Multiple Choice
What is the density of chlorine gas (Cl2) at 0.970 atm and 39.9°C in g/L, given that 1 bar = 0.98692 atm?
7. Gases
The Ideal Gas Law: Density
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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
Verified step by step guidance1
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.
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.
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 \( \rho = \frac{m}{V} = \frac{PM}{RT} \).
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 \( \rho = \frac{PM}{RT} \).
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.
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