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Empirical Formula and Molecular Formula

Empirical Formula and Molecular Formula

Empirical Formula shows the simplest whole-number ratio of the elements in a compound. Molecular Formula indicates the exact number of each type of atom in a molecule. It may be the same as the empirical formula or a multiple of it.

1.0Molecular Formula

  • Represents the actual number of each type of atom present in a molecule.
  • Uses subscripts to indicate the exact count of each atom in a molecule.
  • Reflects the true composition of a compound, not simplified.
  • The molecular mass (or molar mass) of a compound corresponds to a whole-number multiple of the empirical formula mass.
  • Example: The molecular formula for glucose is C6H12O6​, showing that each molecule contains 6 carbon, 12 hydrogen, and 6 oxygen atoms.

2.0Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of atoms of each element present in the compound. It gives the relative number of atoms rather than the actual number in a molecule.

  • Represents the simplest whole-number ratio of the elements in a compound.
  • Provides a reduced or simplified version of the formula, focusing on the ratio, not the exact count.
  • Known as the "simplest formula" because it only shows the basic proportional relationship between elements.
  • The empirical formula is derived directly from the per cent composition of the compound.
  • Example: The empirical formula for glucose is CH2O, indicating the simplest ratio of carbon, hydrogen, and oxygen is 1:2:1.

3.0Steps to Calculate the Empirical Formula

  1. Determine the Mass of Each Element: Use the given data or assume a 100 g sample if percentages are provided.
  2. Convert Mass to Moles: Use the formula: Moles of an element=Mass of the element (g)Atomic mass of the element (g/mol)Moles of an element=Atomic mass of the element (g/mol)Mass of the element (g)​
  3. Find the Simplest Whole-Number Ratio: Divide all mole values by the smallest number of moles calculated.
  4. Write the Empirical Formula: Use the ratio of moles as subscripts in the formula. If the ratios are not whole numbers, multiply by the smallest integer that converts them to whole number
Example

Glucose:

  • Percent composition: C: 40%, H: 6.7%, O: 53.3%
  • Empirical formula: CH2O

Hydrogen Peroxide:

  • Simplest ratio: HO

Solved Example 

  1. Calculation of the Empirical Formula of Phosphoric Acid

Given Composition:

  • Hydrogen (H): 3.06%
  • Phosphorus (P): 31.63%
  • Oxygen (O): 65.31%

Solution:

Assume 100 g of the compound:

    • This simplifies the percentages directly into masses:
      • Mass of H = 3.06 g
      • Mass of P = 31.63 
      • Mass of O = 65.31 g

Calculate the number of moles for each element:

  • Using the formula:
    • For H, Moles of H = (3.06)/1 =3.06
    • For P. Moles of P = (31.63)/31 = 1.02
    • For O, Moles of O = (65.31)/16 =4.08

Find the simplest ratio of moles:

    • Divide all the mole values by the smallest number of moles, 1.02
      • Ratio of H =
      • Ratio of P =
      • Ratio of O =

Write the empirical formula:

  • Use these ratios as subscripts for the elements:
    • Empirical formula = H3PO4
Solved Example
  1. Glucose:

Empirical formula: CH2O

Empirical formula mass: 12+2(1)+16=30 g/mol

Molar mass: 180 g

n = 180/30 = 6

Molecular formula: C6H12O6

  1. Hydrogen Peroxide:

Empirical formula: HO

Empirical formula mass: 1+16=17 g/mol

Molar mass: 34 g/mol

n = 34/17 = 2 

Molecular formula: H2O2

4.0Process to Determine the Molecular Formula from the Empirical Formula

Determine the Empirical Formula:

  • Start with the per cent composition or the masses of each element in the compound.
  • Convert these masses to moles.
  • Find the simplest whole-number ratio of the elements, which gives you the empirical formula.

Calculate the Empirical Formula Mass:

  • Add up the atomic masses of all the elements in the empirical formula. This gives you the empirical formula mass.

Determine the Molecular Weight (Molar Mass) of the Compound:

  • The molar mass (usually given in the problem) is the actual mass of one mole of the compound.
  • This value is needed to relate the empirical formula to the molecular formula.

Find the Integer Multiple (n):

  • Use the formula:
  • This integer n tells you how many times the empirical formula must be multiplied to obtain the molecular formula.

Calculate the Molecular Formula:

  • Multiply each subscript in the empirical formula by the integer n.
  • The result gives the molecular formula.

Solved Example

Empirical formula: CH2

The molar mass of the compound: is 84 g/mol

Steps:

  1. Empirical Formula Mass:

Carbon (C): 12 g/mol

Hydrogen (H): 2×1 g/mol = 2 g/mol

Empirical formula mass = 12+2 = 14 g/mol

  1. Find the Integer Multiple n:

   n = 8414 = 6

  1. Determine the Molecular Formula:

Multiply each subscript in CH2 by 6.

Molecular formula: C6H12​.

5.0Differences Between Empirical and Molecular Formulas

Aspect

Empirical Formula

Molecular Formula

Definition

The simplest whole-number ratio of atoms in a compound.

The exact number of each type of atom in a molecule.

Information Provided

The basic proportion of elements in the compound.

Complete and detailed composition of the molecule.

Relation

A simplified form of the molecular formula.

Often a whole-number multiple of the empirical formula.

Example

CH2​ for ethene.

C2​H4​ for ethene.


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