Concept of the atomic mass unit
Mass is a key parameter characterizing any atom and chemical element as a whole. However, using familiar macroscopic grams to describe single microparticles is extremely inconvenient. Therefore, a special standard was introduced — the atomic mass unit (amu). In modern chemical and biomedical literature, this unit is increasingly designated by the term dalton (abbreviated as Da).
By international agreement, one dalton is defined as exactly $1/12$ of the mass of the most abundant carbon isotope.
Interestingly, the average atomic mass of natural carbon is not exactly 12, but slightly exceeds this value, reaching $12.011$. This deviation is due to the fact that in the natural environment, carbon exists as a mixture containing impurities of heavier isotopes. Despite this, the vast majority of chemical elements are characterized by integer values: their atomic masses are extremely close to whole numbers, which directly stems from the internal structure of atoms.
Relative atomic mass
In practice, calculations use the concept of relative atomic mass, which is denoted by the symbol $A_r$.
By definition, this value represents the ratio of the real mass of a specific atom to the standardized atomic mass unit. Mathematically, this looks like dividing the true mass of a particle ($m_a$) by $1 \text{ amu}$.
The main feature of $A_r$ is that it is a dimensionless quantity. It has no units of measurement, unlike the true mass, which is expressed in grams or daltons. At the same time, the numerical value of $A_r$ completely coincides with the value of the atomic mass of the element. It is precisely because of this numerical equality that in everyday laboratory practice, the terms "atomic mass" and "relative atomic mass" are very often used as synonyms.
Connection between the microworld and macroworld
To smoothly transition from real masses of substances weighed on a scale (in grams) to the masses of individual particles (in amu) and the number of these particles, strict constants are used.
- For converting macroscopic masses to microscopic ones: one gram of a substance contains exactly $6.02 \cdot 10^{23} \text{ amu}$.
- For converting microscopic masses to macroscopic ones: one atomic mass unit is equivalent to $1.66 \cdot 10^{-24} \text{ g}$.
These basic mathematical ratios open the way to calculating the exact number of atoms in any portions of preparations.
Scale of the atomic world: a thought experiment
To fully realize how small the masses of single atoms are, we can perform a theoretical calculation with helium (He). Let us imagine a situation: we take only 4 grams of this substance and evenly distribute it in the lower layer of the Earth's atmosphere, exactly 1 kilometer thick, over the entire surface of the planet. Our task is to estimate the number of helium atoms in one liter of such a highly diluted air.
The calculation algorithm is as follows:
- First, let us convert the initial mass into microscopic units: multiply 4 grams by the constant $6.02 \cdot 10^{23}$. We obtain a total mass of $24.08 \cdot 10^{23} \text{ amu}$.
- Knowing that the mass of a single helium atom is approximately $4 \text{ amu}$, we divide the total mass by the mass of a single particle. It turns out that our portion contains exactly $6.02 \cdot 10^{23}$ atoms.
- Taking into account the Earth's surface area ($5.10 \cdot 10^8 \text{ km}^2$), we calculate the volume of the one-kilometer atmospheric layer and convert it to liters. The result is $5.10 \cdot 10^{20} \text{ L}$.
- We divide the total number of particles by the calculated atmospheric volume. We obtain the concentration: approximately $1180$ atoms in each liter of air.
This example clearly demonstrates a fundamental fact: even negligibly small portions of a substance by mass contain a colossal number of atoms, since the mass of each individual atom is extremely small.
Briefly: answers to topical questions
How are the relative atomic mass and the molar mass of an element related?
The cited sources explicitly state that the molar mass numerically coincides with the relative molecular mass: for example, for water M(H₂O) = 18 g/mol and Mᵣ(H₂O) = 18. Relative atomic mass is a dimensionless quantity, while atomic mass values are taken from the Periodic Table of Elements.
For measuring the mass of which biomolecules in medicine and biochemistry is the dalton (kilodalton) unit most frequently used?
The dalton unit (or kilodalton, kDa) is most commonly used to measure macromolecular mass and evaluate antigen immunogenicity. The mass of the following biomolecules is expressed in these units:
- Proteins (polypeptides) — including specific viral markers (envelope glycoproteins and core proteins).
- Nucleic acids — macromolecules with weak immunogenicity.
- Lipids — classified as high-molecular-weight compounds.
- Polysaccharides — non-protein biopolymers.
Complete antigens have a mass of more than 10 kDa, whereas substances with a mass of less than 450 Da have weak immunogenicity.
What is the constant $6.02 \cdot 10^{23}$ called and what is its physical meaning in chemistry?
This fundamental physical quantity is called the Avogadro constant (or Avogadro number). Its physical meaning lies in the fact that it reflects the exact number of structural units contained in one mole of any substance. The constant also determines the ratio of mass units: it shows that one gram contains $6.02 \cdot 10^{23}$ atomic mass units (amu). This allows transitioning from macroscopic masses in grams to the real masses of individual atoms and calculating their quantity.
To avoid confusing terms, remember: true atomic mass is measured (in daltons or grams), while relative atomic mass (Ar) is simply a comparison coefficient (dimensionless). At the same time, the numbers in the calculations will be identical.
Class and exam questions
Why is the atomic mass of natural carbon not exactly equal to 12?
This is due to the presence of heavy carbon isotopes in the natural material. The final value of 12.011 is an averaged indicator of the mass of all isotopes in the natural mixture.
What is the difference between atomic mass and relative atomic mass ($A_r$)?
Atomic mass is expressed in amu (daltons) or grams. $A_r$ is the dimensionless ratio of the mass of a specific atom to one atomic mass unit. Numerically, they are completely equal.
How to convert atomic mass units into grams?
A constant value is used for this: one dalton (or 1 amu) is strictly equal to $1.66 \cdot 10^{-24}$ grams.
What else to study on this topic
- Isotopes and their effect on the atomic mass of elements
- Calculation of average atomic mass for isotope mixtures
- The Avogadro number and its relation to mass conversion
- Internal structure of the atom determining its mass
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