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Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 47
Chapter 10, Problem 47

Rank the following gases from least dense to most dense at 101.33 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.
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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.
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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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Related Practice
Open Question
In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes, the average cockroach (running at 0.08 km/h) consumed 1.0 mL of O2 at 101.33 kPa pressure and 20 °C per gram of insect mass. (b) This same cockroach is caught by a child and placed in a 2.0-L fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, how much of the available O2 will the cockroach consume in 1 day? (Air is 21 mol % O2.)
Textbook Question

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes the average cockroach (running at 0.08 km/h) consumed 1.0 mL of O2 at 101.33 kPa pressure and 20 °C per gram of insect mass. (a) How many moles of O2 would be consumed in 1 day by a 6.3-g cockroach moving at this speed?

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Textbook Question

The physical fitness of athletes is measured by 'VO2 max,' which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a VO2 max of 45 mL O2/kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL O2/kg body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 85 kg and has a VO2 max reading of 47.5 mL O2/kg body mass/min. (b) If this man lost 10 kg, exercised, and increased his VO2 max to 65.0 mL O2/kg body mass/min, how many mL of oxygen would he consume in 1 hr?

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Textbook Question
Rank the following gases and vapors from least dense to most dense at 101.33 kPa and 298 K: water vapor 1H2O1g22, nitrogen 1N22, hydrogen sulfide 1H2S2.
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Textbook Question

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

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Textbook Question

(a) Calculate the density of NO2 gas at 0.970 atm and 35 °C.

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