Develop via mathematical expressions a valid process or equipment model that relates the input-output variables of the process and associated coefficients. Include both equality and inequality constraints. Use well-known physical principles (mass balances, energy balances), empirical relations, implicit concepts, and external restrictions. Identify the independent and dependent variables (number of degrees of freedom). [Pg.742]

Mixture rule A mathematical expression applying to workers simultaneously exposed to chemicals that act on the same [Pg.1460]

The phase rule is a mathematical expression that describes the behavior of chemical systems in equilibrium. A chemical system is any combination of chemical substances. The substances exist as gas, liquid, or solid phases. The phase rule applies only to systems, called heterogeneous systems, in which two or more distinct phases are in equilibrium. A system cannot contain more than one gas phase, but can contain any number of liquid and solid phases. An alloy of copper and nickel, for example, contains two solid phases. The rule makes possible the simple correlation of very large quantities of physical data and limited prediction of the behavior of chemical systems. It is used particularly in alloy preparation, in chemical engineering, and in geology. [Pg.6]

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. [Pg.355]

Langmuir equations The mathematical expressions that describe vapor adsorption equilibria. [Pg.1454]

Wave equation (Section 1.2) A mathematical expression that defines the behavior of an electron in an atom. [Pg.1253]

It is important to derive the mathematical expression relating y, and xy on the practical-feasibility line. For a given y,, the values of xj can be obtained by evaluating x that is in equilibrium with y, then subtracting Cy. i.e., [Pg.48]

Many attempts have been made to obtain mathematical expressions which describe the time dependence of the strength of plastics. Since for many plastics a plot of stress, a, against the logarithm of time to failure, //, is approximately a straight line, one of the most common expressions used is of the form [Pg.136]

Here a suitable equation of state is required to provide a mathematical expression for the mixture molar volume, V. For some equations of state, it is better to use a form of equation 28 in which the integral is volume expHcit (3). Note also that for an ideal gas — Z — 1, and 0 = 1. [Pg.236]

For computer applications, it is useful to have the friction factor in a mathematical expression (empirical). [Pg.785]

In making certain mathematical approximations to the Schrodinger equation, we can equate derived terms directly to experiment and replace difficult-to-calculate mathematical expressions with experimental values. In other situations, we introduce a parameter for a mathematical expression and derive values for that parameter by fitting the results of globally calculated results to experiment. Quantum chemistry has developed two groups of researchers [Pg.217]

The mathematical formulation of a typical molecular mechanics force field, which is also called the potential energy function (PEF), is shown in Eq. (18). Do not wony yet about the necessary mathematical expressions - they will be explained in detail in the following sections [Pg.340]

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). [Pg.232]

A minimum basis set for molecules containing C, H, O, and N would consist of 2s, 2p, 2py, and 2p oibitals for each C, N, and O and a 1 j orbital for each hydrogen. The basis sets are mathematical expressions describing the properties of the atomic orbitals. [Pg.25]

Essential Features of Optimization Problems The solution of optimization problems involves the use of various tools of mathematics. Consequently, the formulation of an optimization problem requires the use of mathematical expressions. From a practical viewpoint, it is important to mesh properly the problem statement with the anticipated solution technique. Every optimization problem contains three essential categories [Pg.742]

How are the electrons distributed in an atom You might recall from your general chemistry course that, according to the quantum mechanical model, the behavior of a specific electron in an atom can be described by a mathematical expression called a wave equation—the same sort of expression used to describe the motion of waves in a fluid. The solution to a wave equation is called a wave function, or orbital, and is denoted by the Greek letter psi, i/y. [Pg.4]

Several requirements must be met in developing a stmcture. Not only must elementary analysis and other physical measurements be consistent, but limitations of stmctural organic chemistry and stereochemistry must also be satisfied. Mathematical expressions have been developed to test the consistency of any given set of parameters used to describe the molecular stmcture of coal and analyses of this type have been reported (4,6,19,20,29,30). [Pg.218]

The common theme in the evolution of methods for property and parameter prediction is the development of equations, either theoretical or empirical, containing quantities that can be calculated from theoretical considerations or experimental data. Mathematical expressions for correlating thermodynamic data may take several forms. [Pg.232]

In general, the optimum conditions cannot be precisely attained in real reactors. Therefore, the selection of the reactor type is made to approximate the optimum conditions as closely as possible. For this purpose, mathematical models of the process in several different types of reactors are derived. The optimum condition for selected parameters (e.g., temperature profile) is then compared with those obtained from the mathematical expressions for different reactors. Consequently, selection is based on the reactor type that most closely approaches the optimum. [Pg.1045]

An important benefit of QSAR methods is that no enzyme stmcture is required. However, a series of stmcturaHy related inhibitors of known stmcture and known inhibitory activity is required. The limitations of the method involve the difficulties in describing something as compHcated as a stmcture-function relationship in a single mathematical expression. [Pg.327]

See also in sourсe #XX -- [ Pg.60 ]

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