Question

(a) What isotope is used as the standard in establishing the atomic mass scale? (b) The atomic weight of boron is reported as \(10.81\), yet no atom of boron has the mass of \(10.81\) amu. Explain

Short answer

The standard isotope used for establishing the atomic mass scale is Carbon-12. The atomic weight of boron is 10.81 amu because it is the weighted average of the masses of its naturally occurring isotopes, Boron-10 and Boron-11, taking into account their relative abundances. The atomic weight does not correspond to the exact mass of any specific boron atom, but rather represents the average mass of a large number of boron atoms with varying isotopes.

Step-by-step solution

(Step 1: Identify the standard isotope for atomic mass scale)

The standard isotope used in establishing the atomic mass scale is Carbon-12. It is chosen because it is an abundant and stable isotope, and its mass is set to exactly 12 atomic mass units (amu). This standard is used to compare and measure the masses of all other atoms and isotopes.

(Step 2: Understand the concept of atomic weight)

Atomic weight, also known as relative atomic mass, is a weighted average of the masses of all the naturally occurring isotopes of an element relative to the mass of the standard isotope, Carbon-12. It takes into consideration the relative abundance and mass of each isotope.

(Step 3: Explain why the atomic weight of boron is 10.81)

Boron has two naturally occurring isotopes: Boron-10 and Boron-11. Their respective masses are approximately 10 amu and 11 amu. The atomic weight of boron is 10.81 because it is the weighted average of the masses of its isotopes. This value takes into account the relative abundances of Boron-10 and Boron-11 in nature. Since atomic weight is an average and takes into account the abundances of different isotopes, it does not correspond to the exact mass of any specific boron atom. Instead, it represents the average mass of a large number of boron atoms with varying isotopes. In summary, the isotope used as the standard in establishing the atomic mass scale is Carbon-12, and the reported atomic weight of boron at 10.81 amu is a weighted average of the masses of its naturally occurring isotopes, Boron-10 and Boron-11, based on their relative abundances.

Key concepts

Carbon-12 Isotope

Understanding the role of the Carbon-12 isotope is pivotal in the field of chemistry, particularly when discussing the atomic mass scale. Scientists needed a standard to measure atomic masses, and the Carbon-12 isotope fits the bill perfectly. This particular isotope, with six protons and six neutrons, has a mass that chemists have agreed to define as exactly 12 atomic mass units (amu).

The choice of Carbon-12 is not arbitrary; it is abundant in nature and presents a stable form of carbon, making the measurements consistent and reliable. Having this reference point allows chemists to establish a scale where all other atomic masses are compared to this standard. The atomic mass of an element is then expressed relative to this isotope, making it the linchpin holding the atomic mass scale in place.

Furthermore, because every isotope of every element can be measured against Carbon-12, it provides a universal scale for comparing these isotopes, crucial for chemical analysis and understanding the substance's molecular structure.

Atomic Weight

The term atomic weight, also known as relative atomic mass, might be a touch confusing because it does not refer to the actual weight of an atom but rather a comparative value. It is the weighted average of the mass numbers of all isotopes of an element as they occur naturally.

To compute this, scientists take into account the mass and relative abundance of each isotope in nature. In essence, the more abundant an isotope, the more influence it has on the atomic weight. This weighted average is then scaled to the mass of the Carbon-12 isotope. For many students, it's akin to how your overall grade in a class might be calculated, where some assignments (isotopes) count more towards the final grade (atomic weight) than others.

One must remember that atomic weight is not a rounded whole number because it is an average of different isotopes, so although no individual atom may have that exact mass, it represents a statistically correct average for the element.

Boron Isotopes

When it comes to Boron isotopes, there are two stable ones found naturally on Earth: Boron-10 and Boron-11. While the atomic weight of boron is listed as 10.81 amu, neither of these isotopes has that mass individually.

The isotope Boron-10 has an atomic mass close to 10 amu, and Boron-11 is around 11 amu. However, due to the natural abundance of each isotope, the collective average mass of boron in a sample of the element is somewhere in between, hence the 10.81 amu figure. It's similar to having a bag of apples each weighing either close to 1 pound or close to 2 pounds, with the majority being the 2-pound variety. If you were to average the weight of apples in the bag, the number would be closer to 2 than 1. Simplifying this, the atomic weight reflects the mass you would expect from a random boron atom picked from a natural source, considering the proportions of its isotopes.

This concept is fundamental to understanding why elements have atomic weights that are not whole numbers and why isotope abundance must be considered when discussing atomic masses.