A pure compound is found to have the following percent composition: 40.44% C, 7.92%H,
35.92%O, and 15.72%N. Determine the empirical formula of this compound

To find the empirical formula, we can use the percent composition of each element to determine the simplest whole-number ratio of atoms in the compound. Here’s a step-by-step solution:

1. **Assume a 100 g sample:**  
   This assumption allows us to directly use the percentages as grams:
   - Carbon (C): \( 40.44 \, \text{g} \)
   - Hydrogen (H): \( 7.92 \, \text{g} \)
   - Oxygen (O): \( 35.92 \, \text{g} \)
   - Nitrogen (N): \( 15.72 \, \text{g} \)

2. **Convert grams to moles:**  
   Use each element's molar mass to convert grams to moles.
   - Carbon: \( \frac{40.44 \, \text{g}}{12.01 \, \text{g/mol}} = 3.37 \, \text{mol} \)
   - Hydrogen: \( \frac{7.92 \, \text{g}}{1.008 \, \text{g/mol}} = 7.86 \, \text{mol} \)
   - Oxygen: \( \frac{35.92 \, \text{g}}{16.00 \, \text{g/mol}} = 2.25 \, \text{mol} \)
   - Nitrogen: \( \frac{15.72 \, \text{g}}{14.01 \, \text{g/mol}} = 1.12 \, \text{mol} \)

3. **Find the simplest whole-number ratio:**  
   To do this, divide each mole value by the smallest mole quantity:
   - Carbon: \( \frac{3.37}{1.12} \approx 3 \)
   - Hydrogen: \( \frac{7.86}{1.12} \approx 7 \)
   - Oxygen: \( \frac{2.25}{1.12} \approx 2 \)
   - Nitrogen: \( \frac{1.12}{1.12} \approx 1 \)

4. **Write the empirical formula:**  
   The simplest whole-number ratio is \( \text{C}_3\text{H}_7\text{O}_2\text{N} \), so the empirical formula is:

   \[
   \text{C}_3\text{H}_7\text{O}_2\text{N}
   \]

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Would you like a deeper explanation of any steps?

Here are related questions you might find interesting:

1. How would you calculate the molecular formula if the molar mass of the compound is given?
2. What are some real-world applications of empirical formula calculations?
3. How do you determine empirical formulas when dealing with hydrates?
4. How does empirical formula differ from molecular formula?
5. Can empirical formulas be fractions or non-integers?

**Tip:** Always double-check your mole ratios by dividing each result by the smallest number of moles to simplify to whole numbers accurately.

A pure compound is found to have the following percent composition: 40.44% C, 7.92% H, 35.92% O, and 15.72% N. Determine the empirical formula of this compound.

Learn how to calculate the empirical formula of a compound with a percent composition of 40.44% carbon, 7.92% hydrogen, 35.92% oxygen, and 15.72% nitrogen. This detailed step-by-step guide covers mole conversions and the simplest whole-number ratio to determine the empirical formula, ideal for high school chemistry students.

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