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Chapter 5: Problem 27

Which noble gas has the smallest density at STP? Explain

Short Answer

Expert verified
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

01

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.
02

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
03

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.
04

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.

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Most popular questions from this chapter

Consider a sample of ideal gas molecules for the following question. a. How is the average kinetic energy of the gas molecules related to temperature? b. How is the average velocity of the gas molecules related to temperature? c. How is the average velocity of the gas molecules related to the molar mass of the gas at constant temperature?

Ideal gas particles are assumed to be volume less and to neither attract nor repel each other. Why are these assumptions crucial to the validity of Dalton’s law of partial pressures?

Equal moles of sulfur dioxide gas and oxygen gas are mixed in a flexible reaction vessel and then sparked to initiate the formation of gaseous sulfur trioxide. Assuming that the reaction goes to completion, what is the ratio of the final volume of the gas mixture to the initial volume of the gas mixture if both volumes are measured at the same temperature and pressure?

For scuba dives below 150 \(\mathrm{ft}\) , helium is often used to replace nitrogen in the scuba tank. If 15.2 \(\mathrm{g}\) of \(\mathrm{He}(g)\) and 30.6 \(\mathrm{g}\) of \(\mathrm{O}_{2}(g)\) are added to a previously evacuated 5.00 \(\mathrm{L}\) tank at \(22^{\circ} \mathrm{C},\) calculate the partial pressure of each gas present as well as the total pressure in the tank.

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