Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2,HBr,CO2.

Verified step by step guidance

1. Identify the formula for density of a gas: \( \text{Density} = \frac{\text{Molar Mass}}{\text{Molar Volume}} \). At standard conditions, the molar volume is 22.4 L/mol.
2. Calculate the molar mass of each gas: \( \text{SO}_2 \), \( \text{HBr} \), and \( \text{CO}_2 \).
3. For \( \text{SO}_2 \): Add the atomic masses of sulfur (S) and oxygen (O) from the periodic table: \( \text{Molar Mass of SO}_2 = 32.07 + 2 \times 16.00 \).
4. For \( \text{HBr} \): Add the atomic masses of hydrogen (H) and bromine (Br): \( \text{Molar Mass of HBr} = 1.01 + 79.90 \).
5. For \( \text{CO}_2 \): Add the atomic masses of carbon (C) and oxygen (O): \( \text{Molar Mass of CO}_2 = 12.01 + 2 \times 16.00 \).

Key Concepts

Density of Gases

The density of a gas is defined as its mass per unit volume, typically expressed in grams per liter (g/L). It is influenced by the gas's molar mass and the conditions of temperature and pressure. At a constant temperature and pressure, gases with higher molar masses will generally have higher densities.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. This law helps in understanding how gases behave under different conditions and can be used to derive relationships that affect density, such as the relationship between molar mass and density.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in determining the density of gases; substances with higher molar masses will generally be denser than those with lower molar masses when compared under the same conditions of temperature and pressure.