Calculate The Empirical Formula For Naphthalene

Calculating the Empirical Formula for Naphthalene: A Step-by-Step Guide

Naphthalene, a common aromatic hydrocarbon found in mothballs, provides an excellent example for learning how to determine empirical formulas from experimental data. This guide will walk you through the process, explaining the concepts involved and providing a detailed calculation. We'll delve into the theoretical underpinnings and demonstrate the practical application, ensuring a comprehensive understanding of this fundamental chemistry concept.

Understanding Empirical Formulas

Before diving into the naphthalene example, let's clarify the meaning of an empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound. It doesn't necessarily show the actual number of atoms present in a molecule (that's the molecular formula), but rather the ratio between them. For instance, the empirical formula for hydrogen peroxide (H₂O₂) is HO, reflecting the 1:1 ratio of hydrogen to oxygen atoms.

The Combustion Analysis Method

The most common method for determining the empirical formula of organic compounds like naphthalene is combustion analysis. In this technique, a precisely weighed sample of the compound is completely burned in an excess of oxygen. The products of combustion – typically carbon dioxide (CO₂) and water (H₂O) – are carefully collected and weighed. By analyzing the mass of CO₂ and H₂O produced, we can determine the mass of carbon and hydrogen present in the original sample.

Step-by-Step Calculation for Naphthalene

Let's assume we perform a combustion analysis on a 1.000-gram sample of naphthalene. After complete combustion, we collect 3.220 grams of CO₂ and 0.604 grams of H₂O. Now, let's calculate the empirical formula.

Step 1: Calculate the moles of Carbon and Hydrogen

• Carbon: The molar mass of CO₂ is 44.01 g/mol (12.01 g/mol for carbon + 2 * 16.00 g/mol for oxygen). The mass of carbon in the CO₂ produced is:

  (12.01 g C / 44.01 g CO₂) * 3.220 g CO₂ = 0.877 g C

  The number of moles of carbon is:

  0.877 g C / 12.01 g/mol = 0.0730 mol C

• Hydrogen: The molar mass of H₂O is 18.02 g/mol (2 * 1.01 g/mol for hydrogen + 16.00 g/mol for oxygen). The mass of hydrogen in the H₂O produced is:

  (2.02 g H / 18.02 g H₂O) * 0.604 g H₂O = 0.0676 g H

  The number of moles of hydrogen is:

  0.0676 g H / 1.01 g/mol = 0.0669 mol H

Step 2: Determine the Mole Ratio

To find the simplest whole-number ratio of carbon to hydrogen, we divide the number of moles of each element by the smallest number of moles:

• Carbon: 0.0730 mol / 0.0669 mol = 1.09 ≈ 1
• Hydrogen: 0.0669 mol / 0.0669 mol = 1

This gives us a preliminary ratio of approximately 1:1 for carbon and hydrogen. However, empirical formulas require whole numbers. The slight deviation from 1 for carbon is likely due to experimental error. We can round this up to the nearest whole number, giving us a ratio of 1:1.

Step 3: Write the Empirical Formula

Based on the mole ratio obtained, the empirical formula for naphthalene is CH.

Beyond the Empirical Formula: Determining the Molecular Formula

The empirical formula CH only gives us the simplest ratio of atoms. To determine the actual molecular formula, we need additional information, specifically the molar mass of naphthalene. The molar mass of naphthalene is approximately 128 g/mol.

Let's compare the empirical formula mass (CH = 12.01 g/mol + 1.01 g/mol = 13.02 g/mol) to the molar mass:

128 g/mol / 13.02 g/mol ≈ 9.8

This means the molecular formula is approximately 9.8 times larger than the empirical formula. Rounding this to the nearest whole number (10) suggests that the molecular formula is C₁₀H₁₀. However, this isn't quite accurate. The actual molecular formula for naphthalene is C₁₀H₈. The slight discrepancy highlights the limitations of rounding and the importance of precise experimental data.

Sources of Error in Combustion Analysis

It's crucial to acknowledge potential sources of error that can affect the accuracy of the empirical formula calculation:

• Incomplete Combustion: If the combustion is not complete, some carbon may remain as soot, leading to an underestimation of the carbon content.
• Impurities in the Sample: Impurities in the naphthalene sample can affect the results, leading to inaccurate calculations.
• Instrumental Errors: Errors in the weighing of the sample and the products can also affect the results.
• Rounding Errors: Rounding off numbers during calculations can introduce small inaccuracies.

Importance of Empirical Formulas

Determining the empirical formula is a fundamental step in identifying unknown compounds. It provides valuable information about the relative amounts of different elements present in a substance. This information is often used in conjunction with other analytical techniques like spectroscopy to fully characterize a compound and establish its molecular formula and structure.

Conclusion

Calculating the empirical formula for naphthalene, using the combustion analysis method, showcases a crucial skill in chemistry. While our example highlighted a simplified calculation, real-world scenarios involve more complex calculations and potentially larger errors. Understanding the underlying principles and potential pitfalls is essential for accurately determining the empirical formula and ultimately, the molecular structure of compounds. Remember, meticulous laboratory techniques and careful analysis of data are key to minimizing experimental errors and obtaining reliable results.