Models of gases

Chapter I has been reorganized in this edition to give readers a gentler introduction to atoms and their structure. Atoms and molecules, including discussions of quantum mechanics and molecular orbitals, provide the foundation for understanding bulk properties and models of gases, liquids, and solids. 

FIGURE 4.23 In the kinetic model of gases, the molecules are regarded as infinitesimal points that travel in straight lines until they undergo instantaneous collisions. 

FIGURE 4.24 In the kinetic model of gases, the pressure arises from the force exerted on the walls of the container when the impacting molecules are deflected. We need to know the force of each impact and the number of impacts in a given time interval. 

In the kinetic model of gases, we picture the molecules as widely separated for most of the time and in ceaseless random motion. They zoom from place to place, always in straight lines, changing direction only when they collide with a wall of the container or another molecule. The collisions change the speed and direction of the molecules, just like balls in a three-dimensional cosmic game of pool. 

The kinetic model of gases is consistent with the ideal gas law and provides an expression for the root mean square speed of the molecules vnns = (3RT/M)l/2. The molar kinetic energy of a gas is proportional to the temperature. 

The compression factor of an ideal gas is 1, and so deviations from Z = I are a sign of nonideality. Figure 4.28 shows the experimental variation of Z for a number of gases. We see that all gases deviate from Z = 1 as the pressure is raised. Our model of gases must account for these deviations. 

Do all the molecules of a gas strike the walls of their container with the same force Justify your answer on the basis of the kinetic model of gases. 

What Do We Need to Know Already Much of this chapter stands alone, but it would be helpful to review the kinetic model of gases (Section 4.10) and equilibrium constants (Section 9.2). 

Figure 4.26 Cell model of gases, liquids, and solids...

Mass Diffusivity in Liquid Metais and Ailoys. The hard-sphere model of gases works relatively well for self-diffusion in monatomic liquid metals. Several models based on hard-sphere theory exist for predicting the self-diffusivity in liquid metals. One such model utilizes the hard-sphere packing fraction, PF, to determine D (in cm /s) ... 

Ironically, the three principles that had guided Lavoisier s creative researches and organized Part I of the TraitS failed to become a permanent part of chemistry. The caloric model of gases, oxygen as sole supporter of combustion, and oxygen as the principle of acidity, were all quickly abandoned by nineteenth century chemists, chiefly through the discoveries of Humphry Davy. 

Atoms and Molecules First The first three chapters develop models of atoms and molecules, from quantum mechanics to molecular orbitals. The next two chapters show how bulk properties emerge from properties of atoms and molecules. These chapters build and refine models of gases, liquids, and solids. 

Because Vm is a constant at constant temperature and pressure, this expression tells us that doubling the number of moles of molecules at constant temperature and pressure doubles the volume occupied by a gas. This behavior is consistent with our model of gases. In this model, gas molecules are in constant motion and beat against the walls of their container. To keep the pressure constant as more molecules are added, the size of the container must increase. 

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. 

Our two-dimensional lattice model of gases at high temperatures and pressures is the following. 

We shall define the terms components, species, compartments and detached coefficients, and free-energy value in terms of a specific example-r-a sample model of gases in equilibrium with an aqueous solution called the soda pop problem. Figure 1 shows the structure of the.model in the terms used by the program. 

In fact, the kinetic model of gases (Chapter 21) says that the pressure of a gas is equal to - — E where E is the average kinetic energy of the gas molecules-completely consistent with interpreting it as the... 

In expansion, the volume increases, meaning that the box gets bigger. Equation 9.12b tells us that the kinetic energy decreases, even as the quantum numbers remain constant. This is also consistent with what we know of adiabatic expansion and the kinetic model of gases the temperature of the sample drops on expansion, and temperature is related to the kinetic energy (T2 oc E). 

Diffusivity coefficient for PVC matrix plasticate can be determined from the Equation (8) in supposition, that combustion front achieves the sample middle = 2 mm) and its achievement time x is equal to experimental value of putting out a fire time x = 4.5 s. Then = 0.148 x 10 cmVs, that corresponds to experimental data for PVC [7]. The diffusivity coefficient for nanocomposites calculation can be performed within the framework of multifractal model of gases diffusion according to the Equation (7) ... 

M6heut, M. (1997). Designing a learning sequence about a pre-quantitative model of gases the parts played by questions and by a computer-simulation. International Journal of Science Education, 19, 647-660. 

The entropy of a van der Waals gas can be derived in different ways. Let s use a simple lattice model. Recall from the lattice model of gases (Equation (7.9)) that the entropy 5 of distributing N particles onto a lattice of M sites is... 

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