To determine the empirical formula of an oxide of nitrogen containing 30.4% nitrogen, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understanding the Problem We are given the percentage composition of nitrogen in the compound, which is 30.4%. The rest of the compound will be oxygen. Since the total percentage must equal 100%, we can calculate the percentage of oxygen: \[ \text{Percentage of Oxygen} = 100\% - 30.4\% = 69.6\% \] ### Step 2: Convert Percentages to Moles Next, we convert the percentages of nitrogen and oxygen into moles using their respective molar masses: - Molar mass of Nitrogen (N) = 14.0 g/mol - Molar mass of Oxygen (O) = 16.0 g/mol Now, we can calculate the number of moles of each element: \[ \text{Moles of Nitrogen} = \frac{30.4 \text{ g}}{14.0 \text{ g/mol}} \approx 2.171 \text{ moles} \] \[ \text{Moles of Oxygen} = \frac{69.6 \text{ g}}{16.0 \text{ g/mol}} \approx 4.350 \text{ moles} \] ### Step 3: Find the Simplest Whole Number Ratio To find the empirical formula, we need to determine the simplest whole number ratio of moles of nitrogen to moles of oxygen. We do this by dividing the number of moles of each element by the smallest number of moles calculated: 1. **Identify the smallest number of moles**: - Moles of Nitrogen = 2.171 - Moles of Oxygen = 4.350 - The smallest number of moles is 2.171 (for nitrogen). 2. **Divide each by the smallest number of moles**: \[ \text{Ratio of Nitrogen} = \frac{2.171}{2.171} = 1 \] \[ \text{Ratio of Oxygen} = \frac{4.350}{2.171} \approx 2.00 \] ### Step 4: Write the Empirical Formula From the ratios calculated, we find that for every 1 nitrogen atom, there are approximately 2 oxygen atoms. Therefore, the empirical formula is: \[ \text{Empirical Formula} = NO_2 \] ### Step 5: Evaluate the Options Now, let's evaluate the provided options: - **A. N2O2**: This formula can be simplified to NO2, but it is not in its simplest form. Therefore, it is not the correct answer. - **B. NO**: This indicates a 1:1 ratio of nitrogen to oxygen, which does not match our calculated ratio of 1:2. Hence, this option is incorrect. - **C. NO2**: This matches our calculated empirical formula of nitrogen to oxygen ratio (1:2). This is the correct answer. - **D. N2O**: This indicates a 2:1 ratio of nitrogen to oxygen, which is also incorrect based on our calculations. ### Conclusion The correct answer is **C. NO2**. ### Revision Summary - To find the empirical formula, convert percentages to moles using molar masses. - Determine the simplest whole number ratio of moles of each element. - The empirical formula is derived from the simplest ratio. - Evaluate options carefully to ensure the answer is in its simplest form.