Question

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.

Short answer

The atomic weight of rubidium is approximately 85.47 amu, calculated using the formula: Atomic weight = (Atomic mass of Rubidium-85 × Decimal abundance of Rubidium-85) + (Atomic mass of Rubidium-87 × Decimal abundance of Rubidium-87).

Step-by-step solution

Understand the Formula for Atomic Weight

To calculate the atomic weight of an element with multiple isotopes, use the following formula: Atomic weight = (Atomic mass of isotope 1 × Abundance of isotope 1) + (Atomic mass of isotope 2 × Abundance of isotope 2) + ... Notice that the abundances should be in decimal form for this calculation, so we'll have to convert the given percentage values into decimals.

Convert Percent Abundances to Decimal Abundances

To convert the given percent abundances into decimal abundances, simply divide the percentages by 100. Decimal abundance of Rubidium-85: \( \frac{72.15}{100} = 0.7215 \) Decimal abundance of Rubidium-87: \( \frac{27.85}{100} = 0.2785 \)

Calculate the Atomic Weight of Rubidium Using the Formula

Now that we have the decimal abundances, plug the given values into the formula for atomic weight: Atomic weight = (Atomic mass of Rubidium-85 × Decimal abundance of Rubidium-85) + (Atomic mass of Rubidium-87 × Decimal abundance of Rubidium-87) Atomic weight = (84.9118 amu × 0.7215) + (86.9092 amu × 0.2785)

Perform the Calculations

Calculate the individual parts of the formula and then sum them up to find the atomic weight of rubidium: Atomic weight = (84.9118 amu × 0.7215) + (86.9092 amu × 0.2785) = 61.26002 amu + 24.209714 amu Atomic weight = 85.469734 amu

Write Down the Answer

The atomic weight of rubidium is approximately 85.47 amu (rounded to two decimal places).

Key concepts

Exploring Isotopes

Atoms of the same element can differ in the number of neutrons they contain. These variations are known as isotopes. Isotopes of an element have the same number of protons but different numbers of neutrons. This variance causes them to have different atomic masses.
In the case of rubidium, we have two naturally occurring isotopes: rubidium-85 and rubidium-87. Both isotopes contribute to the overall properties of rubidium but do so with slightly different atomic masses due to their differing neutron counts. Understanding isotopes is key to appreciating elements' diversity and their effect on atomic weight calculations.

The Characteristics of Rubidium

Rubidium is a fascinating element. It's an alkali metal found in group 1 of the periodic table. This element is soft and silvery-white. Due to its properties, rubidium has intriguing applications in fields like electronics and atomic clocks.
Rubidium naturally occurs with two isotopes. Rubidium-85 is more abundant, comprising 72.15% of natural rubidium, while rubidium-87 accounts for the remaining 27.85%. These percentages reflect the natural occurrence of each isotope and are crucial in determining the weighted average atomic weight of rubidium.

Understanding Percentage Abundance Calculation

Calculating the percentage abundance of isotopes involves understanding how often each variant of an element is naturally occurring. When performing atomic weight calculations, the percentage abundance is converted to a decimal.
This conversion is done by dividing the percentage by 100. For rubidium, this means converting 72.15% for rubidium-85 into 0.7215 and 27.85% for rubidium-87 into 0.2785. This decimal form is then used in multiplication with the respective atomic masses to find the overall atomic weight.

Determining Atomic Mass

The atomic mass of an element is a measured quantity that indicates the mass of its atoms. It accounts for the masses of the protons, neutrons, and electrons, although the latter contribute the least. Understanding atomic mass helps in many calculations in chemistry. Each isotope of an element has a distinct atomic mass. For example, rubidium-85 has an atomic mass of 84.9118 amu, while rubidium-87 has an atomic mass of 86.9092 amu. Calculating the atomic weight using isotopes involves a weighted average, often termed atomic mass or atomic weight. By multiplying each isotope's atomic mass by its decimal abundance and summing the products, we obtain the overall atomic mass of the element, which is crucial for practical chemical applications.

The Importance of Chemistry Education

Chemistry education builds a foundation of understanding for the natural world and its building blocks—atoms and molecules. It involves learning about concepts such as isotopes, atomic weights, and periodic table trends. These fundamental principles are not just academic exercises. They play a critical role in numerous fields, including health, technology, and environmental science. By grasping the concepts behind ingredients like rubidium and calculations like atomic weight, students prepare themselves for advanced study and real-world applications. Educational exercises bolster problem-solving skills and logical thinking, which are useful beyond chemistry, in everyday decision-making and innovation.