How Do You Find the Molecular Formula From the Percent Composition of an Element?

You can't directly find the molecular formula solely from the percent composition of an element. You can find the empirical formula, but you need the molar mass of the compound to determine the molecular formula. Here's the process:

1. Determine the Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. Here's how to find it using percent composition:

1. Assume 100g Sample: Convert the percentage of each element directly into grams. For example, if a compound is 40% Carbon, assume you have 40g of Carbon.

2. Convert Grams to Moles: Divide the mass of each element (in grams) by its atomic mass (from the periodic table) to find the number of moles of each element.

3. Find the Simplest Mole Ratio: Divide the number of moles of each element by the smallest number of moles calculated. This will give you the preliminary mole ratio.

4. Convert to Whole Numbers: If the mole ratios are not whole numbers, multiply all the ratios by the smallest possible integer to obtain whole numbers. For example, if you have a ratio of 1:1.5, multiply both by 2 to get a ratio of 2:3.

5. Write the Empirical Formula: Use the whole-number mole ratios as subscripts for each element in the empirical formula.

2. Determine the Molecular Formula (Requires Molar Mass)

Once you have the empirical formula, you can find the molecular formula if you know the molar mass of the actual compound.

1. Calculate the Empirical Formula Mass: Determine the molar mass of the empirical formula by adding up the atomic masses of all the atoms in the formula.

2. Determine the Multiplier: Divide the molar mass of the compound (given or experimentally determined) by the empirical formula mass. This will give you a whole number (or very close to it).

3. Multiply Subscripts: Multiply the subscripts in the empirical formula by the multiplier calculated in the previous step. This gives you the molecular formula.

Example

Let's say a compound has the following percent composition: 40.0% Carbon (C), 6.7% Hydrogen (H), and 53.3% Oxygen (O). The molar mass of the compound is known to be 180 g/mol.

1. Empirical Formula Calculation:

• Assume 100g: 40.0 g C, 6.7 g H, 53.3 g O
• Convert to Moles:
  • C: 40.0 g / 12.01 g/mol = 3.33 mol
  • H: 6.7 g / 1.01 g/mol = 6.63 mol
  • O: 53.3 g / 16.00 g/mol = 3.33 mol
• Find Simplest Ratio: Divide by 3.33 (smallest number of moles):
  • C: 3.33 / 3.33 = 1
  • H: 6.63 / 3.33 = 2
  • O: 3.33 / 3.33 = 1
• Empirical Formula: CH₂O

2. Molecular Formula Calculation:

• Empirical Formula Mass: 12.01 (C) + 2(1.01) (H) + 16.00 (O) = 30.03 g/mol
• Determine Multiplier: 180 g/mol (molar mass of compound) / 30.03 g/mol (empirical formula mass) = 6
• Multiply Subscripts: C₍₁₆₎H₍₂6)O_(1*6) = C₆H₁₂O₆
• Molecular Formula: C₆H₁₂O₆ (Glucose)

Without the molar mass of the compound, you can only determine the empirical formula, which in this case is CH₂O.