Ch.10 - Gases

Problem 47

Previous problem

Next problem

Chapter 10, Problem 47

Rank the following gases from least dense to most dense at 1.00 atm and 298 K: CO, N2O, Cl2, HF.

Verified step by step guidance

Step 1: Recall that the density of a gas at a given temperature and pressure can be calculated using the formula: Density = (Molar mass * Pressure) / (R * Temperature). Here, R is the ideal gas constant, which is 0.0821 L*atm/(mol*K) in this case.

Step 2: Understand that the molar mass of a gas is directly proportional to its density under the same conditions of temperature and pressure. This means that the gas with the highest molar mass will be the most dense, and the gas with the lowest molar mass will be the least dense.

Step 3: Look up the molar masses of the given gases. The molar mass of CO is approximately 28 g/mol, N2O is approximately 44 g/mol, Cl2 is approximately 71 g/mol, and HF is approximately 20 g/mol.

Step 4: Rank the gases from least dense to most dense based on their molar masses. The gas with the lowest molar mass will be the least dense, and the gas with the highest molar mass will be the most dense.

Step 5: Therefore, the gases ranked from least dense to most dense at 1.00 atm and 298 K are: HF, CO, N2O, Cl2.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density of Gases

The density of a gas is defined as its mass per unit volume, typically expressed in grams per liter (g/L). It is influenced by the gas's molar mass and the conditions of temperature and pressure. At standard conditions, lighter gases have lower densities, while heavier gases have higher densities, which is crucial for ranking gases based on their density.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. This law helps in understanding how gases behave under different conditions and can be used to derive the density of a gas by rearranging the equation to find density as (PM)/(RT), where M is the molar mass.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in determining the density of gases, as heavier gases will generally have higher molar masses, leading to greater densities. For the gases in the question, calculating their molar masses allows for a direct comparison of their densities.

Recommended video:

Molar Mass Concept

Related Practice

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 55.0 gallons that contains O2 gas at a pressure of 16,500 kPa at 23°C. d. What would be the pressure of the gas, in kPa, if it were transferred to a container at 24°C whose volume is 55.0 L?

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 1 h the average cockroach running at 0.08 km/h consumed 0.8 mL of O2 at 1 atm pressure and 24°C per gram of insect mass. a. How many moles of O2 would be consumed in 1 h by a 5.2-g cockroach moving at this speed?

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.

981

views

Textbook Question

Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2,HBr,CO2.

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.

1663

views

Textbook Question

(a) Calculate the density of NO₂gas at 0.970 atm and 35 °C.

559

views