Pressure law

J. S. F. Pagenstecher found that aq. soln. of disodium hydrophosphate absorb more carbon dioxide, and that more rapidly than is the case with water or soln. of sodium chloride and the soln. reddens litmus more feebly than is the case with water the carbon dioxide is not so easily removed again. J. von Liebig showed that part of the soda probably unites with the carbonic acid, and only that of dissolved gas which is uncombined follows W. Henry s pressure law. R. Ileidenhain and L. Meyer found that soln. with less than one per cent, of Na2HP04.12H20 absorb enough carbon dioxide to sat. the water with ga3 and to transform half the... 

At present, we see only one route to complete solution of the problem for t as r, for example, up to t = 5r or lOr, we solve the partial differential equations with a given pressure law at the piston continuing the solution for t > r in asymptotic (self-similar) form, we determine the constants A and B from the condition that the two solutions coincide at the extreme point to which the calculation is carried. 

Dalton s law of partial pressure law which states that the total atmospheric pressure (.Pt) is the sum of all partial pressures (Pt) exerted by each of the gases in the entire mixture of air. 

Measurement of palladium membrane permeability. The permeation rate of hydrogen gas through the palladium membrane, Q , was assumed to obey the half-power pressure law(20). The permeation flux of hydrogen through the membrane is proportional to the difference between the souare roots of the hydrogen partial pressure on the high and low pressure sides of membrane. 

Dilute solutions. As has already been stated (p. 266), the relationship between the osmotic pressure of a solution and the concentration and chemical character of solvent and solute cannot be derived from purely thermodynamical considerations. There are several ways of attaining this end. In the first instance, the variation of the osmotic pressure with the concentration can be determined experimentally, and the results embodied in an empirical equation of the form p=/(c). Or we may deduce relationships from kinetic conceptions of the nature of solutions, in much the same way as the gas laws were deduced. Or, finally, we may deduce the osmotic pressure laws, with the aid of the thermodynamical equations of the previous paragraph, from empirical or theoretical researches on the vapour pressure of solutions. These methods all lead to the same result, that the osmotic pressure of dilute solutions obeys the same laws as the pressure of a perfect gas. In other words, the osmotic pressure of a substance in solution is equal to the pressure which the substance would exert in the form of a perfect gas occupying, at the same temperature, the volume of the solution. 

This follows from the phase rule, for we have a three-component system (two solvents and one solute) in three phases (two solutions and vapour), and hence two degrees of freedom. When the temperature and one of the concentrations, say c , are given, the concentration c in the second solvent is uniquely determined. The function / can be calculated when the osmotic pressure law is known for both solvents. 

The solubility of a gas is therefore proportional to its partial pressure. Henry discovered and established this law in the beginning of the nineteenth century. It is connected thermodynamically with van t Hoff s osmotic pressure laws, and is therefore strictly accurate only in dilute solutions, that is, for sparingly soluble gases (see p. 258). 

This equation was deduced theoretically and confirmed experimentally by Fick in 1885, long before the discovery of the osmotic pressure laws. D is called the coefficient of diffusion. 

Deviations from the simple laws. The exact proportionality between the osmotic pressure and the concentration can only hold in dilute solutions. No matter how we account for the osmotic pressure laws, whether by an attraction between the solvent and the solute, or by the impacts of the dissolved molecules, or whether we deduce them from the lowering of the vapour pressure of the solution, we are always forced to restrict the applicability of the simple laws of van t Holf to the region of very dilute solutions. Similarly, the laws of perfect gases can only be regarded as valid in the limiting case of very great... 

Mtributed to the absence of the necessary experimental work for 0-5-2 normal solutions of non-electrolytes, that is, of systematic determinations of all the quantities which appear in the equations (namely, concentration by weight and by volume, heat of dilution, etc.). The theoretical interpretation of the data for solutions of electrolytes must be postponed until the behaviour of non-electrolytes has been explained. The dissociation of electrolytes introduces a new complication which cannot be treated with success until the osmotic pressure laws for concentrated solutions have been elucidated. 

Variation with the temperature. The equilibrium constant in solutions as in gases is a function of the temperature. When van t Hoff s osmotic pressure laws are applicable, we can deduce an equation of the form... 

The agreement at low temperatures is remarkably good. The heat of dissociation diminishes as the temperature rises. From this it follows that the free ions H and OH must have a smaller specific heat than the unionised molecules. The calculation of the ionisation of water is one of the most convincing proofs of the correctness of the theory of electrolytic dissociation, as well as of the validity of van t Hoff s osmotic pressure laws on which the deduction of these valuable equations is based. 

Sj. Mixtures of Real Gases Additive Pressure Law.—The rule that the total pressure of a mixture of gases is equal to the sum of the pressures exerted by each gas if it alone occupied the whole of the available volume ( 5b) does not apply to real gases. The total pressure is thus not equal to the sum of the partial pressures defined in the usual manner. However, for some purposes it is convenient to define the partial pressure of a gas in a mixture by means of equation (5.8), i.e., p == n P, where p is the partial pressure and n is the mole fraction of any constituent of the mixture of gases of total pressure P. 

Sk. Additive Volume Law.— The additive pressure law, as given by equation (5.26), is useful for the calculation of the approximate pressure exerted by each gas, and the total pressure, in a mixture of real gases, when the volume is known. If the total pressure is given, however, the evaluation of the volume is somewhat more complicated, involving a series of trial solutions. An alternative approxi-... 

But since perpetual motion (distillation of a via the vapour, from one layer to the other) is impossible, it is necessary (by the Second Law of Thermodynamics) that pai = pan and hence xai — xaji That is, the molar concentration of a in both layeis is identical But this is applicable to all the molecular species present in each layer, and hence both layers are identical, and cannot therefore form two phases We must therefore conclude that the above simple vapour pressure law only holds for mixtures composed of perfectly miscible liquids and cannot apply to the cases in which partial miscibility exists The problem of liquid mixtures is in a rather rudimentary stage at present, and further discussion of it in a book of this kind must be omitted1... 

Experiments on osmotic pressure were carried out in 1877 by the German botanist Wilhelm Pfeffer (1845-1920). The osmotic pressure law was derived on the basis of... 

Bin Din, et al. 2005. Adaptability analysis of therock pressure law and bracket in super-length fully-mechanized mining face. Ground Pressure and Strata Control... 

All of these results are perfectly compatible with such kinetic laws, and especially with the pressure laws. 

If the vapor pressure of the solute is small, and the solvent follows Raoult s vapor pressure law,... 

The pressure law states that for a fixed mass of gas (at constant volume) its absolute temperature is directly proportional to pressure. This behaviour can be expressed mathematically as P OS T, where P represents the pressure and T represents the absolute temperature in Kelvin. Alternatively the pressure law can be expressed as P = K x T or P/T = K (where K represents a constant that varies with the gas). 

The pressure law can be used to calculate the new pressure or temperature if a fixed mass of gas (at constant volume) undergoes a change in temperature or pressure. This is done using the following equation ... 

Remember that the Volume-Pressure Law is an inverse proportion V... 

The preceding pressure laws are amended if the gas results from the association of species. 

The influence of the gas pressure on speeds is apparently complex. It is not possible to associate a kinetic law with a pressure law. This influence of the pressure... 

We note that the pressure law when the internal interface is the rate determining step is different from that given in Table 15.4, whereas it remains the same when the external interface reaction is the rate determining step. In both cases, the kinetic law remains linear. 

Thus, the parabolic constant is proportional to the reactivity. Now take again expression [19.30] if the pressure law is correct, on plotting kp against P ", we obtain a straight line at 330°C, as shown in Figure 19.8. Because the separation of variables in the expression of reactivity, it appears that the result remains the same at the other temperatures. 

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