Mass is a foundational concept in chemistry, but individual atoms and molecules are too small to measure directly with standard laboratory equipment. A single carbon atom, for instance, has a mass on the order of \(10^{-23}\) grams, which is too cumbersome for practical calculations. This disparity between the atomic and macroscopic scales necessitates a different approach. Chemists developed the system of “relative mass” to simplify comparing and calculating atomic masses. This system provides a convenient, unitless way to express the mass of an atom by comparing it to a universally accepted standard, which allows for easy determination of proportions in chemical reactions.
Defining Relative Mass and the Reference Standard
Relative mass is fundamentally a ratio comparing the mass of an atom to a fixed reference point. This approach transforms the absolute mass of an atom into a manageable numerical value.
The current international reference standard is the carbon-12 atom. Carbon-12 is defined as having a mass of exactly twelve atomic mass units (12 u), establishing the scale for all other elements. One unified atomic mass unit (1 u), also known as the Dalton (Da), is defined as precisely one-twelfth of the mass of a single, unbound carbon-12 atom. Carbon-12 was selected as the standard in 1961 because it is abundant, stable, and its mass is a near-perfect whole number, which simplifies calculations.
An element’s relative atomic mass represents the average mass of that element’s atoms compared to the one-twelfth slice of carbon-12. Because relative mass is a ratio of two masses, it is technically a dimensionless quantity, meaning it has no units. Although the value is unitless, the unit “u” is often used for convenience to express the mass of one particle on this relative scale.
The relative atomic mass shown on the periodic table is a weighted average that accounts for all of the element’s naturally occurring isotopes. For example, chlorine has two major stable isotopes, and its relative atomic mass of approximately 35.5 reflects the combined proportion of these forms found in nature. This weighted average ensures the relative mass used in calculations accurately represents the average mass of an atom in any typical sample.
The Necessity of Relative Measurement in Chemistry
The reliance on relative mass stems from the impossibility of working with absolute masses at the atomic level in a practical laboratory setting. While measuring the mass of a substance in grams is simple, trying to weigh atoms in \(10^{-24}\) gram increments is unrealistic. The relative system provides a necessary bridge between the microscopic world of atoms and the macroscopic world of laboratory measurements.
Defining the atomic mass unit (u) based on the carbon-12 standard provides a convenient scale where the mass of a proton or neutron is approximately one unit. This relative scale allows for easy comparison, such as showing that an oxygen atom (16 u) is about four times heavier than a helium atom (4 u). These simple whole-number relationships help determine the combining ratios of elements in chemical reactions.
The relative mass system forms the foundation for the concept of the mole, the standard unit for the amount of substance in chemistry. The numerical value of an element’s relative atomic mass in “u” is exactly equal to the mass, in grams, of one mole of that element. This direct connection allows chemists to transition seamlessly from the relative masses of individual atoms to the grams of substance they weigh out in the laboratory, making stoichiometry and quantitative analysis possible.
Calculating Relative Mass for Compounds
The concept of relative mass extends beyond single atoms to include molecules and ionic compounds. For covalent compounds, which exist as discrete molecules, the term used is Relative Molecular Mass (RMM), often symbolized as \(M_{\text{r}}\). The \(M_{\text{r}}\) is the sum of the relative atomic masses of all atoms that make up the molecule’s chemical formula.
To find the relative molecular mass of water (\(H_2O\)), one adds the mass of two hydrogen atoms and one oxygen atom. Using relative atomic masses of approximately 1 for hydrogen and 16 for oxygen, the calculation is \((2 \times 1) + 16\), resulting in an \(M_{\text{r}}\) of 18. This value indicates that a water molecule is 18 times heavier than one-twelfth the mass of a carbon-12 atom.
For ionic compounds, which form extended crystal lattices, the term Relative Formula Mass (RFM) is used. It shares the same symbol, \(M_{\text{r}}\), and the same calculation method as RMM. The RFM is calculated by summing the relative atomic masses of the atoms in the compound’s empirical formula, which represents the simplest ratio of ions. For sodium chloride (\(NaCl\)), the RFM is found by adding the relative atomic mass of one sodium atom (23) and one chlorine atom (35.5), yielding an RFM of 58.5. This summation method allows chemists to determine the relative mass of any chemical substance.