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?

Short answer

(a) The mass of a carbon-12 atom is \(12 \, amu\). (b) The atomic weight of carbon is reported as 12.011 because it represents the weighted average of the masses of all naturally occurring isotopes, including carbon-12 (98.9%) and carbon-13 (1.1%). The atomic weight calculation takes into account the relative abundance and atomic masses of each isotope, resulting in the slightly higher value of 12.011 amu.

Step-by-step solution

(a) Finding the mass of a carbon-12 atom in amu

To find the mass of a carbon-12 atom in atomic mass units (amu), we need to remember that 1 amu is defined as 1/12 the mass of a carbon-12 atom. Since a carbon-12 atom has a mass of exactly 12 amu, the mass of a carbon-12 atom in amu is: \( Mass_{C-12} = 12 \, amu \)

(b) Explaining the atomic weight of carbon as 12.011

The atomic weight of an element represents the weighted average of the masses of all its naturally occurring isotopes. Carbon has two stable isotopes, carbon-12 and carbon-13. Although carbon-12 is the more abundant isotope (about 98.9%), the presence of carbon-13 (about 1.1%) contributes to the slightly higher atomic weight of 12.011 for carbon. The atomic weight is calculated using the relative abundance of each isotope and their respective atomic masses: \( Atomic \, weight \, of \, Carbon = (fraction \, of \, C-12) \times mass_{C-12} + (fraction \, of \, C-13) \times mass_{C-13} \) We already know the mass of carbon-12 atom is 12 amu. The mass of a carbon-13 atom is 13 amu. So, we can plug in the numbers and calculate the atomic weight of carbon: \( Atomic \, weight \, of \, Carbon = (0.989) \times 12\, amu + (0.011) \times 13\, amu = 11.868\, amu + 0.143\, amu = 12.011\, amu \) So, the atomic weight of carbon is reported as 12.011 in the table of elements and the periodic table due to the presence and contributions from both carbon-12 and carbon-13 isotopes in their natural abundances.

Key concepts

Atomic Mass Unit (AMU)

Understanding the atomic mass unit (amu) is fundamental when studying chemistry. Defined as exactly 1/12 the mass of a carbon-12 atom, one amu serves as a reference for stating the mass of atoms and subatomic particles. This standardized unit makes comparing different atoms' masses possible. Imagine that every atom has its mass expressed in amu, akin to an item's weight being denoted in pounds or kilograms.

The utility of the atomic mass unit becomes evident when considering the atom's incredibly small mass. Without amu, representing atomic masses in kilograms or grams would be impractical, because the numbers would be extraordinarily tiny and difficult to work with. For exemplification, a carbon-12 atom having a mass of 12 amu is much simpler to comprehend than stating its mass in kilograms.

Isotopes of Carbon

Carbon is an intriguing element not only for its versatile bonding capabilities but also for its various isotopes. Isotopes are variants of an element's atoms that differ in neutron count yet maintain the same number of protons. Carbon predominantly exists as carbon-12, with 6 neutrons. However, it has other isotopes, such as carbon-13, which includes 7 neutrons, and the much rarer carbon-14, known for its use in radiocarbon dating.

The existence of carbon isotopes underscores nature's complexity. It is vital to note that isotopes have nearly identical chemical properties due to the unchanged electron configuration, but their atomic weights vary, which influences the element's average atomic mass. To visualize the isotopic diversity, think of a sports team where each player shares the same jersey number, symbolizing carbon's atomic number, yet has a unique weight, representing the distinct atomic mass of carbon isotopes.

Atomic Weight Calculation

The calculation of an element's atomic weight takes a bit of mathematics, blending science with averages. Think of it as determining the overall grade point average (GPA) for a student who takes multiple classes, each with a unique credit amount. Each isotope's contribution to carbon's atomic weight is akin to individual course grades influencing the GPA.

Atomic weight, therefore, is a weighted mean of all isotopic masses, factoring in the natural abundance of each isotope. In carbon's case, most of it is carbon-12, thus heavily influencing the average. However, carbon-13, though present in smaller quantities, still nudges the atomic weight a bit higher than 12 amu. This meticulous averaging process results in carbon's commonly accepted atomic weight of 12.011, displayed on periodic tables worldwide.