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 in amu is exactly 12 amu, since atomic mass unit (amu) is defined based on the mass of a carbon-12 atom. (b) The atomic weight of carbon is reported as 12.011 in the table of elements and the periodic table because it is a weighted average of the masses of its isotopes (carbon-12 and carbon-13) taking into account their natural abundances.

Step-by-step solution

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

The atomic mass unit (amu) is defined such that the mass of a carbon-12 atom is exactly 12 amu. Therefore, the mass of a carbon-12 atom in amu is: \(mass = 12\: amu\)

Part (b) - Explaining the atomic weight of carbon as 12.011

The atomic weight of an element is a weighted average of the masses of all the naturally occurring isotopes of that element. This takes into account both the masses of the isotopes and their relative abundances. In the case of carbon, there are two stable isotopes, carbon-12 and carbon-13. The atomic weight of carbon is calculated using the following formula: \[ \textrm{Atomic Weight} (\textrm{C}) = \displaystyle\sum_{i} w_{i} \times m_{i} \] where \(w_{i}\) represents the natural abundance of isotope i and \(m_{i}\) represents the mass of isotope i. Carbon-12 has an abundance of approximately 98.89% and a mass of 12 amu, and carbon-13 has an abundance of approximately 1.11% and a mass of 13.003355 amu. Using the formula, we can calculate the atomic weight of carbon as: \[ \textrm{Atomic Weight} (\textrm{C}) = 0.9889 \times 12 + 0.0111 \times 13.003355 \] \[ \textrm{Atomic Weight} (\textrm{C}) ≈ 12.011 \] So, the atomic weight of carbon is reported as 12.011 in the table of elements and the periodic table because it is a weighted average of the masses of its isotopes, taking into account their natural abundances.

Key concepts

Atomic Mass Unit

Understanding the term 'atomic mass unit' (amu) is vital when studying chemistry and physics. It's a standard unit of measurement for atoms and molecules. The amu provides a convenient way for scientists to compare different atoms since it's based on a uniform standard. To put it in context, an amu is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 at its nuclear and electronic ground state. This means that a single carbon-12 atom has an atomic mass exactly equal to 12 amu.

When we are dealing with atomic particles that are incredibly small, knowing their mass in grams isn't very practical due to the extremely large quantities those numbers would involve – we're talking about values like 0.00000000000000000000002 grams! An amu, then, acts as a sensible scale for such tiny particles, making it easier to comprehend and utilize in calculations.

It's also essential to recognize why the carbon-12 isotope was chosen as the standard. Carbon is an element that is foundational to life and widely prevalent, plus its atomic number 6 provides a mid-range atomic mass to work with.

Isotopes of Carbon

Carbon, like other elements, doesn't just come in one 'flavor.' It has different forms known as isotopes, which possess varying numbers of neutrons. The isotopes of carbon have the same number of protons (since they are all carbon) but differ in their neutronic content. The most common isotopes of carbon are carbon-12 and carbon-13.

Carbon-12:

Carbon-12 is the most abundant isotope, complete with 6 protons and 6 neutrons. It's used as a reference isotope for defining the atomic mass unit.

Carbon-13:

On the other hand, carbon-13 has 6 protons and 7 neutrons. Despite being heavier, it's much less common than carbon-12.

The additional neutrons do not impact the chemical behavior of the carbon atoms significantly, but they do affect their mass and stability. Isotopes like carbon-14, which is radioactive and has 6 protons and 8 neutrons, have distinct properties used in archaeological dating techniques, such as radiocarbon dating.

Natural Abundance

Natural abundance describes how common an isotope is within a natural environment compared to others. For carbon, the majority of the element in nature is found as carbon-12, consisting of about 98.89%. Carbon-13, despite being an isotope of the same element, exists only in minor amounts of about 1.11%.

The concept of natural abundance is crucial when determining the average atomic mass of an element, as displayed on the periodic table. Since natural abundance reflects the proportion of each isotope in nature, it's factored into the calculations for an element's average atomic weight.

To find this weighted average, you multiply the mass of each isotope by its relative abundance, then sum up these values. This calculation provides us with a more representative number for the element's atomic mass, applicable to any given sample on Earth, rather than just focusing on a single isotope. This is why the atomic weight of carbon isn't just 12 amu like carbon-12, but rather approximately 12.011 amu, accounting for the presence of carbon-13 in nature.