Problem 34 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) What is the mass in \(\mathrm{u}\) of a carbon- 12 atom? (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?

Step-by-Step Solution

Answer

(a) The mass of a Carbon-12 atom is 12 atomic mass units (u). (b) The atomic weight of Carbon is reported as 12.011 in the periodic table because it represents the weighted average of the masses and relative abundances of naturally occurring isotopes, Carbon-12 and Carbon-13. The atomic weight is calculated as: \[Atomic \ Weight \ of \ Carbon = (12 \times 0.9889) + (13 \times 0.0111) \approx 12.011\]

Step 1: Define Atomic Mass Unit (u)

Atomic mass unit (u) is a unit of mass used to express the masses of atoms and molecules. It is defined as exactly 1/12th the mass of one atom of Carbon-12. An atomic mass unit (u) is equal to \(1.66 \times 10^{-27}\) kg.

Step 2: Calculate the mass of Carbon-12 atom

Since the atomic mass unit is defined in relation to the mass of one Carbon-12 atom, we simply need to remember that one atom of Carbon-12 weighs exactly 12 atomic mass units (u). So, the mass of a Carbon-12 atom is 12 u.

Step 3: Explain the difference in atomic weight

The atomic weight (or average atomic mass) of an element reported in the periodic table is not the same as the mass of a specific isotope because it takes into account the abundance of all naturally occurring isotopes of that element. In the case of Carbon, there are two naturally occurring isotopes - Carbon-12 (which accounts for roughly 98.89% of Carbon on Earth) and Carbon-13 (which accounts for the remaining 1.11%). The atomic weight depends on both the mass and relative abundance of each isotope in nature.

Step 4: Calculate the weighted average of Carbon isotopes

To find the atomic weight of Carbon, we need to calculate the weighted average based on the masses and relative abundances of the isotopes. The equation for this calculation is: \[Atomic \ Weight \ of \ Carbon = (mass \ of \ C-12 \times abundance \ of \ C-12) + (mass \ of \ C-13 \times abundance \ of \ C-13)\] We know that Carbon-12 has a mass of 12 u and an abundance of 98.89%, and Carbon-13 has a mass of approximately 13 u and an abundance of 1.11%. Putting these values into the equation, we find the atomic weight of Carbon: \[Atomic \ Weight \ of \ Carbon = (12 \times 0.9889) + (13 \times 0.0111) \approx 12.011\] The atomic weight of Carbon is reported as 12.011 in the periodic table because it represents this weighted average.

Key Concepts

Atomic Weight

Atomic weight, often referred to as the average atomic mass, plays a crucial role in understanding why atomic masses on the periodic table do not match exactly with whole numbers for certain elements. Unlike the specific mass of a single isotope, the atomic weight considers:

• The relative abundance of each isotope in nature
• The individual mass of each isotope

This weighted average reflects the fact that most elements exist as a mixture of isotopes. To calculate it, you multiply the mass of each isotope by its relative abundance (expressed as a decimal), then sum these values. For example, since carbon mainly consists of Carbon-12 and Carbon-13, the atomic weight of carbon is calculated as follows:

\[Atomic \ Weight = (12 \times 0.9889) + (13 \times 0.0111) \approx 12.011\]

This value is what you see listed as the atomic weight in the periodic table, which gives a more practical representation of how the element behaves in the natural world.

Isotopes

Isotopes are fascinating variants of elements that have the same number of protons but differing numbers of neutrons. This means that while they belong to the same element, they have different atomic masses. Isotopes are identifiable by their mass number, which is a sum of protons and neutrons in the nucleus.

For instance, carbon has three naturally occurring isotopes:

• Carbon-12, with 6 protons and 6 neutrons
• Carbon-13, with 6 protons and 7 neutrons
• Carbon-14, which is radioactive and occurs in trace amounts

These isotopes contribute to the average atomic mass because each has a different mass and occurs in varied abundances. This unique property enables isotopes to be used in a range of scientific applications, such as dating archaeological finds with Carbon-14 or medical diagnostics using different isotopic labels.

Periodic Table

The periodic table serves as a comprehensive guide for understanding and predicting the characteristics of elements. It systematically arranges elements based on increasing atomic number, which is the number of protons in an atom's nucleus. Each element's placement hints at certain properties that group similar elements together.

Some key features of the periodic table include:

• Groups or families that hold elements with similar chemical properties due to having the same number of valence electrons
• Periods, or rows, that represent increasing atomic numbers from left to right
• Each element's box displaying its symbol, atomic number, and often its atomic weight

When looking at carbon on the periodic table, its atomic weight of 12.011 reflects the weighted average of its naturally occurring isotopes. This table is a powerful tool for chemists and scientists, providing essential information for research and application in various fields.