Question

Bromine has two naturally occurring isotopes, bromine- 79 (atomic mass \(=78.9183 \mathrm{u} ; \quad\) abundance \(=50.69 \%)\) a \(\mathrm{nd}\) bromine-81 \(\quad\) (atomic mass \(=80.9163 \mathrm{u} ;\) abundance \(=\) \(49.31 \%) .\) Calculate the atomic weight of bromine.

Short answer

The atomic weight of bromine can be calculated using the weighted average of its naturally occurring isotopes, bromine-79 and bromine-81. By multiplying the atomic masses of each isotope by their respective abundances in decimal form and then adding these contributions, we find that the atomic weight of bromine is approximately 79.8910 u.

Step-by-step solution

Determine the atomic mass of each isotope with its abundance.

First, we need to find the product of the atomic mass for bromine-79 and bromine-81 by their respective abundances provided in percentage. For bromine-79: Atomic mass = 78.9183 u Abundance = 50.69 % For bromine-81: Atomic mass = 80.9163 u Abundance = 49.31 %

Convert percentage abundance into decimal form.

To simplify calculations, we need to convert percentage abundance into decimal form. To do this, divide the percentage abundance by 100. For bromine-79: Abundance = 50.69 % / 100 = 0.5069 For bromine-81: Abundance = 49.31 % / 100 = 0.4931

Compute the contribution of each isotope's atomic mass to the atomic weight of bromine.

Multiply the atomic mass of each isotope by their corresponding abundance in decimal form. For bromine-79: Contribution = 78.9183 u * 0.5069 = 39.9943 u For bromine-81: Contribution = 80.9163 u * 0.4931 = 39.8967 u

Calculate the atomic weight of bromine.

Add the contributions of both isotopes to get the atomic weight of bromine. Atomic weight = Contribution of bromine-79 + Contribution of bromine-81 Atomic weight = 39.9943 u + 39.8967 u Atomic weight = 79.8910 u The atomic weight of bromine is approximately 79.8910 u.

Key concepts

Understanding Isotopes

Isotopes are variants of a particular chemical element that have different numbers of neutrons while maintaining the same number of protons. Because of the constant proton number, isotopes of an element have identical atomic numbers but different mass numbers. This distinction in neutron count is what leads to the variation in atomic mass. Isotopes exhibit nearly identical chemical behavior but can differ in physical properties, like atomic mass. Each isotope of an element has its own relative abundance, indicating how much of that isotope is found compared to other isotopes of the same element. For example, bromine has two stable isotopes: bromine-79 and bromine-81. These isotopes have atomic masses of 78.9183 u and 80.9163 u, respectively.

The Role of Atomic Mass in Isotopes

Atomic mass, often expressed in atomic mass units (u), is the total mass of the protons and neutrons in an atom's nucleus. Since protons and neutrons have nearly equal masses, the atomic mass is approximately equal to the mass number of the isotope. For isotopes, each variant has a unique atomic mass because the number of neutrons varies while the number of protons remains constant. Understanding atomic mass is vital when calculating the atomic weight of an element with multiple isotopes. In the case of bromine, the atomic masses are specific to its isotopes—bromine-79 has an atomic mass of 78.9183 u, and bromine-81 is 80.9163 u. These values are crucial in determining the element's overall atomic weight.

Abundance and Its Impact on Atomic Weight

Abundance refers to how common or rare an isotope is in comparison to other isotopes of the same element. The abundance of an isotope directly affects the average atomic weight calculated for a natural element. To calculate an element's atomic weight, you must consider the atomic masses and the relative abundances of its isotopes. The process involves multiplying each isotope's atomic mass by its abundance in decimal form and adding them together. For bromine, the abundances are 50.69% for bromine-79 and 49.31% for bromine-81. By converting these percentages into decimals and using them in calculations, we weight the isotopic masses to find bromine's atomic weight. Thus, the atomic weight balances the contributions of each isotope reflecting their natural occurrence.