Question

If the atomic weight of carbon 12 is exactly 12 amu, find the mass of a single carbon-12 atom.

Short answer

The mass of a single carbon-12 atom is approximately \(3.31 \times 10^{-26}\) grams.

Step-by-step solution

Convert atomic weight into grams

First, let's convert the atomic weight of carbon-12 from atomic mass units (amu) to grams. 1 amu is approximately equal to 1.6605 x 10^{-24} g. So, for carbon-12, 12 amu is equivalent to: 12 amu * 1.6605 x 10^{-24} g/amu ≈ 1.9926 x 10^{-23} g

Use Avogadro's number to find the mass of a single carbon-12 atom

Now, we will use the Avogadro's number, which is approximately 6.022 x 10^{23} atoms/mol, to find the mass of a single carbon-12 atom: (1.9926 x 10^{-23} g) / (6.022 x 10^{23} atoms/mol) ≈ 3.31 x 10^{-26} g/atom So, the mass of a single carbon-12 atom is approximately 3.31 x 10^{-26} grams.

Key concepts

Atomic Weight

Atomic weight, often referred to as atomic mass, is a measure of the mass of one atom of a chemical element. It's expressed in atomic mass units (amu), which provides a standard way to compare the masses of different atoms on a scale relative to carbon-12, the isotope of carbon with a mass number of 12.

When you look at the periodic table, the atomic weight you see is actually the average mass of all the isotopes of that element, weighted by their natural abundance. For many students, understanding atomic weight is crucial as they dive into more complex chemistry topics. It’s important to know not only what atomic weight represents but also how it factors into broader chemical calculations like finding the molar mass of a compound or balancing chemical equations.

Avogadro's Number

Avogadro's number is a constant that is fundamental to understanding chemistry. It represents the number of atoms, ions, or molecules in one mole of any substance, which is approximately 6.022 x 10^{23} particles per mole. This incredibly large number allows chemists to count particles by weighing them, by converting masses in grams to amounts in moles.

Understanding Avogadro's number helps students grasp the concept of a mole, which is a bridge between the microscopic world of atoms and the macroscopic world we interact with every day. Without Avogadro's number, the scales involved in atomic mass calculations would be unimaginably small and impractical for laboratory measurements and real-world applications.

Atomic Mass Units

Atomic mass units (amu) are the units used to express atomic and molecular weights. One atomic mass unit is defined as a twelfth of the mass of a single carbon-12 atom, which sets a baseline for measuring the masses of other atoms and molecules.

The use of amu makes it possible to relate the mass of an atom to the Avogadro's number when determining the molar mass of a substance. This connection is pivotal in converting grams to moles, thereby linking the amount of substance to its weight—a frequent requirement in chemical calculations. Even though the concept of an atomic mass unit might seem abstract at first, students quickly appreciate its value when faced with the practicalities of material quantification in chemistry.

Carbon-12

Carbon-12 is an isotope of carbon, with six protons and six neutrons in its nucleus, making up about 98.9% of all naturally occurring carbon. It's significant because it's the standard against which the atomic masses of all other elements are measured, being the defining reference for one atomic mass unit. The choice of carbon-12 comes from its abundance and stability, making it a solid benchmark.

When students understand the role of carbon-12 in defining atomic mass units, they get a clearer picture of the comparative nature of atomic weights and why carbon-12 is exactly 12 amu by definition. With this understanding, concepts such as molarity, stoichiometry, and empirical formulas become more accessible, as they all depend on accurate and relative atomic mass measurements.