Which Pair Has The Same Empirical Formula

Which Pair Has the Same Empirical Formula? A Deep Dive into Chemical Composition

Determining which pairs of chemical compounds share the same empirical formula is a fundamental concept in chemistry. The empirical formula represents the simplest whole-number ratio of atoms of each element present in a compound. It doesn't necessarily reflect the actual number of atoms in a molecule (the molecular formula), but rather the relative proportions. Understanding how to calculate and compare empirical formulas is crucial for various applications, from identifying unknown substances to understanding stoichiometry in chemical reactions. This comprehensive guide will explore the concept in detail, providing examples and strategies for solving problems related to empirical formulas.

Understanding Empirical Formulas vs. Molecular Formulas

Before diving into comparing pairs of compounds, let's solidify the distinction between empirical and molecular formulas.

• Molecular Formula: This formula represents the actual number of atoms of each element present in one molecule of a compound. For example, the molecular formula for glucose is C₆H₁₂O₆.

• Empirical Formula: This formula represents the simplest whole-number ratio of atoms of each element in a compound. To find the empirical formula, we divide the subscripts in the molecular formula by their greatest common divisor. For glucose (C₆H₁₂O₆), the greatest common divisor of 6, 12, and 6 is 6. Dividing each subscript by 6 gives the empirical formula CH₂O.

Key Difference: A molecular formula provides the exact composition of a molecule, while an empirical formula only provides the relative ratios of atoms. Multiple compounds can share the same empirical formula but have different molecular formulas.

Calculating Empirical Formulas

To determine if two compounds have the same empirical formula, we must first know how to calculate the empirical formula from either the percent composition or the mass of each element present in a sample.

Method 1: Using Percent Composition

Assume we have a compound with the following percent composition:

• Carbon (C): 40%
• Hydrogen (H): 6.7%
• Oxygen (O): 53.3%

To calculate the empirical formula, follow these steps:

1. Assume a 100g sample: This simplifies the calculations, as the percentages directly translate to grams. So we have 40g C, 6.7g H, and 53.3g O.

2. Convert grams to moles: Use the molar mass of each element to convert grams to moles.

   • Moles of C = 40g / 12.01 g/mol ≈ 3.33 mol
   • Moles of H = 6.7g / 1.01 g/mol ≈ 6.63 mol
   • Moles of O = 53.3g / 16.00 g/mol ≈ 3.33 mol

3. Find the mole ratio: Divide each number of moles by the smallest number of moles to get the simplest whole-number ratio.

   • C: 3.33 mol / 3.33 mol = 1
   • H: 6.63 mol / 3.33 mol ≈ 2
   • O: 3.33 mol / 3.33 mol = 1

4. Write the empirical formula: The empirical formula is CH₂O.

Method 2: Using Mass Data

If you're given the mass of each element in a sample, you can follow a similar process. Let's say you have a sample containing:

• 2.4g of Magnesium (Mg)
• 1.6g of Oxygen (O)

1. Convert grams to moles:

   • Moles of Mg = 2.4g / 24.31 g/mol ≈ 0.099 mol
   • Moles of O = 1.6g / 16.00 g/mol = 0.100 mol

2. Find the mole ratio:

   • Mg: 0.099 mol / 0.099 mol ≈ 1
   • O: 0.100 mol / 0.099 mol ≈ 1

3. Write the empirical formula: The empirical formula is MgO.

Comparing Pairs of Compounds for Identical Empirical Formulas

Now, let's apply this knowledge to comparing pairs of compounds. Consider the following pairs:

Pair 1:

• Compound A: C₂H₄O₂ (Acetic Acid)
• Compound B: CH₂O (Formaldehyde)

To compare, we find the empirical formula for each compound.

• Compound A (Acetic Acid): The greatest common divisor of 2, 4, and 2 is 2. Dividing each subscript by 2 gives the empirical formula CH₂O.

• Compound B (Formaldehyde): The empirical formula is already in its simplest form: CH₂O.

Conclusion: Pair 1 has the same empirical formula (CH₂O).

Pair 2:

• Compound C: C₆H₁₂O₆ (Glucose)

• Compound D: C₁₂H₂₄O₁₂ (Sucrose)

• Compound C (Glucose): The empirical formula is CH₂O (as calculated earlier).

• Compound D (Sucrose): The greatest common divisor of 12, 24, and 12 is 12. Dividing each subscript by 12 gives the empirical formula CH₂O.

Conclusion: Pair 2 also has the same empirical formula (CH₂O).

Pair 3:

• Compound E: H₂O (Water)

• Compound F: H₂O₂ (Hydrogen Peroxide)

• Compound E (Water): The empirical formula is H₂O.

• Compound F (Hydrogen Peroxide): The empirical formula is HO.

Conclusion: Pair 3 does not have the same empirical formula.

Real-World Applications of Empirical Formulas

The concept of empirical formulas has several practical applications in various fields:

• Identifying Unknown Compounds: By determining the empirical formula of an unknown compound through elemental analysis, chemists can narrow down the possibilities and potentially identify the compound.

• Stoichiometry: In chemical reactions, the empirical formula provides the relative ratios of reactants and products, crucial for balancing equations and predicting yields.

• Polymer Chemistry: The empirical formula is used to represent the repeating units in polymers, allowing for the characterization and analysis of these large molecules.

• Geochemistry: The empirical formula is used extensively to describe the composition of minerals and rocks.

Advanced Considerations and Challenges

While calculating empirical formulas is generally straightforward, some challenges can arise:

• Hydrated Compounds: Compounds containing water molecules (hydrates) require careful consideration when calculating the empirical formula. The water molecules must be included in the analysis.

• Complex Compounds: Compounds with many elements or large subscripts can make the calculations more complex and prone to errors.

• Impurities: The presence of impurities in a sample can affect the accuracy of the empirical formula calculation.

Conclusion

Determining whether pairs of compounds share the same empirical formula is a crucial skill in chemistry. By understanding the difference between empirical and molecular formulas and mastering the calculation methods, one can confidently analyze and compare the compositions of various substances. The applications of empirical formulas extend across numerous scientific disciplines, highlighting its importance in chemical analysis and understanding the fundamental building blocks of matter. Remember to always double-check your calculations and consider potential sources of error to ensure accurate results.