Laws and Models A Review

We know the total pressure (754 torr) and the partial pressure of water (vapor pressure = 21 torr). We can find the partial pressure of O2 from Dalton s law of partial pressures  

We can solve for Pq by subtracting 21 torr from both sides of the equation. 

P02 = 754 torr 21 torr = 733 torr Next we solve the ideal gas law for the number of moles of O2. 

In this case, Pq = 733 torr. We change the pressure to atmospheres as follows  

EXERCISE 13.10 Consider a sample of hydrogen gas collected over water at 25 °C where the vapor pressure of water is 24 torr. The volume occupied by the gaseous mixture is 0.500 L, and the total pressure is 0.950 atm. Calculate the partial pressure of H2 and the number of moles of H2 present. 

I AIM To understand the relationship between laws and models (theories). 

At this point we want to build a model (a theory) to explain why a gas behaves as it does. We want to answer the question. What are the characteristics of the individual gas particles that cause a gas to behave as it does However, before we do this let s briefly review the scientific method. Recall that a law is a generalization about behavior that has been observed in many experiments. Laws are very useful they allow us to predict the behavior of similar systems. For example, a chemist who prepares a new gaseous compound can assume that that substance will obey the ideal gas equation (at least at low P and/or high T). 

However, laws do not tell us why nature behaves the way it does. Scientists try to answer this question by constructing theories (building models). The models in chemistry are speculations about how individual atoms or molecules (microscopic particles) cause the behavior of macroscopic systems (collections of atoms and molecules in large enough numbers so that we can observe them). 

A model is considered successful if it explains known behavior and predicts correctly the results of future experiments. But a model can never be proved absolutely true. In fact, by its very nature any model is an approximation and is destined to be modified, at least in part. Models range from the simple (to predict approximate behavior) to the extraordinarily complex (to account precisely for observed behavior). In this text, we use relatively simple models that fit most experimental results. 

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Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

Modelling biouptake processes helps in the understanding of the key factors involved and their interconnection [1]. In this chapter, uptake is considered in a general sense, without distinction between nutrition or toxicity, in which several elementary processes come together, and among which we highlight diffusion, adsorption and internalisation [2-4], We show how the combination of the equations corresponding with a few elementary physical laws leads to a complex behaviour which can be physically relevant. Some reviews on the subject, from different perspectives, are available in the literature [2,5-7]. 

The CRE approach for modeling chemical reactors is based on mole and energy balances, chemical rate laws, and idealized flow models.2 The latter are usually constructed (Wen and Fan 1975) using some combination of plug-flow reactors (PFRs) and continuous-stirred-tank reactors (CSTRs). (We review both types of reactors below.) The CRE approach thus avoids solving a detailed flow model based on the momentum balance equation. However, this simplification comes at the cost of introducing unknown model parameters to describe the flow rates between various sub-regions inside the reactor. The choice of a particular model is far from unique,3 but can result in very different predictions for product yields with complex chemistry. 

In the first period, which ended with a review [18], the complex susceptibility x (0)) was expressed through the law of motion of the particles perturbed by a.c. external field E(t). The results of these calculations rigorously coincide with those obtained, for example, in Refs. 22 and 23, respectively, for the planar and spatial extended diffusion model (compare with our Ref. 18, pp. 65 and 68). The most important results of this period are (i) the planar confined rotator model [ 17, p. 70 20], which has found a number of applications in our and other [24—31] works (ii) the composite so-called confined rotator-extended diffusion model. However, this approach had no perspectives because of troublesome calculations of the susceptibility x ( )-... 

A review by Bird and Wiest [6] gives a more complete list of existing viscoelastic models. The upper convective model and the White-Metzner model are very similar with the exception that the White-Metzner model incorporates the strain rate effects of the relaxation time and the viscosity. Both models provide a first order approximation to flows, in which shear rate dependence and memory effects are important. However, both models predict zero second normal stress coefficients. The Giesekus model is molecular-based, non-linear in nature and describes thepower law region for viscosity andboth normal stress coefficients. The Phan-Thien Tanner models are based on network theory and give non-linear stresses. Both the Giesekus and Phan-Thien Tanner models have been successfully used to model complex flows. 

The present chapter is not meant to be exhaustive. Rather, an attempt has been made to introduce the reader to the major concepts and tools used by catalytic reaction engineers. Section 2 gives a review of the most important reactor types. This is deliberately not done in a narrative way, i.e. by describing the physical appearance of chemical reactors. Emphasis is placed on the way mathematical model equations are constructed for each category of reactor. Basically, this boils down to the application of the conservation laws of mass, energy and possibly momentum. Section 7.3 presents an analysis of the effect of the finite rate at which reaction components and/or heat are supplied to or removed from the locus of reaction, i.e. the catalytic site. Finally, the material developed in Sections 7.2 and 7.3 is applied to the design of laboratory reactors and to the analysis of rate data in Section 7.4. 

Model guidelines for the use of controlled substances for the treatment of pain are available. " These guidelines recommend the following steps when evaluating the use of controlled substances for pain control 1) evaluate the patient, 2) develop a treatment plan, 3) sign an informed consent/agreement for treatment, 4) review patient periodically, 5) seek consultation when appropriate, 6) maintain medical records, and 7) comply with controlled substance laws and regulations. 

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