Problem 20 - Chemistry and Chemical Reactivity

Question

Strontium has four stable isotopes. Strontium-84 has a very low natural abundance, but \(^{86} \mathrm{Sr},^{87} \mathrm{Sr}_{t}\) and \(^{88}\) Sr are all reasonably abundant. Knowing that the atomic weight of strontium is \(87.62,\) which of the more abundant isotopes predominates?

Step-by-Step Solution

Answer

Strontium-88 is the predominant isotope.

Step 1: Understanding Isotopes

Isotopes are variants of a particular chemical element that have different numbers of neutrons, and therefore, different mass numbers. The question involves isotopes of strontium: - Strontium-84 - Strontium-86 - Strontium-87 - Strontium-88 We need to identify which of the plentiful isotopes ( 86 Sr, 87 Sr, 88 Sr) has the highest contribution to the atomic weight of strontium.

Step 2: Atomic Weight Calculation

The atomic weight of an element is calculated as the weighted average of the atomic masses of its isotopes, based on their abundances. Given the atomic weight of strontium is 87.62, this value is closest to the mass number of Strontium-88. We aim to compare this atomic weight to the exact mass numbers of each isotope to determine the predominant isotope.

Step 3: Comparison of Mass Numbers

Let's compare the given atomic weight 87.62 with the mass numbers of the abundant isotopes: - Strontium-86: 86 - Strontium-87: 87 - Strontium-88: 88 The atomic weight of 87.62 is closest to the mass number 88, which suggests that the isotope with a mass number of 88 contributes the most to the atomic weight.

Step 4: Conclusion

Since the atomic weight of strontium (87.62) is closest to the mass number of Strontium-88, this isotope is the predominant form among those with a reasonable natural abundance.

Key Concepts

Atomic Weight Calculation

Atomic weight calculation is a key concept in understanding an element's isotopes and their relative abundances. The atomic weight of an element is not a whole number because it represents a weighted average of all naturally occurring isotopes. Each isotope contributes to the atomic weight in relation to its natural abundance.

To figure out an element's atomic weight, scientists take into account each isotope's mass and its percentage abundance. They then multiply each isotope's mass by its fractional abundance and add these products together. This can be expressed with the formula:

\[\text{Atomic Weight} = (\text{mass of Isotope 1} \times \text{abundance of Isotope 1}) + ... + (\text{mass of Isotope n} \times \text{abundance of Isotope n})\]

In our example of strontium, the calculated atomic weight is 87.62, indicating that certain isotopes contribute more substantially due to their closer mass numbers to this weighted average.

Mass Number

The mass number of an isotope is the total number of protons and neutrons in its nucleus. It is a critical identifier for isotopes and plays a decisive role in atomic weight calculation. While the atomic number of an element remains constant, equal to the number of protons, the mass number can vary due to different numbers of neutrons.

In the case of strontium, the identification includes a range of isotopes: Strontium-84, Strontium-86, Strontium-87, and Strontium-88. These numbers depict each isotope's mass number, revealing how many protons and neutrons are present. The mass number is crucial as it helps to calculate the atomic weight and to determine which isotopes have a greater presence in nature.

Understanding mass numbers allows us to correlate the isotopes with the element's calculated atomic weight, as seen with strontium's predominant form being indicated by its mass number that is closest to strontium's atomic weight of 87.62.

Strontium

Strontium is an alkaline earth metal represented in the periodic table with the symbol "Sr" and an atomic number of 38. It is known for its similarities with calcium and commonly appears in a variety of minerals.

Strontium's isotopes play an essential role in various scientific fields, including radiometric dating and climate science. The naturally occurring isotopes in significant amounts include Strontium-84, Strontium-86, Strontium-87, and Strontium-88. Each of these isotopes has distinct applications and contributes differently to the atomic weight, as demonstrated by the previous exercise.

The atomic weight of strontium, at 87.62, suggests that Strontium-88, with a mass number of 88, predominates among the other isotopes. This is important in chemistry and physics, as the predominance provides insights into the element's chemical behavior and role in natural processes.