Rank the following gases from least dense to most dense at101.33 kPa and 298 K: O2, Ar, NH3, HCl.

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Step 1: Recall that the density of a gas can be calculated using the equation: Density = (Pressure * Molar mass) / (R * Temperature). Here, R is the ideal gas constant, which is 8.314 J/(mol*K) in SI units.

Step 2: Identify the molar mass of each gas. The molar mass of O2 is 32 g/mol, Ar is 39.95 g/mol, NH3 is 17.03 g/mol, and HCl is 36.46 g/mol.

Step 3: Substitute the given pressure (101.33 kPa), temperature (298 K), and the molar mass of each gas into the density equation. Remember to convert the pressure from kPa to Pa by multiplying by 1000, as the SI unit for pressure is Pa (Pascal).

Step 4: After substituting the values into the equation, you will get four different density values for the four gases. Do not calculate these values, but understand that the gas with the smallest molar mass will have the smallest density, and the gas with the largest molar mass will have the largest density.

Step 5: Based on the molar masses, rank the gases from least dense to most dense. The order should be NH3 (smallest molar mass), O2, HCl, and Ar (largest molar mass).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density of Gases

Density is defined as mass per unit volume. For gases, density can be influenced by temperature and pressure. At a constant temperature and pressure, the density of a gas is directly proportional to its molar mass. Thus, understanding how to calculate and compare the densities of different gases is essential for ranking them.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. This law can be used to derive the density of a gas by rearranging it to the form ρ = PM/RT, where ρ is density, P is pressure, M is molar mass, R is the ideal gas constant, and T is temperature. This relationship is crucial for determining the densities of the gases in the question.

Molar Mass of Gases

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Different gases have different molar masses, which directly affect their densities. For example, O2 has a molar mass of about 32 g/mol, while Ar is approximately 40 g/mol. Knowing the molar masses of the gases in the question allows for accurate density comparisons.

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