Determine the Empirical Formula of a Compound with Given Percentages: A Comprehensive Guide

When analyzing the composition of a compound, one of the most important tasks is to determine its empirical formula. This involves finding the simplest whole-number ratio of the atoms present in the compound. In this guide, we discuss the methodology to derive the empirical formula of a compound that contains 69.9% carbon (C), 6.86% hydrogen (H), and 23.3% oxygen (O). We will follow a step-by-step approach, illustrating each process with detailed calculations.

1. Understanding the Process

Before determining the empirical formula, it is necessary to perform a combustion experiment on a small sample of the given material. The main elements of interest are C, N, and H. The element O is often determined by subtracting the sum of the given percentages of C and H from 100%.

2. Steps to Determine the Empirical Formula

2.1. Assumption of a 100g Sample

We start by assuming that we have a 100g sample of the compound. This assumption simplifies the calculations significantly:

Carbon (C): 69.9g Hydrogen (H): 6.86g Oxygen (O): 23.3g (100 - 69.9 - 6.86 23.3)

2.2. Conversion of Mass to Moles

The next step is to convert each element's mass into the number of moles. The molar mass of each element is as follows:

Carbon (C): 12.01g/mol Hydrogen (H): 1.01g/mol Oxygen (O): 16.00g/mol

Using the formula Moles Mass / Molar Mass, we can calculate the moles for each element:

Moles of Carbon (C) 69.9g / 12.01g/mol 5.82 moles Moles of Hydrogen (H) 6.86g / 1.01g/mol 6.80 moles Moles of Oxygen (O) 23.3g / 16.00g/mol 1.46 moles

2.3. Deriving the Simplest Whole-Number Ratio

Next, we divide each mole value by the smallest mole value (1.46 moles for Oxygen) to find the simplest whole-number ratio:

C: 5.82 moles / 1.46 moles 3.98 ≈ 4 H: 6.80 moles / 1.46 moles 4.66 ≈ 4.7 O: 1.46 moles / 1.46 moles 1

Since we are aiming for whole numbers, we can round the ratios to the nearest integers. However, because 4.7 is not a whole number, we may need to multiply the entire ratio by 2 to obtain a simple whole number ratio:

2.4. Adjusting to Whole Numbers

Multiplying the entire ratio by 2 gives us:

C: 4 * 2 8 H: 4.7 * 2 ≈ 9.4 ≈ 9 O: 1 * 2 2

Thus, the empirical formula of the compound is C8H10O2.

3. Conclusion

Through the series of steps outlined in this guide, we have demonstrated how to determine the empirical formula of a compound given its percentage composition. This method involves converting the mass of each element into moles, finding the simplest whole-number ratio, and adjusting the ratios to obtain whole numbers if necessary.

4. Additional Resources

For further information, you can explore additional resources such as textbooks on organic chemistry, online calculators for empirical formulas, and academic papers on the topic. These resources can provide deeper insights and practical applications of the empirical formula in various scientific fields.