Two 112 L tanks are filled with gas at 330 K . One contains 5.00 mol of Kr , and the other conta

step 1 So in this question, we're asked to compare Krypton and oxygen. And they're in two tanks that ha

Two 112 L tanks are filled with gas at 330 K . One contains...

Two 112 L tanks are filled with gas at 330 $\mathrm{K}$ . One contains 5.00 mol of $\mathrm{Kr}$ , and the other contains 5.00 $\mathrm{mol}$ of $\mathrm{O}_{2}$ Considering the assumptions of kinetic-molecular theory, rank the gases from low to high for each of the following properties: $\begin{array}{ll}{\text { (a) collision frequency }} & {\text { (b) density }(\mathrm{g} / \mathrm{L})} \\ {\text { (c) average speed }} & {\text { (d) pressure }}\end{array}$

Two 112 L tanks are filled with gas at 330 $\mathrm{K}$ . One contains 5.00 mol of $\mathrm{Kr}$ , and the other contains 5.00 $\mathrm{mol}$ of $\mathrm{O}_{2}$ Considering the assumptions of kinetic-molecular theory, rank the gases from low to high for each of the following properties:
$\begin{array}{ll}{\text { (a) collision frequency }} & {\text { (b) density }(\mathrm{g} / \mathrm{L})} \\ {\text { (c) average speed }} & {\text { (d) pressure }}\end{array}$

Key Concepts

Kinetic Molecular Theory

This theory provides the foundation for understanding gas behavior by assuming that gas molecules are point particles in constant, random motion, and that collisions between them are elastic. It underlies many gas properties including pressure, temperature, and the frequency of molecular collisions, serving as a framework for the ideal gas approximation.

Collision Frequency

Collision frequency refers to the number of collisions a molecule makes per unit time. It depends on factors such as the speed of the molecules, the number density (molecules per volume), and the effective cross-sectional area of the molecules. This concept helps predict how often gas particles interact, which in turn influences macroscopic properties like pressure.

Density

Density in the context of gases is defined as the mass per unit volume. It is directly influenced by the molar mass of the gas and the conditions of pressure and temperature. For gases under the same conditions (same volume, temperature, and number of moles), a heavier molecule results in a higher density.

Maxwell-Boltzmann Distribution and Average Speed

The Maxwell-Boltzmann distribution describes the spread of molecular speeds in a gas. At a given temperature, lighter molecules tend to move faster on average than heavier ones because the average (or root-mean-square) speed is inversely proportional to the square root of the molecular mass. This concept is key for understanding variations in kinetic properties between different gases.

Ideal Gas Law and Pressure

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. Under identical conditions of temperature, volume, and mole number, different gases will exert the same pressure regardless of molecular mass, illustrating that pressure is a collective effect of molecular collisions rather than an individual property of the gas molecules.

Transcript

00:03 So in this question, we're asked to compare krypton and oxygen.

00:08 And they're in two tanks that have the exact same volume and the exact same temperature.

00:14 And we're asked to compare each of these properties.

00:18 So i'm going to bring it a step further.

00:20 And i'm going to say, let's assume that these tanks are as identical as they can possibly be, with the exception that one is krypton and the other is oxygen.

00:32 So assume that every particle is in exactly the same place and moving in exactly the same direction at the beginning of the experiment.

00:44 Perfectly identical containers, just that one of them happens to be oxygen and the other is krypton.

00:49 Obviously, this is theoretically impossible, but everything is going to average out, so it should be something that we can imagine is identical to get started.

00:59 And i'm actually going to come back to a.

01:01 I'm going to start with b.

01:04 So we have the same number of particles.

01:06 We have the same volume, which means that the particles are in the exact same space.

01:14 We have the same number of particles per unit volume.

01:17 However, the krypton is heavier.

01:22 Every particle of krypton is heavier than the corresponding particle of oxygen gas.

01:28 So in this case, the density of o2 is going to be less than that of krypton, because we have less mass for the oxygen in the same amount of space...

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