Gas Properties Relating to the Kinetic-Molecular Theory

This gives PV = nNpjnu. But Nj m is just the molar mass, M. Therefore, 

By comparing this result to the ideal gas equation, PV = nRT, we conclude that RT = IMu and, thus, = 3RT/M. Since the root-mean-square speed, 

we have now also justified the result given earlier for M ms (see expression 6.19). 

NH3(g) escapes from NH3(aq) (but labeled ammonium hydroxide in this photograph), and HCI(g) escapes from HCI(aq). The gases diffuse toward each other, and, where they meet, a white cloud of ammonium chloride forms as a result of the following reaction  

Because of their greater average speed, NH3 molecules diffuse faster than HCI. As a result, the cloud forms close to the mouth of the HCI(aq) container. 

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Ideal Gas Equation and the General Gas Equation 6-8 Gas Properties Relating to the Kinetic-Molecular Theory... 

Relate the kinetic-molecular theory to the properties of an ideal gas. 

How are gas temperature and volume related The French physicist Jacques Charles (1746-1823) studied the relationship between volume and temperature. In his experiments, he observed that as temperature increases, so does the volume of a gas sample when the pressure is held constant. This property can be explained by the kinetic-molecular theory at a higher temperature, gas particles move faster, striking each other and the walls of their container more frequently and with greater force. For the pressure to stay constant, volume must increase so that the particles have farther to travel before striking the walls. Having to travel farther decreases the frequency with which the particles strike the walls of the container. 

The kinetic molecular theory of gases relates the macroscopic properties of a gas to the structure of the constituent molecules, the forces between them, and their motions. Because the number... 

An example of this type of model is the kinetic molecular theory (KMT), a simple model that attempts to explain the properties of an ideal gas. This model is based on speculations about the behavior of the individual gas particles (atoms or molecules). The postulates of the kinetic molecular theory as they relate to the particles of an ideal gas can be stated as follows ... 

Kinetic Molecular Theory of Gases Macroscopic properties like pressure and temperature of a gas can be related to the kinetic motion of molecules. The kinetic molecular theory of gases assumes that the molecules are ideal, the number of molecules is very large, and that their motions are totally random. Both gas diffusion and gas effusion demonstrate random molecular motion and are governed by the same mathematical laws. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

Unfortunately, even though (9.5) provides valuable insights into the dependence of X.BB on the gas concentration and molecular size, it is not convenient for the estimation of the mean free path of a pure gas, because one needs to know the diameter of the molecule ob, a rather ill-defined quantity as most molecules are not spherical. To make things even worse, the mean free path of a gas cannot be measured directly. However, the mean free path can be theoretically related to measurable gas microscopic properties, such as viscosity, thermal conductivity, or molecular diffusivity. One therefore can use measurements of the above gas properties to estimate theoretically the gas mean free path. For example, the mean free path of a pure gas can be related to the gas viscosity using the kinetic theory of gases... 

The model of the ideal gas ignores intermolecular interactions. Given some intermolecular interactions, statistical mechanics must be employed to obtain the equation of state of the real fluid. For fluids of high density, approximations are necessary, but these naturally evolve from the formal, general statistical mechanical framework. For polymers in bulk, the present theories are of the kinetic theory variety since they do not, in principle, relate all macroscopic properties to the constituent molecular properties. In approaching a statistical mechanical theory of polymers in bulk, we can first ask if we can learn from these successes in the statistical mechanics of gases. One way to accomplish this is to consider a bulk polymer situation whicli simulates as closely as possible ideal gas situations. This model illustrates the following ... 

It was during the first half of the 17th century that scientists began to study chemical reactions experimentally. Jan Baptista van Helmont laid the foundations of the law of conservation of mass. Van Helmont showed that in a number of reactions an aerial fluid was liberated which he defined as a gas. A new class of substances with their own physical properties was shown to exist. A kinetic-molecular theory of gases began to develop. Notable in this field were the experiments of Robert Boyle whose studies, later known as Boyle s law, provided an equation describing the inverse relation between pressure and volume of gas (see the ideal gas law in Chapter 3). 

In specific cases the gas mixture is almost isotherm and the chemical process are not altering the mixture molecular mass very much, thus the system and transport properties may be considered constant. Otherwise, the system and transport properties have to be considered temperature and composition dependent and calculated from approximate parameterizations or kinetic theory relations. 

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