Calculate to three significant digits the density of dinitrogen difluoride gas at exactly \( -20^{\circ} \mathrm{C} \) and exactly 1 atm , You can assume dinitrogen difluoride gas behaves as an ideal gas under these conditions. (I) \( \frac{\mathrm{g}}{\mathrm{L}} \)

To calculate the density (\( \rho \)) of dinitrogen difluoride (\( \text{N}_2\text{F}_2 \)) gas under the given conditions, we'll use the ideal gas law and the relationship between density and the ideal gas equation. ### Given: - **Temperature (\( T \))**: \( -20^\circ\text{C} = 253.15\ \text{K} \) - **Pressure (\( P \))**: \( 1\ \text{atm} \) - **Molar Mass (\( M \)) of \( \text{N}_2\text{F}_2 \)**: \[ \text{M} = 2 \times 14.01\ \text{g/mol (N)} + 2 \times 19.00\ \text{g/mol (F)} = 66.02\ \text{g/mol} \] - **Ideal Gas Constant (\( R \))**: \( 0.082057\ \text{L atm/mol K} \) ### Formula: The density of an ideal gas can be calculated using the formula: \[ \rho = \frac{PM}{RT} \] ### Calculation: 1. **Plugging in the values**: \[ \rho = \frac{1\ \text{atm} \times 66.02\ \text{g/mol}}{0.082057\ \text{L atm/mol K} \times 253.15\ \text{K}} \] 2. **Calculate the denominator**: \[ RT = 0.082057 \times 253.15 \approx 20.7727\ \text{L atm/mol} \] 3. **Calculate the density (\( \rho \))**: \[ \rho = \frac{66.02}{20.7727} \approx 3.18\ \text{g/L} \] ### Final Answer: The density of dinitrogen difluoride gas under the specified conditions is **3.18 g L⁻¹**. **Answer:** The density of dinitrogen difluoride under these conditions is 3.18 g L⁻¹