What is the density of NO_2(g) at 50^ext{o}C and 0.85 atm? (R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 1.32 g/L
• B. 0.98 g/L
• C. 0.56 g/L
• D. 2.05 g/L

Answer: (A)

Verified step by step guidance

1. Identify the known variables: temperature (T) = 50\degree C, pressure (P) = 0.85 atm, and the gas constant (R) = 0.0821 L\cdot atm\cdot mol^{-1}\cdot K^{-1}. Convert the temperature to Kelvin using the formula \(T(K) = T(\degree C) + 273.15\).
2. Recall the ideal gas law in the form \(PV = nRT\), and understand that density (\(\rho\)) is mass per unit volume, \(\rho = \frac{m}{V}\). We want to express density in terms of pressure, temperature, and molar mass.
3. Express the number of moles \(n\) as \(n = \frac{m}{M}\), where \(m\) is the mass and \(M\) is the molar mass of NO\(_2\). Substitute \(n\) into the ideal gas law to get \(P V = \frac{m}{M} R T\).
4. Rearrange the equation to solve for density \(\rho = \frac{m}{V}\): multiply both sides by \(\frac{M}{V}\) and rearrange to get \(\rho = \frac{P M}{R T}\).
5. Calculate the molar mass \(M\) of NO\(_2\) by adding the atomic masses of nitrogen and oxygen atoms. Then, plug in the values for \(P\), \(M\), \(R\), and \(T\) into the density formula \(\rho = \frac{P M}{R T}\) to find the density in g/L.