Relative Molecular Mass (\(\text{M}_r\)) is a fundamental concept in chemistry used to compare the masses of different molecules on a standardized scale. This measurement provides a simple, relative number that reflects how heavy one molecule of a substance is compared to a defined reference point. Using this relative scale allows chemists to avoid working with the extremely small actual masses of individual atoms. The concept is a universal tool for understanding substance composition and predicting chemical behavior.
Defining Relative Molecular Mass (\(\text{M}_r\))
Relative Molecular Mass (\(\text{M}_r\)) is defined as the ratio of the average mass of one molecule of a substance to one-twelfth of the mass of a single atom of carbon-12. Because it is a ratio of two masses, \(\text{M}_r\) is a dimensionless quantity, meaning it has no units like grams or kilograms.
The standard reference is carbon-12, a stable and abundant isotope that provides a consistent basis for comparison across the periodic table. By definition, the carbon-12 atom is assigned a mass of exactly 12 units on this relative scale. This \(\text{M}_r\) value applies specifically to covalent compounds, which exist as discrete molecules. For substances that form ionic lattices, such as table salt, the calculation is referred to as the Relative Formula Mass, since these compounds do not exist as individual molecules.
Calculating \(\text{M}_r\) for Compounds
The procedure for determining the Relative Molecular Mass of any compound is straightforward. It involves summing the relative atomic masses (\(\text{A}_r\)) of every atom present in the compound’s chemical formula. The \(\text{A}_r\) values for each element are readily available on the periodic table.
For a simple molecule like water (\(\text{H}_2\text{O}\)), the calculation requires the relative atomic masses of two hydrogen atoms and one oxygen atom. Using standard values, the calculation is \((2 \times 1.01) + (1 \times 16.00)\), which results in an \(\text{M}_r\) of 18.02 for water. The subscripts in the chemical formula indicate how many atoms of each element must be included in the total summation.
For carbon dioxide (\(\text{CO}_2\)), the calculation sums the mass of one carbon atom and two oxygen atoms. Using the \(\text{A}_r\) values, the total is \((1 \times 12.01) + (2 \times 16.00)\), yielding an \(\text{M}_r\) of 44.01. This systematic addition ensures that the calculated \(\text{M}_r\) accurately represents the total relative mass of the entire molecule.
Distinguishing \(\text{M}_r\) from Molar Mass
Relative Molecular Mass (\(\text{M}_r\)) and Molar Mass (\(\text{M}\)) share the exact same numerical value but represent distinct concepts in chemistry. \(\text{M}_r\) is a dimensionless number describing the mass of a single molecule relative to the carbon-12 standard.
Molar Mass is the mass of one mole of a substance. A mole is defined as \(6.022 \times 10^{23}\) particles, known as Avogadro’s number. This change in context requires Molar Mass to have units, specifically grams per mole (\(\text{g/mol}\)).
For example, the \(\text{M}_r\) of water is 18.02, while its Molar Mass is 18.02 \(\text{g/mol}\). The numerical identity exists because the mole’s definition was intentionally set to link the relative atomic mass scale to a practical mass in grams. Molar Mass is derived directly from \(\text{M}_r\) by applying the \(\text{g/mol}\) unit, making it the quantity used for macroscopic measurements.
Relevance in Chemistry
The ability to calculate \(\text{M}_r\) is a fundamental skill that underpins much of quantitative chemistry. It serves as the basis for calculating Molar Mass, which is the necessary bridge between the microscopic world of atoms and macroscopic laboratory measurements. This conversion is crucial for stoichiometry, the area of chemistry concerned with the quantitative relationships between reactants and products in a chemical reaction.
Using Molar Mass, chemists accurately determine the mass of a substance needed to react completely with a given amount of another substance. This is also applied in concentration calculations, such as determining the molarity of a solution (moles of solute dissolved per liter of solution). Furthermore, \(\text{M}_r\) is used to determine a compound’s percentage composition by mass, which helps establish its empirical and molecular formulas.