Understanding Empirical Formulas from Percent Composition

In chemistry, the empirical formula of a compound represents the simplest whole-number ratio of the elements present in that compound. Often, we start with a percent composition—indicating the mass percentage of each element in the compound—and use that information to derive the empirical formula. Below are three diverse examples that illustrate this process.

Example 1: Determining the Empirical Formula of a Hydrocarbon

Context

Hydrocarbons are organic compounds consisting solely of hydrogen and carbon. Understanding their empirical formulas is essential in fields like petrochemistry and organic synthesis.

To find the empirical formula of a hydrocarbon that is 85.7% carbon and 14.3% hydrogen, we can follow these steps:

1. Convert Percent to Mass: Assume we have 100 g of the compound. This means there are 85.7 g of carbon and 14.3 g of hydrogen.

2. Convert Mass to Moles:

   • Moles of Carbon = 85.7 g / 12.01 g/mol = 7.13 mol
   • Moles of Hydrogen = 14.3 g / 1.008 g/mol = 14.17 mol

3. Find the Simplest Ratio:

   • Divide both by the smaller number of moles:
   • Carbon: 7.13 mol / 7.13 = 1
   • Hydrogen: 14.17 mol / 7.13 = 1.98 (approximately 2)
4. Write the Empirical Formula: Therefore, the empirical formula is CH₂.

Notes

• This process can be applied to any hydrocarbon, and the empirical formula gives insight into its reactivity and properties.

Example 2: Analyzing a Metal Oxide

Context

Metal oxides play a significant role in various industrial processes, including metallurgy and catalysis. Knowing their empirical formulas can assist in understanding their characteristics.

Consider a metal oxide composed of 63.5% iron and 36.5% oxygen. We can determine its empirical formula through the following steps:

1. Convert Percent to Mass: For 100 g of the compound, we have 63.5 g of iron and 36.5 g of oxygen.

2. Convert Mass to Moles:

   • Moles of Iron = 63.5 g / 55.85 g/mol = 1.14 mol
   • Moles of Oxygen = 36.5 g / 16.00 g/mol = 2.28 mol

3. Find the Simplest Ratio:

   • Divide both by the smaller number of moles:
   • Iron: 1.14 mol / 1.14 = 1
   • Oxygen: 2.28 mol / 1.14 = 2
4. Write the Empirical Formula: The empirical formula for this metal oxide is FeO₂.

Notes

• This empirical formula can indicate the oxidation state of the metal in the compound, which is crucial for understanding its chemical behavior.

Example 3: Formulating a Salt Compound

Context

Salts are ionic compounds resulting from the neutralization of acids and bases. Knowing the empirical formula is vital for stoichiometric calculations in chemistry.

Let’s analyze a salt that is composed of 39.1% sodium and 60.9% chlorine. The steps to find its empirical formula are:

1. Convert Percent to Mass: For 100 g of the compound, we have 39.1 g of sodium and 60.9 g of chlorine.

2. Convert Mass to Moles:

   • Moles of Sodium = 39.1 g / 22.99 g/mol = 1.70 mol
   • Moles of Chlorine = 60.9 g / 35.45 g/mol = 1.72 mol

3. Find the Simplest Ratio:

   • Divide both by the smaller number of moles:
   • Sodium: 1.70 mol / 1.70 = 1
   • Chlorine: 1.72 mol / 1.70 = 1.01 (approximately 1)
4. Write the Empirical Formula: Thus, the empirical formula is NaCl.

Notes

• This example represents table salt, which is a common compound used in everyday life and highlights the importance of empirical formulas in practical scenarios.