Problem 34 - Chemistry The Central Science

Question

(a) What is the mass in amu 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 amu because the atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. (b) The atomic weight of carbon is reported as 12.011 because it is a weighted average of the masses of its naturally occurring isotopes (carbon-12 and carbon-13), taking into account their natural abundance in the environment.

Step 1: Define atomic mass unit and carbon-12 atom

An atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. The carbon-12 atom is an isotope of carbon, which has 6 protons, 6 electrons, and 6 neutrons. The existence of isotopes means that elements can have the same number of protons (defining their atomic number) but with different numbers of neutrons, giving them slightly different atomic masses.

Step 2: Find the mass of a carbon-12 atom in amu

Since an atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom, the mass of a carbon-12 atom is exactly 12 amu by definition. Answer to (a): The mass of a carbon-12 atom is 12 amu.

Step 3: Discuss isotopes and atomic weight calculation

The atomic weight of an element is the weighted average of the masses of all the naturally occurring isotopes of the element. This means that all the isotopes of that element have a specific contribution to the atomic weight considering their abundance in nature. Carbon has two isotopes: carbon-12 (with 6 neutrons) and carbon-13 (with 7 neutrons).

Step 4: Explain the reason for atomic weight deviation

The atomic weight of carbon is reported as 12.011 rather than an exact 12 due to the presence of the carbon-13 isotope. The atomic weight is slightly higher than 12 because carbon-13 is heavier than carbon-12 (having an additional neutron) and carbon-13 has a natural abundance in the environment. Answer to (b): The atomic weight of carbon is reported as 12.011 because it is a weighted average of the masses of its naturally occurring isotopes (carbon-12 and carbon-13) and takes into account their natural abundance in the environment.

Key Concepts

Carbon-12 Atom

In the vast world of chemistry, the carbon-12 atom holds great significance. It is considered a standard when it comes to defining atomic mass units (amu). A carbon-12 atom is an isotope of carbon, characterized by having six protons, six neutrons, and six electrons.

This configuration makes it perfectly balanced and serves as a benchmark for other isotopes. When scientists talk about an atomic mass unit, they refer to it as one-twelfth of the mass of a carbon-12 atom. This makes calculations standardized and clear. Hence, the mass of a carbon-12 atom is exactly 12 amu by definition. Carbon-12 plays a crucial role not just in defining atomic mass units, but also in the study and understanding of isotopic compositions in elements.

Atomic Weight

Atomic weight is a concept that focuses on the average mass of atoms of an element. However, it isn't as straightforward as just summing up masses.

Instead, atomic weight is a weighted average that considers the mass of all the naturally occurring isotopes of an element and their respective abundances.

For example, carbon has an atomic weight of 12.011 amu. This is not due to a singular carbon atom, but rather a mix of carbon-12 and carbon-13 isotopes. While carbon-12 is the most plentiful, carbon-13, though less common, is slightly heavier. Thus, the average calculated weights, like that of carbon, aren't whole numbers. They beautifully balance out the masses and abundances of all contributing isotopes, ensuring accuracy in scientific data.

Isotopes

Isotopes are fascinating variants of elements. They share the same number of protons but differ in the number of neutrons. This means isotopes of a given element have nearly identical chemical properties, but differing atomic masses.

Take carbon as an example; it has isotopes like carbon-12 and carbon-13. Carbon-12, with six neutrons, is much more common, while carbon-13 has seven neutrons.

Isotopes are crucial in science because they affect an element's atomic weight. When isotopic abundance varies, it impacts the calculated average, causing the atomic weight to be a decimal and not a whole number. In practical applications, isotopes play vital roles. They're used in radiometric dating, medical diagnostics, and even in studying environmental conditions. Thus, isotopes add depth to our understanding of the elements and their weights.