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

The mass of a carbon-12 atom is $12amu$ because one atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. The atomic weight of carbon is reported as 12.011 in the table of elements and periodic table because it is a weighted average of all its isotopes' masses, mainly carbon-12 and carbon-13, with natural abundances of 98.89% and 1.11%, respectively.

Step-by-step solution

Defining Atomic Mass Unit (amu)

An atomic mass unit (amu) is a unit of mass used to express atomic and molecular weights. It is defined as one-twelfth the mass of a carbon-12 atom, which is approximately equal to 1.66054 x 10^{-24} grams.

Mass of Carbon-12 Atom in amu

By definition, one atomic mass unit (amu) is equal to one-twelfth the mass of a carbon-12 atom. So, the mass of one carbon-12 atom is equal to 12 atomic mass units. Therefore, the mass of a carbon-12 atom is $12amu$.

Explaining the Atomic Weight of Carbon

The atomic weight of an element is the weighted average of the masses of all its isotopes. Carbon has two stable isotopes: carbon-12 and carbon-13. Most carbon atoms in nature are carbon-12, with a mass of 12 amu, but some carbon atoms are carbon-13, with a mass of 13 amu. The natural abundance of carbon-12 is about 98.89%, and the natural abundance of carbon-13 is about 1.11%. Therefore, the atomic weight of carbon is a weighted average of the two isotopes' masses: Atomic weight of carbon = (0.9889)(12 amu) + (0.0111)(13 amu) ≈ 12.011 amu This is why the atomic weight of carbon is reported as 12.011 in the table of elements and periodic table.

Key concepts

Mass of a Carbon-12 Atom

The mass of a carbon-12 atom is central to understanding atomic mass units (amu). To keep it simple, imagine carbon-12 as the standard from which scientists measure the mass of atoms. Precisely, a carbon-12 atom has a mass of exactly 12 atomic mass units (12 amu).

The beauty of this standard is its consistency; since it's based on a specific isotope of carbon (carbon-12), it stays the same no matter where you are in the universe. This uniformity allows for a solid foundation when scientists talk about atomic masses across various elements.

Definition of AMU

Diving into the definition of an atomic mass unit (amu) takes us to the realm of tiny, almost unimaginable scales. An amu is the standard unit that is used to measure the mass of atoms and molecules. To get to grips with it, know that it is one-twelfth the mass of a single carbon-12 atom.

Let me break it down: when scientists say 'atomic mass unit', they’re talking about a super small unit of mass--it's like comparing the weight of a bee to that of an elephant! This tiny unit, the amu, is roughly equivalent to 1.66054 x 10^-24 grams.

Atomic Weight of Carbon

Why does the atomic weight of carbon show up as 12.011 and not a neat 12, you might wonder? It's because the atomic weight is the average mass of all the different isotopes of an element, each with their own unique mass, which considers their natural abundance. Carbon is mostly carbon-12 (about 98.89%), which gives us the 12 we might expect, but carbon also has a heavier sibling, carbon-13 (about 1.11%), slightly tipping the scale. That's why, after mathematically blending these isotopes, you get an atomic weight of approximately 12.011 amu for carbon.

This blending of isotopes is much like making a smoothie with different fruits—each fruit (isotope) will affect the final flavor (weight), so the more of one type you have, the more it'll influence the taste (in carbon’s case, the atomic weight).