Relations at constant temperature

The first conclusion to be drawn from the application of the fundamental equation is that when only one substance is present as gas or vapour, which is absent in the solid form, its concentration must be constant at any given temperature, i. e. its pressure must be. The phenomenon thus, by the existence of a maximum pressure, connects with that of simple evaporation e. g. there is a maximum pressure for the partial decomposition of calcium carbonate  

If more than one gas or vapour occurs in the gaseous phase, and not condensed, the fundamental equation leads 

Accordingly the relation between partial pressure of hydrogen and water vapour is constant, as appears from the following data — 

The same relation is observed in the equilibrium between ammonium carbonate on the one side, ammonia and carbon dioxide on the other the latter in varying ratios produced by intentional addition of one or other gas. We have then Pco.P ism, = const., 

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If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

An adsorption isotherm for a single gaseous adsorptive on a solid is the function which relates at constant temperature the amount of substance adsorbed at equilibrium to the pressure (or concentration) of the adsorptive in the gas phase. The surface excess amount rather than the amount adsorbed is the quantity accessible to experimental measurement, but, at lower pressures, the difference between the two quantities becomes negligible (see Appendix II, Part I, 1.1.11). 

Much information about protein absorption can be obtained by measuring the electrochemical isotherm, the 0 - csoln relation at constant temperature for a series of fixed potentials. One takes the protein (P) as absorbing fast upon the metal, and transferring n electrons, corresponding to n carbonyl interactions. The dissociation reaction is taken to be rate determining. Then (Roscoe, 1996) ... 

The relation, at constant temperature, between the amount adsorbed (properly defined in Section 11.2.1.3.B) and the equilibrium pressure of the gas is known as the adsorption isotherm. 

The terms adsorption and desorption are often used to indicate the direction from which the equilibrium states have been approached. Adsorption hysteresis arises when the amount adsorbed is not brought to the same level by the adsorption and desorption approach to a given equilibrium pressure or bulk concentration. The relation, at constant temperature, between the amount adsorbed and the equilibrium pressure, or concentration, is known as the adsorption isotherm. 

The investigations in this direction are only in their first stages, and we can only describe the relations at constant temperature. 

In the preceding chapter we considered the changes in the solubility of double salts and of mixtures of their constituent salts with the temperature noting, more especially, the relationships between the two systems at the transition point. It is now proposed to conclude the study of the three-component systems by discussing very briefly the solubility relations at constant temperature, or the isothermal solubility curves. In this way fresh light will be thrown on the change in the solubility of one component by the addition of another component, and also on the conditions of formation and stable existence of double salts in solution. With the help of these isothermal curves, also, the phenomena of crystallisation at constant temperature—phenomena which have not only a scientific interest but also an important bearing on the industrial pieparation of double salts— will be more clearly understood. ... 

Adsorption isotherm The relation at constant temperature between the amount adsorbed and equilibrium pressure or concentration... 

Surface Excess Isotherm A function relating, at constant temperature and pressure, the relative adsorption, reduced adsorption, or similar surface excess quantity to the concentration of component in the equilibrium bulk phase. 

Current density-concentration relation at constant temperature and potential... 

Isotherm Ts9- th9rm [F isotherme, adj (1859) n. Constant temperature line used on graphs of climatic conditions or thermodynamic relations, such as pressure-volume relations at constant temperature. Ready RG (1996) Thermodynamics. Plenum Publishing Co., New York. 

Fugaeity fi of component i is defined by the following relation at constant temperature T ... 

The volume of 1.000 mole of any gas is 22.42 L, assuming the gas behaves ideally. Therefore, the molar volume of He(g) and N2(g) at STP both equal 22.42 L/mol. If the temperature increases to 25.0°C (298.2 K), the molar volume of a gas will be larger than 22.42 L/mol because volume and temperature are directly related at constant pressure. If 1.000 mole of a gas is collected over water at a total pressure of 1.000 atm, the partial pressure of the collected gas will be less than 1.000 atm because water vapor is present (Ftotai = PgiB + Fhjo)- At some partial pressure below 1.000 atm, the molar volume of a gas will be larger the 22.42 L/mol because volume and pressure are inversely related at constant temperature. 29. No At any nonzero Kelvin temperature, there is a distribution of kinetic energies. Similarly, there is a distribution of velocities at any nonzero Kelvin temperature. 31.2NH3(g) —4 N2(g) 4- 3H2(g) At constant P and T, volume is directly proportional to the moles of gas present. In the reaction, the moles of gas double as reactants are converted to products, so the volume of the container should double. At... 

Boyle s law shows how P and V are related at constant temperature, and Charles s law shows how V and T are related at constant pressure. But what if two of these variables change at once For example, what happens to the volume of a gas if both its pressure and its temperature are changed ... 

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