Calculate to three significant digits the density of dinitrogen difluoride gas at exactly 30 °C and exactly 1 atm. You can assume dinitrogen
Answer
Density of Dinitrogen Difluoride (N₂F₂) Gas at 30 °C
🧪 Problem Statement
Calculate the density of dinitrogen difluoride gas (N₂F₂) at:
- Temperature: 30 °C
- Pressure: 1.00 atm
Assume the gas behaves as an ideal gas. Express the result in g/L and round to three significant digits.
📘 Theoretical Background
We use the density form of the ideal gas law:
d = (PM) / (RT)
Where:
- P = Pressure (atm)
- M = Molar mass of N₂F₂ = 66.00 g/mol
- R = Ideal gas constant = 0.0821 L·atm/mol·K
- T = Temperature in Kelvin = 30 °C + 273 = 303 K
📋 Given Values
| Quantity | Symbol | Value |
|---|---|---|
| Pressure | P | 1.00 atm |
| Temperature | T | 30 °C = 303 K |
| Molar Mass of N₂F₂ | M | 66.00 g/mol |
| Gas Constant | R | 0.0821 L·atm/mol·K |
🧮 Step-by-Step Calculation
Step 1: Plug into the formula
d = (1.00 × 66.00) / (0.0821 × 303)
Step 2: Compute the denominator
RT = 0.0821 × 303 = 24.8763
Step 3: Calculate the density
d = 66.00 / 24.8763 ≈ 2.653 g/L
✅ Final Answer
Density of N₂F₂ = 2.65 g/L (to three significant digits)
📌 Conclusion
At 30 °C and 1.00 atm, the density of dinitrogen difluoride gas (N₂F₂) is:
2.65 g/L
This result is obtained using the ideal gas law and is a reasonable approximation for gases at standard laboratory conditions.