Problem 25 - Chemistry An Atoms First Approach

Question

Which noble gas has the smallest density at STP? Explain.

Step-by-Step Solution

Answer

Helium (He) has the smallest density among the noble gases at standard temperature and pressure (STP) because it has the lowest molar mass (4.0026 g/mol) compared to other noble gases. At STP, the density of a gas is directly proportional to its molar mass, and since helium has the smallest molar mass, it also has the smallest density.

Step 1: Identify the noble gases

Noble gases are found in Group 18 of the periodic table. These elements are known for their low reactivity due to their stable electron configurations. The noble gases are: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

Step 2: Understand the relationship between molar mass and density at STP

Density (\( \rho \)) is defined as mass per unit volume. At standard temperature and pressure, the density of a gas can be calculated using the formula: \[ \rho = \frac{molar~mass}{molar~volume} \] where molar mass is given in grams per mole and molar volume is typically represented as 22.4 L/mol for any ideal gas at STP.

Step 3: Compare the molar masses of the noble gases

The molar masses of the noble gases are as follows: - Helium (He): 4.0026 g/mol - Neon (Ne): 20.1797 g/mol - Argon (Ar): 39.948 g/mol - Krypton (Kr): 83.798 g/mol - Xenon (Xe): 131.293 g/mol - Radon (Rn): 222 g/mol

Step 4: Determine the noble gas with the smallest density at STP

Comparing the molar masses of the noble gases, we can see that helium (He) has the smallest molar mass. Since the molar volume at STP is the same for all ideal gases, a smaller molar mass will result in a smaller density. Therefore, helium (He) has the smallest density among the noble gases at standard temperature and pressure.