Rank the following gases and vapors from least dense to most dense at 101.33 kPa and 298 K: water vapor 1H2O1g22, nitrogen 1N22, hydrogen sulfide 1H2S2.

Verified step by step guidance

1. Step 1: The density of a gas can be calculated using the Ideal Gas Law, which is PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. However, we need to rearrange this equation to solve for density (d), which is mass (m) divided by volume (V). So, the equation becomes d = m/V = (n*M)/V, where M is the molar mass of the gas.
2. Step 2: We can substitute the Ideal Gas Law (PV = nRT) into the density equation to get d = (n*M)/V = (P*M)/(RT). This equation tells us that the density of a gas is directly proportional to its molar mass (M) and pressure (P), and inversely proportional to the temperature (T).
3. Step 3: In this problem, the pressure (P) and temperature (T) are the same for all gases, so we can ignore them when comparing densities. Therefore, the density of each gas is directly proportional to its molar mass.
4. Step 4: Calculate the molar mass of each gas. The molar mass of water vapor (H2O) is approximately 18 g/mol, the molar mass of nitrogen (N2) is approximately 28 g/mol, and the molar mass of hydrogen sulfide (H2S) is approximately 34 g/mol.
5. Step 5: Rank the gases from least dense to most dense based on their molar masses. The gas with the smallest molar mass will be the least dense, and the gas with the largest molar mass will be the most dense. Therefore, the order from least dense to most dense is water vapor (H2O), nitrogen (N2), and hydrogen sulfide (H2S).

Key Concepts

Density of Gases

Density is defined as mass per unit volume and is a critical property of gases. It can be influenced by temperature and pressure, as described by the ideal gas law. At a constant temperature and pressure, gases with higher molar masses will generally have higher densities.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for comparing the densities of different gases, as gases with higher molar masses tend to be denser. For example, water vapor (H2O) has a molar mass of about 18 g/mol, while hydrogen sulfide (H2S) has a molar mass of about 34 g/mol.

Ideal Gas Law

The ideal gas law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. This law helps predict the behavior of gases under various conditions and is useful for calculating density when rearranged to D = PM/RT, where D is density, P is pressure, M is molar mass, and T is temperature.