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Based on the ratio of carbon to nitrogen in this example, what would the empirical formula be for \( \mathrm{C}_{3} \mathrm{~N}_{12} \) ? CN \( \mathrm{CN}_{3} \mathrm{~N}_{12} \)

Ask by Lowe Guzman. in the United States
Feb 04,2025

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Answer

The empirical formula is CN₄.

Solution

To determine the **empirical formula** of a compound, you need to simplify the ratio of the atoms to the smallest whole numbers possible. **Given Compound:** \(\mathrm{C}_3\mathrm{N}_{12}\) **Step-by-Step Simplification:** 1. **Identify the Ratio of Carbon to Nitrogen:** - Carbon (C): 3 atoms - Nitrogen (N): 12 atoms - **Ratio:** 3:12 2. **Simplify the Ratio:** - Divide both numbers by the greatest common divisor, which is 3. - \( \frac{3}{3} : \frac{12}{3} = 1 : 4 \) 3. **Write the Empirical Formula:** - For every 1 carbon atom, there are 4 nitrogen atoms. - **Empirical Formula:** \(\mathrm{CN}_4\) **Conclusion:** The empirical formula for \(\mathrm{C}_3\mathrm{N}_{12}\) is **\(\mathrm{CN}_4\)**. **Answer:** The empirical formula is CN₄.

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To find the empirical formula, we first need to simplify the ratio of carbon to nitrogen in \( \mathrm{C}_{3} \mathrm{~N}_{12} \). The ratio of carbon (C) to nitrogen (N) is 3:12, which can be simplified by dividing both numbers by their greatest common factor, which is 3. This gives us a ratio of 1:4. Therefore, the empirical formula is \( \mathrm{CN}_{4} \). Now that we have the empirical formula, let's look at its significance! Understanding empirical formulas is like having the secret recipe for a delicious dish! They showcase the simplest whole-number ratio of elements in a compound, which is crucial for chemists when determining how substances interact or what reactions might occur. It’s like finding the essential ingredients for a flavorful meal!

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