Calculate Relative Mass

Relative Atomic Mass ($A_r$) is the weighted average mass of an atom of an element compared to 1/12th of the mass of an atom of carbon-12. It accounts for the naturally occurring isotopes of the element.

Relative Formula Mass ($M_r$), also known as relative molecular mass, represents the total relative mass of a chemical compound's formula unit.

Both $A_r$ and $M_r$ are unitless quantities because they are ratios relative to a standard atom, though they are numerically equivalent to the mass in grams of one mole of the substance.

The $A_r$ of any element is found on the Periodic Table, typically as the larger of the two numbers provided for each element cell (the mass number).

Step 1: Identify the Atoms: List every element present in the chemical formula and determine its $A_r$ value from the periodic table.

Step 2: Account for Subscripts: Multiply the $A_r$ of each element by the small number appearing after its symbol. If no number is shown, the count is one.

Step 3: Resolve Parentheses: If brackets are used, multiply all $A_r$ values inside the bracket by the external subscript before adding them to the rest of the formula.

Step 4: Final Summation: Add all calculated mass components together to reach the final $M_r$ of the substance.

Periodic Table Usage: Always use the larger of the two numbers provided for an element (the mass number). Using the atomic (proton) number is a common mistake that leads to incorrect results.

Double-Check Multipliers: Ensure that subscripts outside parentheses are applied to every atom inside the brackets. For example, in $Ca(OH)_2$, there are two oxygens and two hydrogens.

Sanity Check: Does the $M_r$ seem reasonable? For instance, the $M_r$ of a compound must always be greater than the $A_r$ of any single element it contains.

Rounding: Do not round $A_r$ values significantly until the final summation is complete to avoid compounding precision errors.

Confusing Addition and Multiplication: A common error is adding subscripts (e.g., treating $H_2$ as $1+2$) instead of multiplying the atomic mass by the count (e.g., $1 \times 2$).

Ignoring Brackets: Students often fail to distribute the external subscript across all elements within parentheses, leading to undercounting of atoms.

Atomic Number Substitution: Using the atomic number (position in the table) instead of the relative atomic mass is the most frequent procedural error in $M_r$ calculations.