Multiple Choice
Using the Ideal Gas Law, calculate the density in g/L of chlorine gas at 39.5 °C and a pressure of 1.95 atm. (Molar mass of Cl₂ = 70.90 g/mol)
7. Gases
The Ideal Gas Law: Density
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What is the density of hydrogen sulfide (H₂S) at 1.7 atm and 265 K? Answer in units of g/L.
A
0.98 g/L
B
1.52 g/L
C
2.34 g/L
D
3.10 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 the number of moles \( n \) in terms of mass \( m \) and molar mass \( M \): \( n = \frac{m}{M} \). Substitute this into the ideal gas law to get \( PV = \frac{m}{M}RT \).
Rearrange the equation to solve for density \( \rho \), which is mass per unit volume \( \rho = \frac{m}{V} \): \( \rho = \frac{PM}{RT} \).
Identify the values needed: \( P = 1.7 \) atm, \( T = 265 \) K, and the molar mass \( M \) of hydrogen sulfide \( H_2S \). Calculate \( M \) using the atomic masses: \( M = 2 \times 1.01 + 32.07 \) g/mol.
Use the ideal gas constant \( R = 0.0821 \) L atm/mol K. Substitute all known values into the density equation \( \rho = \frac{PM}{RT} \) to find the density in g/L.
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