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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) 脳 Pressure (P)) / (Ideal Gas Constant (R) 脳 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 鈭� 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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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掳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.

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Most popular questions from this chapter

Consider three identical flasks filled with different gases. Flask \(\mathrm{A} : \mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{B} : \mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{C} : \mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?

As \(\mathrm{NH}_{3}(g)\) is decomposed into nitrogen gas and hydrogen gas at constant pressure and temperature, the volume of the product gases collected is twice the volume of \(\mathrm{NH}_{3}\) reacted. Explain. As \(\mathrm{NH}_{3}(g)\) is decomposed into nitrogen gas and hydrogen gas at constant volume and temperature, the total pressure increases by some factor. Why the increase in pressure and by what factor does the total pressure increase when reactants are completely converted into products? How do the partial pressures of the product gases compare to each other and to the initial pressure of \(\mathrm{NH}_{3}?\)

A gas sample containing 1.50 moles at \(25^{\circ} \mathrm{C}\) exerts a pressure of 400. torr. Some gas is added to the same container and the temperature is increased to 50\(\cdot^{\circ} \mathrm{C}\). If the pressure increases to 800. torr, how many moles of gas were added to the container? Assume a constant-volume container.

A 2.747 -g sample of manganese metal is reacted with excess \(\mathrm{HCl}\) gas to produce 3.22 \(\mathrm{L} \mathrm{H}_{2}(g)\) at 373 \(\mathrm{K}\) and 0.951 atm and a manganese chloride compound \(\left(\mathrm{Mn} \mathrm{Cl}_{x}\right)\). What is the formula of the manganese chloride compound produced in the reaction?

Consider the following reaction: $$4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$$ It takes 2.00 L of pure oxygen gas at STP to react completely with a certain sample of aluminum. What is the mass of aluminum reacted?
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