The formula weight (FW) of a compound represents the mass of all atoms contained within its chemical formula. This value is determined by summing the atomic weights of every atom represented in the formula. Calculating the formula weight is a foundational skill in chemistry, used to measure and compare substances based on their composition. The resulting formula weight is typically expressed in atomic mass units (amu).
Interpreting Chemical Formulas and Atomic Weight
Before calculation, one must understand how to read a chemical formula and locate the necessary atomic weight values. A chemical formula, such as \(\text{H}_2\text{O}\) for water, uses element symbols and small subscript numbers to show the types and quantities of atoms present. The subscript number following an element symbol indicates how many atoms of that element are in the formula unit. For example, the ‘2’ in \(\text{H}_2\text{O}\) means there are two hydrogen atoms, while the absence of a subscript implies there is just one atom.
The second necessary component is the atomic weight for each element in the formula. Atomic weight represents the average mass of a single atom, taking into account the natural abundance of its isotopes. This value is listed on the Periodic Table of Elements, usually as a decimal number beneath the element’s symbol.
The unit for the atomic weight is the atomic mass unit (amu). When performing calculations, it is sufficient to use the atomic weight rounded to two or three decimal places for common elements, such as Carbon (\(\approx 12.01\text{ amu}\)), Hydrogen (\(\approx 1.01\text{ amu}\)), and Oxygen (\(\approx 16.00\text{ amu}\)). The final formula weight will also carry the atomic mass unit.
Step-by-Step Guide to Calculation
The process for determining the formula weight is a systematic, four-step mathematical procedure. The first step involves examining the chemical formula to identify all distinct elements and count the number of atoms for each. For compounds with parentheses, such as \(\text{Ca}(\text{OH})_2\), the subscript outside the parentheses applies to every element within the grouping.
The second step requires consulting a Periodic Table to find the average atomic weight for each identified element. It is important to record these values accurately, using a consistent number of decimal places for all elements in the calculation.
Next, calculate the total mass contribution for each individual element within the compound. This is achieved by multiplying the element’s atomic weight by the total number of atoms counted in the first step.
The final step is to add together the total mass contributions calculated for every element in the compound. The resulting sum represents the compound’s total formula weight, expressed in atomic mass units.
Applying the Method with Examples
Simple Molecular Compound: Water (\(\text{H}_2\text{O}\))
Calculating the formula weight for water demonstrates the method clearly. First, the formula \(\text{H}_2\text{O}\) indicates the presence of two hydrogen (\(\text{H}\)) atoms and one oxygen (\(\text{O}\)) atom.
Next, the atomic weights are identified from the Periodic Table: Hydrogen is approximately \(1.01\text{ amu}\), and Oxygen is approximately \(16.00\text{ amu}\).
The total mass contribution for each element is calculated by multiplying the atomic weight by the number of atoms. For Hydrogen, the calculation is \(2 \times 1.01\text{ amu} = 2.02\text{ amu}\), and Oxygen’s contribution is \(1 \times 16.00\text{ amu} = 16.00\text{ amu}\).
Finally, summing these individual contributions yields the formula weight for water: \(2.02\text{ amu} + 16.00\text{ amu}\), which totals \(18.02\text{ amu}\).
Complex Compound with Parentheses: Calcium Hydroxide (\(\text{Ca}(\text{OH})_2\))
The calculation for calcium hydroxide, \(\text{Ca}(\text{OH})_2\), illustrates how to handle subscripts outside of parentheses. The formula shows one atom of Calcium (\(\text{Ca}\)). Since the subscript ‘2’ applies to the entire hydroxide group (\(\text{OH}\)), there are two Oxygen (\(\text{O}\)) atoms and two Hydrogen (\(\text{H}\)) atoms in the compound.
The atomic weights used are Calcium (\(\approx 40.08\text{ amu}\)), Oxygen (\(\approx 16.00\text{ amu}\)), and Hydrogen (\(\approx 1.01\text{ amu}\)). The individual mass contributions are found by multiplying the count of each atom by its respective atomic weight. Calcium’s contribution is \(1 \times 40.08\text{ amu}\), totaling \(40.08\text{ amu}\).
For the elements inside the parentheses, the calculation is \(2 \times 16.00\text{ amu}\) for Oxygen, equaling \(32.00\text{ amu}\). Hydrogen’s contribution is \(2 \times 1.01\text{ amu}\), which is \(2.02\text{ amu}\).
The final formula weight is the sum of these three contributions: \(40.08\text{ amu} + 32.00\text{ amu} + 2.02\text{ amu}\), resulting in a total formula weight of \(74.10\text{ amu}\) for calcium hydroxide. This calculation confirms that every atom in the formula is correctly accounted for.