What is the density (in g/L) of a sample of N_2 gas at 70.0 °C and 2.50 atm pressure? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 0.98 g/L
• B. 3.45 g/L
• C. 1.12 g/L
• D. 2.86 g/L

Answer: (D)

Verified step by step guidance

1. Identify the known variables: pressure \(P = 2.50\) atm, temperature \(T = 70.0\ ^\circ\mathrm{C}\), and the gas constant \(R = 0.0821\ \mathrm{L \cdot atm \cdot mol^{-1} \cdot K^{-1}}\). Also, note that the gas is nitrogen (\(\mathrm{N_2}\)), so find its molar mass \(M\) (approximately 28.0 g/mol).
2. Convert the temperature from Celsius to Kelvin using the formula: \(T(K) = T(^\circ C) + 273.15\). This is necessary because the ideal gas law requires temperature in Kelvin.
3. Use the ideal gas law in the form that relates density \(d\) to pressure, molar mass, gas constant, and temperature: \(d = \frac{PM}{RT}\) where \(d\) is the density in g/L, \(P\) is pressure in atm, \(M\) is molar mass in g/mol, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
4. Substitute the known values of \(P\), \(M\), \(R\), and \(T\) into the equation to set up the calculation for density.
5. Perform the calculation to find the density \(d\) in g/L. This will give you the density of nitrogen gas under the given conditions.