Ch.2 - Atoms, Molecules, and Ions

Problem 36

Chapter 2, Problem 36

Rubidium has two naturally occurring isotopes, rubidium-85 (atomic mass = 84.9118 amu; abundance = 72.15%) and rubidium-87 (atomic mass = 86.9092 amu; abundance = 27.85%). Calculate the atomic weight of rubidium

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Identify the isotopes of rubidium and their respective atomic masses and abundances: Rubidium-85 with an atomic mass of 84.9118 amu and an abundance of 72.15%, and Rubidium-87 with an atomic mass of 86.9092 amu and an abundance of 27.85%.

Convert the percentage abundances into decimal form by dividing each by 100. For Rubidium-85, it becomes 0.7215, and for Rubidium-87, it becomes 0.2785.

Calculate the contribution of each isotope to the atomic weight by multiplying the atomic mass of each isotope by its decimal abundance. For Rubidium-85, multiply 84.9118 amu by 0.7215. For Rubidium-87, multiply 86.9092 amu by 0.2785.

Add the contributions from each isotope to find the atomic weight of rubidium. This is done by summing the results from the previous step.

The result from the addition gives the atomic weight of rubidium, which is the weighted average of the atomic masses of its isotopes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, rubidium has two isotopes: rubidium-85 and rubidium-87. Understanding isotopes is crucial for calculating the average atomic weight of an element based on the relative abundances of its isotopes.

Atomic Weight Calculation

The atomic weight of an element is calculated by taking the weighted average of the atomic masses of its isotopes, considering their relative abundances. This involves multiplying the atomic mass of each isotope by its percentage abundance (expressed as a fraction) and summing these values. This concept is essential for determining the overall atomic weight of rubidium in this question.

Percentage Abundance

Percentage abundance refers to the proportion of each isotope of an element present in a natural sample, expressed as a percentage. In the case of rubidium, the abundances of rubidium-85 and rubidium-87 are 72.15% and 27.85%, respectively. This information is vital for accurately calculating the atomic weight, as it directly influences the contribution of each isotope to the final average.

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Only two isotopes of copper occur naturally: ⁶³Cu (atomic mass = 62.9296 amu; abundance 69.17%) ⁶⁵Cu (atomic mass = 64.9278 amu; abundance 30.83%). Calculate the atomic weight (average atomic mass) of copper.

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Open Question

(b) What are the labels on the axes of a mass spectrum? (c) To measure the mass spectrum of an atom, the atom must first lose one or more electrons. Which ion would you expect to be deflected more by the same setting of the electric and magnetic fields, a Cl+ or a Cl2+ ion?

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