What is the density of sulfur trioxide gas (SO3) at 315 K and 2.10 atm, given that the molar mass of SO3 is 80.07 g/mol?

• A. 3.12 g/L
• B. 1.98 g/L
• C. 4.05 g/L
• D. 2.68 g/L

Answer: (D)

Verified step by step guidance

1. Start by recalling the ideal gas law equation: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature.
2. To find the density, we need to express it in terms of mass per unit volume. Density (\( \rho \)) can be calculated using the formula \( \rho = \frac{m}{V} \), where \( m \) is mass and \( V \) is volume.
3. Using the ideal gas law, substitute \( n = \frac{m}{M} \) (where \( M \) is molar mass) into the equation to get \( PV = \frac{m}{M}RT \). Rearrange this to find \( \rho = \frac{m}{V} = \frac{PM}{RT} \).
4. Plug in the given values: \( P = 2.10 \) atm, \( M = 80.07 \) g/mol, \( R = 0.0821 \) L·atm/(mol·K), and \( T = 315 \) K into the density formula \( \rho = \frac{PM}{RT} \).
5. Calculate the density using the formula \( \rho = \frac{2.10 \times 80.07}{0.0821 \times 315} \) to find the density of sulfur trioxide gas in g/L.