What is the density of NO_2 gas in a 4.50 L tank at 760.0 torr and 25.0 °C? (Express your answer in g/L.)

• A. 2.05 g/L
• B. 1.88 g/L
• C. 3.22 g/L
• D. 0.98 g/L

Answer: (B)

Verified step by step guidance

1. Identify the known variables: volume (V) = 4.50 L, pressure (P) = 760.0 torr, temperature (T) = 25.0 °C. Convert the temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
2. Convert the pressure from torr to atmospheres because the ideal gas constant R is commonly used in atm units. Use the conversion \$1\, \text{atm} = 760\, \text{torr}\(, so \)P(\text{atm}) = \frac{760.0\, \text{torr}}{760}$.
3. Use the ideal gas law equation \(PV = nRT\) to find the number of moles of NO\(_2\) gas. Rearrange the equation to solve for \(n\): \(n = \frac{PV}{RT}\), where \(R = 0.0821\, \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K}\).
4. Calculate the molar mass of NO\(_2\) by adding the atomic masses: nitrogen (N) = 14.01 g/mol and oxygen (O) = 16.00 g/mol. Since there are two oxygen atoms, molar mass = \$14.01 + 2 \times 16.00$ g/mol.
5. Find the mass of NO\(_2\) using \(\text{mass} = n \times \text{molar mass}\). Then calculate the density using \(\text{density} = \frac{\text{mass}}{\text{volume}}\) in g/L.