Volume kinetic molecular theory

Suppose that we double the length of each side of a rectangular box containing a gas. (a) What would happen to the volume (b) What would happen to the pressure (c) Explain the effect on the pressure on the basis of the kinetic molecular theory. 

While studying gases in this chapter you will consider four main physical properties—volume, pressure, temperature, and amount—and their interrelationships. These relationships, commonly called gas laws, show up quite often on the AP exam, so you will spend quite a bit of time working problems in this chapter. But before we start looking at the gas laws, let s look at the Kinetic Molecular Theory of Gases, the extremely useful model that scientists use to represent the gaseous state. 

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we ll show how to modify our equations to account for non-ideal behavior. 

Continuing to use a syringe as a container, the basic gas laws can be explained. These laws apply to what is referred to as an ideal or perfect gas. An ideal or perfect gas can be thought of as a gas that conforms to the kinetic molecular theory. In reality, gas molecules do have volume and exert forces on each other. Under normal conditions of temperature and pressure, though, the kinetic molecular theory explains the behavior of gases quite well. It is only when a gas is at very low temperatures and/or under extremely high pressure that a gas no longer behaves ideally. 

All gas particles have some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But imperfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon the kinetic molecular theory of ideal gases. In this chapter, you re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called gas laws. ... 

This relationship makes sense if you think about pressure in terms of kinetic molecular theory. Adding a gaseous sample into a particular volume that already contains other gases increases the number of particles in that space. Because pressure depends on the number of particles colliding with the container walls, increasing the number of pcirticles increases the pressure proportionally. 

The kinetic molecular theory (KMT see Sidebar 2.7) of Bernoulli, Maxwell, and others provides deep insight into the molecular origin of thermodynamic gas properties. From the KMT viewpoint, pressure P arises merely from the innumerable molecular collisions with the walls of a container, whereas temperature T is proportional to the average kinetic energy of random molecular motions in the container of volume V. KMT starts from an ultrasimplified picture of each molecule as a mathematical point particle (i.e., with no volume ) with mass m and average velocity v, but no potential energy of interaction with other particles. From this purely kinetic picture of chaotic molecular motions and wall collisions, one deduces that the PVT relationships must be those of an ideal gas, (2.2). Hence, the inaccuracies of the ideal gas approximation can be attributed to the unrealistically oversimplified noninteracting point mass picture of molecules that underlies the KMT description. 

Before ending this discussion of gases, it s worthwhile expanding on a point made earlier The behavior of a real gas is often a bit different from that of an ideal gas. For instance, kinetic-molecular theory assumes that the volume of the gas particles themselves is negligible compared with the total gas volume. The assumption is valid at STP, where the volume taken up by molecules of a typical gas is only about 0.05% of the total volume, but the assumption is not valid at 500 atm and 0°C, where the volume of the molecules is about 20% of the total volume (Figure 9.14). As a result, the volume of a real gas at high pressure is larger than predicted by the ideal gas law. 

The Van der Waal s equation takes into account the deviations of real gases from the kinetic molecular theory of gases (nonzero molecular volume and nonelastic collisions). 

The kinetic molecular theory describes how an ideal gas behaves when conditions such as temperature, pressure, volume or quantity of gas are varied within a system. An ideal gas is an imaginary gas that obeys all of the assumptions of the kinetic molecular theory. The assumptions of the kinetic molecular theory help explain the behavior of gas molecules and their physical properties. 

C) This statement is correct. The sulfur hexafluoride molecule has a much larger volume than the other molecules and is much more likely to experience molecular attractions than the other two molecules. These two factors will make this molecule most likely to deviate from the key postulates in the kinetic-molecular theory (size of the molecule is negligible and molecular attractions are negligible). 

The gas laws and the kinetic molecular theory describe gas temperatures using the Kelvin, or absolute, temperature scale. Gas volumes are usually described in liters, and gas pressures are described in terms of atmospheres, or mm Hg. 

When we refer to the volume of a gas, we are in fact talking about the volume of the container. The definition of the volume of a gas is the space available for gas molecules to move around in. The kinetic molecular theory of gases assumes that the volume of each gas molecule is essentially zero. Thus, the amount of space for them to move around in is the volume of the container. For all gases, Vgas = the volume of the container holding the gas. (Do not confuse this with the molar volume of gases. You will learn about molar volume in Chapter 12.)... 

Think about how the relationship between pressure and area for solids would apply if you were testing a gas in a three-dimensional container. You know that according to the kinetic molecular theory, gas molecules exert pressure over the entire inside surface of their container. If the volume of the container is halved, what would happen to the pressure of the gas inside the container ... 

GZ9 Use the kinetic molecular theory. Explain why the air pressure inside a capped syringe increases if the volume decreases from 15 cm3 to 10 cm3. 

Using the kinetic molecular theory, explain why the density of a gas is less than that of a liquid. (Density is mass per unit of volume.)... 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

The kinetic molecular theory explains the behavior of gases in terms of characteristics of their molecules. It postulates that gases are made up of molecules that are in constant, random motion and whose sizes are insignificant relative to the total volume of the gas. Forces of attraction between the molecules are negligible, and when the molecules collide, the collisions are perfectly elastic. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature (Section 12.10). 

The molecules themselves occupy less than 0.10% of the volume of the gas, in accord with the kinetic molecular theory. 

We have seen that a very simple model, the kinetic molecular theory, by making some rather drastic assumptions (no interparticle interactions and zero volume for the gas particles), successfully explains ideal behavior. However, it is important that we examine real gas behavior to see how it differs from that predicted by the ideal gas law and to determine what modifications of the kinetic molecular theory are needed to explain the observed behavior. Since a model is an approximation and will inevitably fail, we must be ready to learn from such failures. In fact, we often learn more about nature from the failures of our models than from their successes. 

The origin of the pressure exhibited by a gas, as well as the interplay among the parameters of pressure, temperature, volume, and the number of moles, is explained by a theory called the kinetic molecular theory of gas. The fundamental premise of this theory is that gases are made up of individual particles (hence molecular) and that these particles are in constant motion (hence kinetic, as in kinetic art). How this theory explains the properties of gases can be better understood if one compares the properties of gases to the properties of another collection of particles constantly in motion a swarm of gnats. 

The kinetic-molecular theory states that gas particles are in constant random motion, are relatively far apart, and have volumes that are negligible when compared with the total volume of a gas. 

Explain in terms of the kinetic-molecular theory why increasing the temperature of a gas at constant volume increases the pressure of the gas. 

In Chapter 3, you learned that a liquid can take the shape of its container but that its volume is fixed. In other words, the particles in a liquid can flow to adjust to the shape of a container, but the liquid cannot expand to fill its container. Kinetic-molecular theory predicts the constant motion of the liquid particles. Individual liquid molecules do not have fixed positions in the liquid. However, forces of attraction between liquid particles limit their range of motion so that the particles remain closely packed in a fixed volume. 

According to the kinetic-molecular theory, a mole of solid particles has as much kinetic energy as a mole of liquid particles at the same temperature. By definition, the particles in a solid must be in constant motion. So why do solids have a definite shape and volume For a substance to be a solid rather than a liquid at a given temperature, there must be strong attractive forces acting between particles in the solid. These forces limit the motion of the particles to vibrations around fixed locations in the solid. Thus, there is more order in a solid than in a liquid. Because of this order, solids are much less fluid than liquids and gases. In fact, solids are not classified as fluids. 

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