Calculating Molecular Weight
What is Molecular Weight?
Definition: Molecular weight (MW) is the sum of the atomic weights of all atoms in a molecule, expressed in atomic mass units (amu) or grams per mole (g/mol).
Basic Formula:
\[ \text{Molecular Weight} = \sum (\text{Atomic Weight} \times \text{Number of Atoms}) \]
\[ \text{Molecular Weight} = \sum (\text{Atomic Weight} \times \text{Number of Atoms}) \]
Sum this calculation for each element in the compound
General Formula:
\[ MW = \sum_{i=1}^{n} (A_i \times N_i) \]
\[ MW = \sum_{i=1}^{n} (A_i \times N_i) \]
Where: Ai = atomic weight of element i, Ni = number of atoms of element i
Step-by-Step Calculation Process
Step 1: Write the molecular formula of the compound
Step 2: Identify each element and count the number of atoms
Step 3: Find the atomic weight of each element from the periodic table
Step 4: Multiply atomic weight by number of atoms for each element
Step 5: Add all the products together to get the molecular weight
Worked Examples
Example 1: Water (H₂O)
Given: H₂O
Elements: Hydrogen (H) = 2 atoms, Oxygen (O) = 1 atom
Calculation:
\[ MW = (2 \times 1.008) + (1 \times 15.999) \]
\[ MW = 2.016 + 15.999 = 18.015 \text{ amu} \]
Elements: Hydrogen (H) = 2 atoms, Oxygen (O) = 1 atom
Calculation:
\[ MW = (2 \times 1.008) + (1 \times 15.999) \]
\[ MW = 2.016 + 15.999 = 18.015 \text{ amu} \]
Example 2: Carbon Dioxide (CO₂)
Given: CO₂
Elements: Carbon (C) = 1 atom, Oxygen (O) = 2 atoms
Calculation:
\[ MW = (1 \times 12.011) + (2 \times 15.999) \]
\[ MW = 12.011 + 31.998 = 44.009 \text{ amu} \]
Elements: Carbon (C) = 1 atom, Oxygen (O) = 2 atoms
Calculation:
\[ MW = (1 \times 12.011) + (2 \times 15.999) \]
\[ MW = 12.011 + 31.998 = 44.009 \text{ amu} \]
Example 3: Glucose (C₆H₁₂O₆)
Given: C₆H₁₂O₆
Elements: Carbon (C) = 6 atoms, Hydrogen (H) = 12 atoms, Oxygen (O) = 6 atoms
Calculation:
\[ MW = (6 \times 12.011) + (12 \times 1.008) + (6 \times 15.999) \]
\[ MW = 72.066 + 12.096 + 95.994 = 180.156 \text{ amu} \]
Elements: Carbon (C) = 6 atoms, Hydrogen (H) = 12 atoms, Oxygen (O) = 6 atoms
Calculation:
\[ MW = (6 \times 12.011) + (12 \times 1.008) + (6 \times 15.999) \]
\[ MW = 72.066 + 12.096 + 95.994 = 180.156 \text{ amu} \]
Example 4: Sulfuric Acid (H₂SO₄)
Given: H₂SO₄
Elements: Hydrogen (H) = 2 atoms, Sulfur (S) = 1 atom, Oxygen (O) = 4 atoms
Calculation:
\[ MW = (2 \times 1.008) + (1 \times 32.065) + (4 \times 15.999) \]
\[ MW = 2.016 + 32.065 + 63.996 = 98.077 \text{ amu} \]
Elements: Hydrogen (H) = 2 atoms, Sulfur (S) = 1 atom, Oxygen (O) = 4 atoms
Calculation:
\[ MW = (2 \times 1.008) + (1 \times 32.065) + (4 \times 15.999) \]
\[ MW = 2.016 + 32.065 + 63.996 = 98.077 \text{ amu} \]
Common Atomic Weights Reference
| Element | Symbol | Atomic Weight (amu) |
|---|---|---|
| Hydrogen | H | 1.008 |
| Carbon | C | 12.011 |
| Nitrogen | N | 14.007 |
| Oxygen | O | 15.999 |
| Sodium | Na | 22.990 |
| Chlorine | Cl | 35.453 |
| Sulfur | S | 32.065 |
| Calcium | Ca | 40.078 |
Important Formulas
Molar Mass Relationship:
\[ \text{Molar Mass (g/mol)} = \text{Molecular Weight (amu)} \]
\[ \text{Molar Mass (g/mol)} = \text{Molecular Weight (amu)} \]
Number of Moles:
\[ n = \frac{\text{Mass (g)}}{\text{Molecular Weight (g/mol)}} \]
\[ n = \frac{\text{Mass (g)}}{\text{Molecular Weight (g/mol)}} \]
Mass Calculation:
\[ \text{Mass (g)} = n \times \text{Molecular Weight (g/mol)} \]
\[ \text{Mass (g)} = n \times \text{Molecular Weight (g/mol)} \]
Percentage Composition:
\[ \text{Percentage of Element} = \frac{\text{Mass of Element in Compound}}{\text{Molecular Weight}} \times 100\% \]
\[ \text{Percentage of Element} = \frac{\text{Mass of Element in Compound}}{\text{Molecular Weight}} \times 100\% \]
Practice Problems
Problem 1: Calculate the molecular weight of methane (CH₄)
Problem 2: Find the molecular weight of calcium carbonate (CaCO₃)
Problem 3: Determine the molecular weight of ethanol (C₂H₅OH)
Problem 4: Calculate the molecular weight of ammonium sulfate ((NH₄)₂SO₄)
Key Tips for Success
✓ Always double-check: Count atoms carefully, especially in complex formulas with parentheses
✓ Use accurate atomic weights: Round to appropriate significant figures based on the problem requirements
✓ Handle parentheses correctly: Multiply the subscript outside parentheses by each subscript inside
✓ Units matter: Keep track of whether you need amu or g/mol in your final answer
🧪 Remember: Molecular weight is fundamental to stoichiometry, molarity calculations, and understanding chemical reactions!