Can You Determine the Molecular Formula of a Substance From Its Percent Composition?

Yes, you can determine the molecular formula of a substance from its percent composition, though it requires an intermediate step.

Here's how the process works:

Using Percent Composition to Find the Molecular Formula

1. Determine the Empirical Formula:

   • As stated in the reference, "the percent composition of a sample can be used to determine its empirical formula."
   • The percent composition tells you the mass percentage of each element in a compound.
   • You can convert these percentages into grams (assuming a 100g sample), then to moles, and then obtain the simplest whole-number ratio of these moles to find the empirical formula.

2. Determine the Molecular Formula:

   • Once you have the empirical formula, you need the molar mass of the actual compound.
   • The molar mass can be determined using experimental techniques like mass spectrometry.
   • Calculate the molar mass of the empirical formula.
   • Divide the molar mass of the compound by the molar mass of the empirical formula. This gives you a whole number.
   • Multiply the subscripts of the empirical formula by that whole number. The result is the molecular formula.

Example

Let’s say a compound has the following percent composition: 40.00% Carbon, 6.71% Hydrogen, and 53.29% Oxygen. Also let’s assume we know the molar mass of the compound is 180 g/mol.

1. Empirical Formula:

   • Assume a 100 g sample: 40.00g C, 6.71g H, 53.29 g O
   • Convert to moles:
     • C: 40.00 g / 12.01 g/mol = 3.33 mol
     • H: 6.71 g / 1.01 g/mol = 6.64 mol
     • O: 53.29 g / 16.00 g/mol = 3.33 mol
   • Find the simplest ratio (divide by the smallest number, 3.33):
     • C: 3.33 / 3.33 = 1
     • H: 6.64 / 3.33 = ~ 2
     • O: 3.33 / 3.33 = 1
   • The empirical formula is therefore CH₂O.

2. Molecular Formula:

   • Empirical formula mass of CH₂O = 12.01 + 2(1.01) + 16.00 = 30.03 g/mol
   • Molar mass of the compound = 180 g/mol (given)
   • Divide the molar mass of compound by the molar mass of the empirical formula: 180 g/mol / 30.03 g/mol = ~6
   • Multiply empirical subscripts by 6: C₁₆H₂6O_1*6 or C₆H₁₂O₆
   • The molecular formula is C₆H₁₂O₆

Conclusion

The reference confirms that "the percent composition of a sample can be used to determine its empirical formula, which can then be used to determine its molecular formula". So, while percent composition doesn't directly give you the molecular formula, it is a crucial stepping stone in obtaining it, especially when combined with the compound's molar mass. The empirical formula derived from the percent composition acts as a base from which the true molecular formula can be calculated.