Molecular kinetic theory

The kinetic-molecular theory consists of five postulates about gases. These postulates are assumptions from which gas behavior is explained. Everything discussed so far in this chapter is consistent with kinetic-molecular theory. The five postulates of the theory are  

Q The size of a gas molecule is negligible in comparison to the distance between gas molecules. That is, in a sample of a gas, most of the sample consists of empty space. Gas particles are very small and very far apart. 

Q Gas molecules move randomly in straight-line paths in all directions and at different speeds. This means that in a sample of gas, there is an equal probability of finding gas particles with similar properties anywhere in the sample. You won t have a closed flask where all of the gas particles are on one side of the flask. 

Q The attractive or repulsive forces between gas particles are considered very weak or negligible. This can be explained because the particles are moving quickly and are 

Q When gas particles do collide, the collisions are elastic. An elastic collision is one in which the particles bounce off each other in such a way that the energy each particle leaves a collision with is exactly the same as the energy it had just before it collided. No kinetic energy is lost. 

The Kinetic Molecular Theory attempts to represent the properties of gases by modeling 

Gases are composed of very small particles, either molecules or atoms. 

The gas particles are tiny in comparison to the distances between them, so we assume that the volume of the gas particles themselves is negligible. 

These gas particles are in constant motion, moving in straight lines in a random fashion and colliding with each other and the inside walls of the container. The collisions with the inside container walls comprise the pressure of the gas. 

The gas particles are assumed to neither attract nor repel each other. They may collide with each other, but if they do, the collisions are assumed to be elastic. No kinetic energy is lost, only transferred from one gas molecule to another. 

In the following sections, you will see how the intepretation of a gas in terms of the kinetic-molecular theory (or simply kinetic theory) leads to the ideal gas law. 

According to this theory, a gas consists of molecules in constant random motion. The word kinetic describes something in motion. Kinetic euCTgy, Ej is the energy associated with the motion of an object of mass m. From physics, 

We will use the concept of kinetic energy in describing the kinetic theory. 

To better understand the complex behavior of gases, scientists have theorized a model of an ideal gas. This model is called the kinetic molecular theory. In the kinetic molecular theory, an ideal gas lacks certain real gas characteristics. Ideal gas has the following four characteristics not shared by a real gas  

Gas molecules exert no forces other than repulsive forces due to collisions  

The average kinetic energy of gas molecules is directly proportional to the temperature of the gas. 

Notice that the ideal gas law does not change for different gases behaving ideally. (Of course not, it s written for an ideal gas.) This means that all gases (behaving ideally) will have the same volume, if they have the same temperature, pressure, and number of molecules. At STP one mole of any gas (behaving ideally) will occupy the standard molar volume of 22.4 liters. 

As well as pure gases, we can apply the kinetic molecular theory to mixtures of gases. In a mixture of gases, each gas contributes to the pressure in the same proportion as it contributes to the number of molecules of the gas. This makes sense, given the kinetic molecular theory, because molecules have no volume, no interactive forces other than collisions, and kinetic energy is conserved when they collide. Thus, each gas in a mixture essentially behaves as if it were in its container alone. The 

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In addition to and r nis ai other way of characterizing coil dimensions is to consider which end-to-end distance has the greatest probability of occurring for specified n and 1 values. Derive an expression for this most probable value of r, r, from Eq. (1.44). Compare the ratio r ms/ m the ratio from the kinetic molecular theory of gases (consult, say,... 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

While thermodynamics does not describe the nature of this internal energy, it is helpful to consider the insights gained from kinetic molecular theory. According to this theory, the internal energy can be partitioned into kinetic and potential energy terms associated with various motions and positions of the nuclei of the atoms or molecules that make up the gas, and with energies associated with their electrons. 

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... 

The energy system we choose to use in deriving an expression for / is the translational energy of the ideal gas. From kinetic-molecular theory we know that f/trans, the average translational energy is given by... 

We now have enough information to turn our qualitative ideas about a gas into a quantitative model that can be used to make numerical predictions. The kinetic model ( kinetic molecular theory, KMT) of a gas is based on four assumptions (Fig. 4.23) ... 

Equations and can be derived from our simple molecular picture and kinetic molecular theory. The derivation is independent of the nature of solute and solvent, so the equations are valid for other solvents besides water, except that Kf and have... 

The kinetic-molecular theory of gases explains the behavior of gases at the molecular level. All of the following are part of this theory EXCEPT —... 

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. 

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. 

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. 

Ans. The gas laws work for unbonded atoms as well as for multiatom molecules, and so it is convenient to classify the unbonded atoms as molecules. If these atoms were not classified as molecules, it would be harder to state the postulates of the kinetic molecular theory. For example, postulate 1 would have to be stated "Molecules or unbonded atoms are in constant random motion. ... 

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 ... 

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... 

According to the kinetic-molecular theory of gases, the internal energy of an ideal gas, U,... 

Gas stoichiometry Kinetic-Molecular theory Nonideal gases... 

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