Temperature kinetic molecular theory

Kinetic Moiecuiar Theory The kinetic molecular theory is a model for gases. In this model, gases are composed of widely spaced, noninteracting particles whose average kinetic energy depends on temperature. Kinetic Molecular Theory The kinetic molecular theory predicts many of the properties of gases, including their low density in comparison to solids, their compressibility, and their tendency to assume the shape and volume of their container. The kinetic molecular theory also predicts the ideal gas law. 

Temperature must be held constant in equation (1.15), since changing the temperature changes the energy. The internal kinetic and potential energy of the molecules in a system is often referred to as the thermal energy. Kinetic-molecular theory predicts that motion will stop at the absolute zero of temperatures where the thermal energy will be zero. 

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... 

Graham s law may be explained in terms of the kinetic molecular theory as follows Since the two gases are at the same temperature, their average kinetic energies are the same ... 

Does the kinetic molecular theory state that all the molecules of a given sample of gas have the same velocity since they are all at one temperature ... 

Ans. No. The kinetic molecular theory states that the average kinetic energy is related to the temperature, not the velocity or kinetic energy of any one molecule. The velocity of each individual molecule changes as it strikes other molecules or the walls. 

According to the Kinetic-Molecular Theory, all gas molecules have the same average kinetic energy (= M2 mu2) at the same temperature, where u is the average velocity. Hence, at the same T ... 

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. 

Drawing a Conclusion How does the rate of evaporation of warm ethanol compare to ethanol at room temperature Use kinetic-molecular theory to explain your observations. 

According to kinetic-molecular theory, if two different gases are at the same temperature, their molecules have the same average kinetic energy. Average kinetic energy is proportional to temperature. 1 point for correct answer and explanation. 

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. 

Kinetic Molecular Theory model that defines an ideal gas and assumes the average kinetic energy of gas molecules is directly proportional to the absolute temperature... 

The rate constant for adsorption, A , is also temperature dependent, but the dependence is small compared to that for k r The value and temperature dependence of k, are determined by the rate of gas-solid collisions, which from kinetic molecular theory is given by... 

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. 

Kinetic Molecular Theory A theory that states all molecules are in constant motion at all temperatures above absolute zero molecules will move (or vibrate) faster at higher temperatures... 

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. 

One of the more important conclusions from kinetic-molecular theory comes from assumption 5—the relationship between temperature and EK, the kinetic energy of molecular motion. It can be shown that the total kinetic energy of a mole of gas particles equals 3RT/2 and that the average kinetic energy per particle is thus 3RT/2Na, where NA is Avogadro s number. Knowing this relationship makes it possible to calculate the average speed u of a gas particle. To take a helium atom at room temperature (298 K), for example, we can write... 

The connection between temperature and kinetic energy obtained from the kinetic-molecular theory makes it possible to calculate the average speed of a gas particle at any temperature. An important practical consequence of this relationship is Graham s law, which states that the rate of a gas s effusion, or spontaneous passage through a pinhole in a membrane, depends inversely on the square root of the gas s mass. 

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 temperature of an ideal gas is proportional to the average kinetic energy of the particles in a sample of the gas. The relationship between kinetic energy and temperature is derived from the Kinetic Molecular Theory of Gases and is given by ... 

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 ... 

In a solid, the energy of intermolecular attractive forces is much stronger than the kinetic energy of the molecules, so kinetic energy and kinetic molecular theory are not very important. As temperature increases in a solid, the vibrations of individual molecules grow more intense and the molecules spread slightly further apart, decreasing the density of the solid. 

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 also predicts that reaction rate constants (values for k) increase with temperature because of two reasons ... 

As you teach yourself about gases in this unit, develop a mental picture of how the molecules of a gas behave. The model for the action of gas molecules in a confined space is called kinetic molecular theory. Because kinetic means moving, the theory describes how molecules behave as a result of their motion. The speed of molecules is related to their temperature, in that the hotter they are, the faster they move. In an enclosed space, molecules randomly strike each other and collide with the walls of the container as they travel (Figure 6.1). 

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. 

While the AP test tends to convert temperatures to Kelvins for gas law problems, they will often leave them in Celsius, on kinetic-molecular theory questions. Be on the lookout for that. Any problems involving temperature of gases require absolute term-perature, regardless of what you are given ... 

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. 

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