Intensive property concentration

We have defined solutions as homogeneous phases, with uniform concentrations throughout. Clearly, the surface of a solution provides a different environment than its bulk, and we should expect intensive properties (concentrations as well as intensive thermodynamic properties) to vary in this region. The mechanical and thermal variables, P and T, however, can be taken as uniform throughout the solution. It should be emphasized that the surface region of the solution is very thin, just a few molecular diameters thick. Bulk properties of the solution will, thus, only be affected by the surface if the solution is composed of very small droplets. 

Determination of purity. The ultraviolet and visible absorption is often a fairly intensive property thus e values of high intensity bands may be of the order of 10 -10 . In infrared spectra e values rarely exceed 10 . It is therefore often easy to pick out a characteristic band of a substance present in small concentration in admixture with other materials. Thus small amounts of aromatic compounds can be detected in hexane or in cyclohexane. 

The driving force behind the spontaneous reaction in a voltaic cell is measured by the cell voltage, which is an intensive property, independent of the number of electrons passing through the cell. Cell voltage depends on the nature of the redox reaction and the concentrations of the species involved for the moment, we ll concentrate on the first of these factors. 

The state (or behaviour) of a system is described by variables or properties which may be classified as (a) extensive properties such as mass, volume, kinetic energy and (b) intensive properties which are independent of system size, e.g., pressure, temperature, concentration. An extensive property can be treated like an intensive property by specifying that it refers to a unit amount of the substance concerned. Thus, mass and volume are extensive properties, but density, which is mass per unit volume, and specific volume, which is volume per unit mass, are intensive properties. In a similar way, specific heat is an intensive property, whereas heat capacity is an extensive property. 

We can express the use of all the different units in evolution in the language of thermodynamics. While the genome is defined by a DNA sequence so that each base has a singular intensive property as in a computer code of symbols, by way of contrast, the protein content of a cell is an extensive property being concentration dependent and therefore varies under circumstances such as temperature and pressure although... 

This equation implies a double dependence of scattering intensities on concentration and observation angle [9]. By extrapolating the scattering data for each concentration to zero angle, the second virial coefficient, which is related to thermodynamic properties, may be measured [9,10,15-18],... 

Various properties of crystals can be used to inspect c,( ,r), provided that appropriate detectors for the intensity of input and output signals are available. If the monitor response is sufficiently fast, one may determine the time dependence of solid state reactions. The monitoring of reactants and/or reaction products can serve this purpose, but the relation between signal intensity (property) and concentration Cj) must always be established first. Since functions of state are related to one another in a unique way, any equilibrium property can, in principle, be used to determine However, the necessary assumption of local equilibrium must still be... 

The properties of a substance can be classified as either intensive or extensive. Intensive properties, which include density, pressure, temperature, and concentration, do not depend on the amount of the material. Extensive properties, such as volume and weight, do depend on the amount. Most thermodynamic properties are extensive including energy (E), enthalpy (H), entropy (5), and free energy (G). 

The state of a system is defined by its properties. Extensive properties are proportional to the size of the system. Examples include volume, mass, internal energy, Gibbs energy, enthalpy, and entropy. Intensive properties, on the other hand, are independent of the size of the system. Examples include density (mass/volume), concentration (mass/volume), specific volume (volume/mass), temperature, and pressure. 

From its form, the chemical potential is obviously an intensive property and therefore must be a function only of other intensive variables and independent of the size of the system. We can write it as p,(7, P, Cj), where c] is some measure of concentration of component /. 

The Gibbs phase rule allows /, the number of degrees of freedom of a system, to be determined. / is the number of intensive variables that can and must be specified to define the intensive state of a system at equilibrium. By intensive state is meant the properties of all phases in the system, but not the amounts of these phases. Phase equilibria are determined by chemical potentials, and chemical potentials are intensive properties, which are independent of the amount of the phase that is present. The overall concentration of a system consisting of several phases, however, is not a degree of freedom, because it depends on the amounts of the phases, as well as their concentration. In addition to the intensive variables, we are, in general, allowed to specify one extensive variable for each phase in the system, corresponding to the amount of that phase present. 

Because the surface tension, y, is an intensive property, it can depend on P, T and concentrations, but not on the area of the surface phase. 

When CRs are in extra vascular volume, they occupy extra cellular space, and are designated as CRo (outside) where they directly bind with extra cellular water. 1H2O0. Since the transverse relaxation time, T is an intensive property of F O, its CR induced change depends directly on the molar ratio of CRo to H2O0. Thus measurement of T allows the direct determination of the concentration of CR (i.e.) [CR]o in the space in which CR is distributed. Further, because most of the water is intracellular ( F Oj), the change in the tissue l- O T from the entire voxel by CR allows the determination of the kinetics of water movement across the cell membrane. The kinetics is characterized by the average lifetime of a water molecule inside a cell, x. and is inversely proportional... 

A pure substance in the absence of motion, gravity, surface effects, electricity and magnetism, has three intensive properties only two of which are independent, viz., pressure, temperature and concentration (conclusion based on experimental or day-to-day observation). The two independent intensive properties are often referred to as the two degrees of freedom. For example, if we keep water vapour in an evacuated chamber - say, above its critical... 

In the context of how we use the term, intensity refers to the intensive property of the disinfectant. Intensive properties, in turn, are those properties that are independent of the total mass or volume of the disinfectant. For example, concentrations are expressed as mass per unit volume the phrase per unit volume makes concentration independent of the total volume. Hence, concentration is an intensive property and it expresses the intensity of the disinfectant. Another intensive property is radiation from an ultraviolet light. This radiation is measured as power impinging upon a square unit of area. The per unit area here is analogous to the per unit volume. Thus, radiation is independent of total area and is, therefore, an intensive property that expresses the intensity of the radiation, which, in this case, is the intensity of radiation of the ultraviolet light. 

The single-scattering albedo of an aerosol, = (Ts /(crsp + (Tap)- As the ratio of two extensive properties, it is an intensive property, independent of the concentration of particulate matter. 

Flow processes inevitably result from pressure gradients witliin tire fluid. Moreover, temperature, velocity, and even concentration gradients may exist witliin the flowing fluid. This contrasts witlr tire uniform conditions tlrat prevail at equilibrium in closed systems. The distribution of conditions in flow systems requires tlrat properties be attributed to point masses of fluid. Thus we assume tlrat intensive properties, such as density, specific enthalpy, specific entropy, etc., at a point are determined solely by the temperature, pressure, and composition at tire point, uirinfluenced by gradients tlrat may exist at tire point. Moreover, we assume that the fluid exlribits tire same set of intensive properties at the point as tlrough it existed at equilibrium at tire same temperature, pressure, and composition. The implication is tlrat an equation of state applies locally and instantaneously at any point in a fluid system, and tlrat one may invoke a concept of local state, independent of tire concept of equilibrium. Experience shows tlrat tlris leads for practical purposes to results in accord with observation. 

Variables of the kind with which the phase rule is concerned are called phase-rule variables, and they are intensive properties of the system. By this we mean properties that do not depend on the quantity of material present. If you think about the properties we have employed so fer in this book, you have the feeling that pressure and temperature are independent of the amount of material present. So is concentration, but what about volume The total volume of a system is called an extensive property because it does depend on how much material you have the specific volume, on the other hand, the cubic meter per kilogram, for example, is an intensive property because it is independent of the amount of material present. In Chap. 4 we take up additional intensive properties, such as internal energy and enthalpy. You should remember that the specific (per unit mass) values of these quantities are intensive properties the total quantities are extensive properties. 

The intensive property must be uniform throughout the phase. If a system at equilibrium consists of two nonreacting components such as NH3 and H2O, and two phases, liquid and vapor, intensive variables would be temperature (the same in both phases), pressure (the same in both phases), concentration in a phase (different in each phase), specific volume (different in each phase), and so on. The overall concentration (including both phases) for the system would not be an intensive property because it is not a value equal to the actual value of the concentration in either phase. 

Fourier s law is the simplest form of a general energy flux and is strictly applicable only when the system is uniform in all respects except for the temperature gradient, that is, there are no mass concentration gradients or gradients in other intensive properties. 

The discussion of luminescence has, up to the present, been based on the properties of dilute solutions in which the analyte molecules were presumed not to interact with one another. It has already been established that at high absorbance at the wavelength of excitation, deviations from linearity of the fluorescence in-tensity-versus-concentration relationship may occur because of the exponential variation of luminescence intensity with concentration. However, over a wide range of solute concentrations, solute-solute interactions may also account for loss of luminescence intensity with increasing solute concentration. 

We recall from Chapter 1 and Part 1 of this chapter that the kinetic rate law e.g.. —= kC ) is a function solely of the intensive properties of the reacting system (e.g., temperature, pressure, concentration, and catalysts, if any). The reaction rate, usually depends on the concentration of the... 

As you can see, the unit of molarity is moles per liter, so a 500-mL solution containing 0.730 mole of C6Hx206 is equivalent to 1.46 mol/L or 1.46 M. Note that concentration, like density, is an intensive property, so its value does not depend on how much of the solution is present. 

Again, the prime for K here is to distinguish it from the final form of equilibrium constant to be derived below.) However, the concentration of a solid, like its density, is an intensive property and does not depend on how much of the substance is present. For example, the molar concentration of copper (density 8.96 g/crff) at 20°C is the same, whether we have 1 gram or 1 ton of the metal ... 

Sometimes it helps to assume a value to work with, especially with intensive properties such as concentrations. We will encounter problems of this type later, for example in molality to mole fraction conversions (Section 6.4). 

Concentration is the proportion of a substance in a mixture, so it is an intensive property, one that does not depend on the quantity of mixture present 1.0 L of... 

The state of the system is given by a set of values of properly chosen physical variables. To determine unambiguously the state of the simplest system (a pure substance in one phase) one should know two properties (e.g. temperature and pressure) in addition to the quantity (moles). To describe the state of more complex systems one should know more properties (e.g. the concentrations of individual species). The thermodynamic properties of the system depending only on the state and not on the way by which the system has reached the given state, are called state functions. The typical fundamental state functions are temperature, pressure, volume and concentration of the individual components of the system. The thermodynamic properties are usually classified into extensive and intensive ones. The extensive properties are proportional to the quantity of the substance in the system. Therefore, they are additive, i.e. the total extensive property of the system equals the sum of the extensive properties of the individual parts of the system. Typical extensive quantities are weight, energy, volume, number of moles. On the other hand, the intensive properties do not depend on the quantity of the substance in the system (pressure, temperature, concentration, specific quantities, specific resistance, molar heat, etc.). 

It is possible to subdivide the properties used to describe a thermodynamic system (e.g., T, P, V,U,...) into two main classes termed intensive and extensive variables. This distinction is quite important since the two classes of variables are often treated in significantly different fashion. For present purposes, extensive properties are defined as those that depend on the mass of the system considered, such as volume and total energy content, indeed all the total system properties (Z) mentioned above. On the other hand, intensive properties do not depend on the mass of the system, an obvious example being density. For example, the density of two grams of water is the same as that of one gram at the same P, T, though the volume is double. Other common intensive variables include temperature, pressure, concentration, viscosity and all molar (Z) and partial molar (Z, defined below) quantities. ... 

The accumulation rate may be expressed in term of total mass M or energy E of the system, denoted as time-derivatives dM / dt and dE/dt. In systems with chemical reaction it is useful to consider the molar rate variation of individual components, dNj dt. The accumulation can be expressed by means of a holdup term as the product of an intensive property, as density, concentration, or volumetric enthalpy, by the control volume ... 

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