Question

Which noble gas has the smallest density at STP? Explain

Short answer

Helium (He) has the smallest density at STP among the noble gases because it has the smallest molar mass (4 g/mol), and density is directly proportional to molar mass at STP.

Step-by-step solution

Recall the relationship between density, molar mass, and STP conditions

Density at STP is directly proportional to the molar mass of a gas. This means that a gas with a lower molar mass will have a lower density at STP. Mathematically, this relationship can be expressed as follows: Density (D) = (Molar mass (M) × Pressure (P)) / (Ideal Gas Constant (R) × Temperature (T)) In this exercise, we want to compare the densities of noble gases at STP, meaning that Pressure (P) = 1 atm, and Temperature (T) = 273.15K. Since P, R, and T remain constant, the density is directly proportional to molar mass: D ∝ M.

Determine the molar masses of the noble gases

We will now determine the molar masses of the following noble gases: 1. Helium (He) 2. Neon (Ne) 3. Argon (Ar) 4. Krypton (Kr) 5. Xenon (Xe) 6. Radon (Rn) You can find the molar masses by referring to the periodic table. They are as follows: 1. Helium (He) - 4 g/mol 2. Neon (Ne) - 20 g/mol 3. Argon (Ar) - 40 g/mol 4. Krypton (Kr) - 84 g/mol 5. Xenon (Xe) - 131 g/mol 6. Radon (Rn) - 222 g/mol

Identify the noble gas with the smallest molar mass

Compare the molar masses of the noble gases from Step 2: - Helium (He) - 4 g/mol - Neon (Ne) - 20 g/mol - Argon (Ar) - 40 g/mol - Krypton (Kr) - 84 g/mol - Xenon (Xe) - 131 g/mol - Radon (Rn) - 222 g/mol From the comparison, we can see that Helium (He) has the smallest molar mass of 4 g/mol.

Conclude which noble gas has the smallest density

Since density at STP is directly proportional to molar mass, and Helium (He) has the smallest molar mass among the noble gases, we can conclude that Helium (He) has the smallest density at STP.

Key concepts

Density

Density is a measure of how much mass is contained in a given volume. For gases, especially noble gases at standard temperature and pressure (STP), the density helps us understand how the mass of an individual gas compares to its volume. The relationship between mass, volume, and density is simple:

• Density (D) = Mass/Volume

At STP, where the conditions are fixed, density depends directly on the molar mass of the gas. The lower the molar mass, the lower the density, given that all other factors remain constant. This is crucial for understanding why different gases have different densities even in similar conditions.

Molar Mass

Molar mass is a key concept in understanding how different gases behave under similar conditions. It represents the mass of one mole of a given substance and is typically expressed in grams per mole (g/mol). Each noble gas has a distinct molar mass, found in the periodic table, which directly affects its density at STP. Helium, for example, has a molar mass of 4 g/mol while Xenon has a molar mass of 131 g/mol.
In the context of density, a lower molar mass correlates to a lower density; this is why helium, with the lowest molar mass among noble gases, also has the smallest density at STP.

STP Conditions

STP stands for Standard Temperature and Pressure, which provides a baseline set of conditions for scientists and engineers to carry out calculations and experiments. At STP, the temperature is set at 273.15 K (0°C) and the pressure at 1 atmosphere (atm). These conditions are crucial since they allow us to standardize measurements and facilitate comparisons between different gases.
When comparing the density of noble gases, STP offers a level playing field, removing variables such as differing temperatures and pressures so we can focus solely on the inherent properties of the gases, like density and molar mass.

Ideal Gas Law

The Ideal Gas Law is a pivotal equation in chemistry, represented as \[ PV = nRT \]where:

• P is the pressure
• V is the volume
• n is the number of moles
• R is the ideal gas constant
• T is the temperature

This law helps describe the behavior of ideal gases by connecting pressure, volume, and temperature with the number of moles of a gas. At STP, understanding this relationship helps simplify how we determine gas density since many variables are constant.
By rearranging the equation, we see that the density of a gas can be expressed in terms of its molar mass: \[ D = \frac{M \cdot P}{R \cdot T} \]At STP, this simplifies further, emphasizing the dependency of density on molar mass, which is particularly useful when comparing gases like the noble gases.