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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Textbook Question

The atomic weight of boron is reported as 10.81, yet no atom of boron has the mass of 10.81 amu. Which is the best explanation?

a. The measurement of atomic mass is only reliable to two significant figures.

b. The atomic weight is an average of many individual atoms.

c. The atomic weight is an average of many isotopes of the same nuclear composition.

Textbook Question

(b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

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Textbook Question

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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Textbook Question

(a) Thomson's cathode-ray tube (Figure 2.4) and the mass spectrometer (Figure 2.11) both involve the use of electric or magnetic fields to deflect charged particles. What are the charged particles involved in each of these experiments?

Consider the mass spectrometer shown in Figure 2.11. Determine whether each of the following statements is true or false. If false, correct the statement to make it true: (a) The paths of neutral (uncharged) atoms are not affected by the magnet.

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Textbook Question

Consider the mass spectrometer shown in Figure 2.11. Determine whether each of the following statements is true or false. If false, correct the statement to make it true: (b) The height of each peak in the mass spectrum is inversely proportional to the mass of that isotope.

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