Question

Rubidium has two naturally occurring isotopes: \(\mathrm{Rb}-85\) with mass \(84.9118\) amu and a natural abundance of \(72.17 \%\), and \(\mathrm{Rb}-87\) with mass \(86.9092\) amu and a natural abundance of \(27.83 \%\). Calculate the atomic mass of rubidium.

Short answer

The atomic mass of rubidium is approximately 85.47 amu.

Step-by-step solution

Identify the masses and relative abundances

The first step is to note down the given information for each isotope of rubidium. For Rb-85: Mass = 84.9118 amu, Abundance = 72.17%. For Rb-87: Mass = 86.9092 amu, Abundance = 27.83%.

Convert the percentage abundances to decimal form

To use these percentages in calculations, convert them to decimal form by dividing each by 100. For Rb-85: Decimal Abundance = 72.17 / 100 = 0.7217. For Rb-87: Decimal Abundance = 27.83 / 100 = 0.2783.

Calculate the contribution of each isotope to the atomic mass

Multiply the mass of each isotope by its decimal abundance to find the contribution of each isotope to the overall atomic mass. For Rb-85: Contribution = 84.9118 amu * 0.7217. For Rb-87: Contribution = 86.9092 amu * 0.2783.

Calculate the atomic mass of rubidium

The atomic mass of rubidium is the sum of the contributions from both isotopes. Atomic Mass = (Rb-85 Contribution) + (Rb-87 Contribution) = (84.9118 amu * 0.7217) + (86.9092 amu * 0.2783).

Perform the calculations and obtain the result

Perform the multiplications and then add the results together to find the atomic mass of rubidium. Atomic Mass = (84.9118 amu * 0.7217) + (86.9092 amu * 0.2783) = 61.26474126 amu + 24.20622966 amu = 85.47097092 amu.

Key concepts

Isotope Abundance

Understanding the concept of isotope abundance is crucial in the field of chemistry, especially when determining atomic mass. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. Isotope abundance refers to the percentage of each isotope of an element that occurs naturally.

For example, if we consider the element Rubidium (Rb), which has isotopes Rb-85 and Rb-87, we have to look at how much of Rubidium is made up of each isotope in nature. Typically, this is expressed in percentage but for calculations, it's converted to a decimal form. The abundance tells us how much each isotope contributes to the overall atomic mass of the element. It is essential to accurately measure and comprehend these abundances to calculate the atomic mass of an element, which is an average mass reflecting the mixture of its isotopes.

Average Atomic Mass

The average atomic mass is a weighted average that reflects the masses of all the isotopes of an element, taking into account their relative abundances. It's similar to calculating the average grade in a class where different assignments have different weights.

In the case of Rubidium, we calculate the average atomic mass by multiplying the atomic mass of each isotope by its abundance (after converting percentages to decimals), then adding these values together. The result is a single number that represents the atomic mass on the periodic table. This value is particularly important as it is used to determine the amount of an element that reacts or combines in a chemical reaction. To put it simply, when chemists work in a lab, they're using this average atomic mass to measure out the element for their experiments, even though they're actually working with a blend of different isotopes.

Chemistry Education

Chemistry education aims to establish a strong foundation in chemical concepts, making them accessible and understandable for students of all levels. Atomic mass calculation exercises such as the one with Rubidium isotopes are typical in chemistry curriculum as they enhance problem-solving skills and provide insight into the atomic structure.

When teaching these concepts, it is important to break them down into manageable steps and relate them to real-world applications. For instance, in the exercise, understanding how to calculate the atomic mass has direct implications for tasks such as finding the reactants in a chemical reaction or determining the dosage of a radioactive medicine. Effective chemistry education promotes curiosity and equips students with the tools needed to explore the world of atoms and molecules, preparing them for advanced studies or careers in science and technology.