Empirical & Molecular Formula

Molecular Formula: This represents the exact number and type of each atom present in a single molecule of a compound. It is the 'true' formula for discrete molecular substances, such as organic molecules like glucose ($C_6H_{12}O_6$).

Empirical Formula: This is the simplest whole-number ratio of the elements present in a compound. For many substances, such as ionic lattices (e.g., $NaCl$) or giant covalent structures, the empirical formula is the only standard way to represent the substance.

Relationship: The molecular formula is always a whole-number multiple ($n$) of the empirical formula, where $n = 1, 2, 3, \dots$. If $n=1$, the empirical and molecular formulae are identical.

Step 1: Obtain Mass Data: Start with the mass of each element in a sample (in grams) or the percentage composition by mass. If percentages are given, assume a 100g sample so that % values equal mass in grams.

Step 2: Convert to Moles: Divide the mass of each element by its specific $A_r$ value using the formula $n = \frac{m}{A_r}$. This converts the bulk mass into the number of particles (moles).

Step 3: Find the Simplest Ratio: Divide all the resulting mole values by the smallest mole value obtained in Step 2. This normalizes the data to a 1:X ratio.

Step 4: Convert to Whole Numbers: If the results are not whole numbers (e.g., 1.5 or 1.33), multiply all values by a common factor (e.g., 2 or 3) to achieve the simplest whole-number ratio.

Requirement: To find the molecular formula, you must already know the Empirical Formula and the Relative Molecular Mass ($M_r$) of the actual compound.

Step 1: Calculate Empirical Mass: Sum the $A_r$ values of all atoms in the empirical formula. For example, if the empirical formula is $CH_2$, the empirical mass is $12.0 + (2 \times 1.0) = 14.0$.

Step 2: Determine the Multiplier ($n$): Divide the actual $M_r$ of the compound by the empirical mass calculated in Step 1: $n = \frac{\text{Relative Molecular Mass}}{\text{Empirical Formula Mass}}$

Step 3: Scale the Formula: Multiply every subscript in the empirical formula by the integer $n$ to obtain the molecular formula.

Rounding Errors: Never round values like 1.5 to 2 or 1.33 to 1 during the ratio step. These indicate that you must multiply the entire set by 2 or 3 respectively to reach the correct whole-number ratio.

Atomic vs. Molecular Mass: When calculating moles for the empirical formula, always divide by the Relative Atomic Mass ($A_r$) of the element, even for diatomic elements like Oxygen ($O_2$). Use 16.0, not 32.0, because you are finding the ratio of atoms.

Sanity Check: Always ensure your final molecular formula mass matches the $M_r$ given in the question. If the empirical mass is larger than the $M_r$, a calculation error has occurred.