What is the density in g/L of laughing gas, dinitrogen monoxide (N₂O), at a temperature of 321 K and a pressure of 131 kPa, using the Ideal Gas Law?

• A. 3.12 g/L
• B. 1.96 g/L
• C. 0.98 g/L
• D. 2.45 g/L

Answer: (B)

Verified step by step guidance

1. Start by recalling the Ideal Gas Law, which is given by the equation: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. To find the density \( \rho \) in g/L, we need to express it in terms of mass \( m \) and volume \( V \). Density is defined as \( \rho = \frac{m}{V} \).
3. We can relate the number of moles \( n \) to the mass \( m \) and molar mass \( M \) of the gas using the equation \( n = \frac{m}{M} \). Substitute this into the Ideal Gas Law to get \( PV = \frac{m}{M}RT \).
4. Rearrange the equation to solve for density: \( \rho = \frac{m}{V} = \frac{PM}{RT} \). This equation allows us to calculate the density directly from the pressure, molar mass, and temperature.
5. Substitute the given values into the equation: \( P = 131 \text{ kPa} \), \( T = 321 \text{ K} \), and the molar mass of \( N_2O \) is approximately 44.01 g/mol. Use the ideal gas constant \( R = 8.314 \text{ J/(mol K)} \) and convert pressure to the appropriate units if necessary. Calculate the density using \( \rho = \frac{PM}{RT} \).