An unknown compound has the following chemical formula: where \( x \) stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 8.7 mol of nitrogen and 13.2 mol of oxygen. Write the complete chemical formula for the unknown compound.

To determine the complete chemical formula for the unknown compound, we need to find the ratio of nitrogen (N) to oxygen (O) in the sample. Given: - Moles of nitrogen (N) = 8.7 mol - Moles of oxygen (O) = 13.2 mol Next, we can find the simplest whole number ratio of nitrogen to oxygen by dividing both values by the smaller number of moles, which is 8.7 mol. 1. Calculate the ratio for nitrogen: \[ \text{Ratio of N} = \frac{8.7 \, \text{mol}}{8.7 \, \text{mol}} = 1 \] 2. Calculate the ratio for oxygen: \[ \text{Ratio of O} = \frac{13.2 \, \text{mol}}{8.7 \, \text{mol}} \approx 1.52 \] Now, we need to convert the ratio of oxygen to a whole number. Since 1.52 is approximately 1.5, we can multiply both ratios by 2 to eliminate the fraction: - For nitrogen: \( 1 \times 2 = 2 \) - For oxygen: \( 1.5 \times 2 = 3 \) Thus, the ratio of nitrogen to oxygen is 2:3. Therefore, the complete chemical formula for the unknown compound is: \[ \text{N}_2\text{O}_3 \]