Pressure kinetic molecular theory

Kinetic-molecular theory provides an explanation on a molecular level for this equilibrium. Evaporation from the liquid occurs as fast moving molecules on the surface escape from the liquid. In turn, molecules in the gas phase strike the liquid and condense, As the concentration (pressure) of gas molecules builds up in the gas phase, the rate of condensation increases. Eventually, a pressure is reached where the rate of condensation and rate of evaporation just balance, and equilibrium is achieved. The equilibrium pressure is denoted by p and is known as the vapor pressure. The magnitude ofp depends upon the substance, composition of the liquid, and any two of our thermodynamic variables such as temperature and total pressure. The criteria for equilibrium that we will now derive provide the thermodynamic relationships that will help... 

In Chap. 11 the laws governing the behavior of gases were presented. The fact that gases exert pressure was stated, but no reasons why gases should exhibit such behavior were given. The kinetic molecular theory explains all the gas laws that we have studied and some additional ones also. It describes gases in terms of the behavior of the molecules that make them up. 

Kinetic molecular theory explains why gases exert pressure. The constant bombardment of the walls of the vessel by the gas molecules, like the hitting of a target by machine gun bullets, causes a constant force to be applied to the wall. The force applied, divided by the area of the wall, is the pressure of the gas. 

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. 

According to Kinetic-Molecular Theory, the pressure exerted by a gas upon the walls of its container is caused by gas molecules hitting the walls. Pressure depends on... 

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. 

We can understand how atmospheric pressure is just the weight of the atmosphere pushing down on the Earth s surface, but how can we apply the basic definition of pressure to a confined gas To expand our concept of pressure and provide a basic framework for understanding the behavior of gases, we use a simple model for a confined gas. This model is known as the kinetic molecular theory. The kinetic molecular theory states ... 

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. 

Using gas kinetic molecular theory, show that under typical atmospheric conditions of pressure and temperature corresponding to an altitude of 5 km (see Appendix V) collisional deactivation of a C02 molecule will be much faster than reemission of the absorbed radiation. Take the collision diameter to be 0.456 nm and the radiative lifetime of the 15-/rm band of C02 to be 0.74 s (Goody and Yung, 1989). 

Kinetic molecular theory first made a name for itself when scientists attempted to explain and predict the properties of gases and, in particular, how those properties changed with varying temperature and pressure. The idea emerged that the particles of matter within a gas (atoms or molecules) undergo a serious amount of motion as a result of the kinetic energy within them. 

The pressure of the gas over the surface of a liquid is called the vapor pressure. Understandably, liquids with low boiling points tend to have high vapor pressures because the particles are weakly attracted to each other. At the surface of a liquid, weakly interacting particles have a better chance to escape into the vapor phase, thereby increasing the vapor pressure. See how kinetic molecular theory helps make sense of things ... 

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. 

This familiar equation gives the variation of barometric pressure with elevation and is known as the barometric equation. Once again we are reminded of the connection between the material of this chapter and kinetic molecular theory. 

Instead, we must turn to the kinetic molecular theory of gases for an estimate of the frequency with which molecules collide with a solid surface. We shall not be misled, however, if we anticipate that this pressure is low. Example 9.6 is a numerical examination of gas collisions with walls. 

EXAM PLE 9.6 Rate of Atomic Collisions as a Function of Pressure. Assuming 1019 atoms per square meter as a reasonable estimate of the density of atoms at a solid surface, estimate the time that elapses between collisions of gas molecules at 10 6 torr and 25°C with surface atoms. Use the kinetic molecular theory result that relates collision frequency to gas pressure through the relationship Z = 1/4 vNIV, for which the mean velocity of the molecules v = (BRTI-kM) 12 and NIV is the number density of molecules in the gas phase and equals pNJRT. Repeat the calculation at 10 8 and 10 10 torr. 

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. 

Evaporation and vapor pressure are both explained on a molecular level by the kinetic-molecular theory developed in Section 9.6 to account for the behavior of gases. The molecules in a liquid are in constant motion, but at a variety of speeds depending on the amount of kinetic energy they have. In considering a large sample, molecular kinetic energies follow a distribution curve like that... 

Experimental evidence for the notion of an activation energy barrier comes from a comparison of collision rates and reaction rates. Collision rates in gases can be calculated from kinetic-molecular theory (Section 9.6). For a gas at room temperature (298 K) and 1 atm pressure, each molecule undergoes approximately 109 collisions per second, or 1 collision every 10 9 s. Thus, if every collision resulted in reaction, every gas-phase reaction would be complete in about 10-9 s. By contrast, observed reactions often have half-lives of minutes or hours, so it s clear that only a tiny fraction of the collisions lead to reaction. 

The mean free path m is related to the pressure by simple kinetic molecular theory according to equation 4... 

Ideal gases obey the ideal gas law at all temperatures and pressures. However, there are no ideal gases, only real gases. Real gases deviate from ideal behavior most strongly at high pressures and/or low temperatures. So, where do the basic tenets of Kinetic Molecular Theory fail ... 

Dalton s Law of Partial Pressures 139 Relative Humidity 141 Kinetic Molecular Theory of Gases 143... 

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. 

Kinetic molecular theory may be applied to reaction rates in addition to physical constants like pressure. Reaction rates increase with reactant concentration... 

Pressure does not dramatically alter the solubility of solids or liquids, but kinetic molecular theory predicts that increasing the partial pressure of a gas will increase the solubility of the gas in a liquid. If a substance is distributed between gas and solution phases and pressure is exerted, more gas molecules will impact the gas/liquid interface per second, so more will dissolve until a new equilibrium is reached at a higher solubility. Henry s law describes this relationship as a direct proportionality ... 

This chapter is the first of two devoted to specific states of matter, and in it you will focus your attention on the gaseous state of matter. However, all of the states will be described within a larger framework that looks at the state of matter as a series of interrelated factors, including kinetic energy (or temperature), pressure, and intermolecular forces. Gases are usually described by a series of postulates known as kinetic molecular theory, which constitute the ideal gas law. To begin the chapter, you will look at a historical development of the ideal gas law, during which you will review some of the equations used to create the ideal gas law. 

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. 

The molecular-level interpretation of gas behaviour given by the kinetic molecular theory helps to explain the macroscopic, or larger picture, properties of gases in the real world. One of the most important properties of gases is their compressibility—how they react to the application of an external force. In the next section, you will observe how gases behave under pressure. Later in this chapter, you will learn about some interesting applications of pressurized gases. 

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. 

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. 

Use the kinetic molecular theory to explain why the number of moles of gas enclosed in a certain container at a certain temp>erature is directly proportional to the gas pressure. 

Use the kinetic molecular theory to explain why Dalton s law of partial pressure works. 

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