.