Vapor pressure variation with temperature

The formation of dew and fog are consequences of this variation in relative humidity. Warm air at high relative humidity may cool below the temperature at which its partial pressure of H2O equals the vapor pressure. When air temperature falls below this temperature, called the dew point, some H2 O must condense from the atmosphere. Example shows how to work with vapor pressure variations with temperature, and our Chemistry and the Environment Box explores how variations in other trace gases affect climate. 

The mixture has a mass composition of ethylbenzene (14), p-xylene (20), m-xylene (40) and o-xylene (26). Examination of the boiling points in Table 3.15 reveals that the separation by distillation is very difficult, the largest temperature difference ethylbenzene/o-xylene being of only 8.2 °C at a relative volatility of 1.25. Using vacuum does not help since the vapor-pressure variation with the temperature is similar for all isomers. 

At the saturation pressure, the viscosity variation with temperature follows a law analogous to that of Clapeyron for the vapor pressure f ) ... 

Clausius-Clapeyron Equation. This equation was originally derived to describe the vaporization process of a pure liquid, but it can be also applied to other two-phase transitions of a pure substance. The Clausius-Clapeyron equation relates the variation of vapor pressure (P ) with absolute temperature (T) to the molar latent heat of vaporization, i.e., the thermal energy required to vajxirize one mole of the pure liquid ... 

Let s use Eq. 3 to obtain a quantitative expression for the temperature variation of the vapor pressure. It is known experimentally that neither the enthalpy nor the entropy of vaporization varies much with temperature so, for a given substance, ASvap° and AHvap° can both be treated approximately as constant. It follows that the vapor pressures P, and P2 at any two temperatures 7 , and T2 are related by writing Eq. 3 for two temperatures and subtracting one from the other. In the process, the entropy terms cancel ... 

Estimation of gas-liquid mass-transfer rates also requires the knowledge of solubilities of absorbing and/or desorbing species and their variations with temperature (i.e., knowledge of heats of solution). In some reactions, such as hydrocracking, significant evaporation of the liquid occurs. The heat balance in a hydrocracker would thus require an estimation of the heat of vaporization of the oil as a function of temperature and pressure. The data for the solubility, heat of solution, and heat of vaporization for a given reaction system should be obtained experimentally if not available in the literature. 

The Kirchhoff equation as derived above riiould be applicable to both chemical and physical processes, but one highly important limitation must be borne in mind. For a chemical reaction there is no difficulty concerning (dAH/dT)p, i.e., the variation of AH with temperature, at constant pressure, since the reaction can be carried out at two or more temperatures and AH determined at the same pressure, e.g., 1 atm., in each case. For a phase change, such as fusion or vaporization, however, the ordinary latent heat of furion or vaporization (AH) is the value under equilibrium conditions, when a change of temperature is accompanied by a change of pressure. If equation (12.7) is to be applied to a phase change the AH s must refer to the same pressure at different temperatures these are consequently not the ordinary latent heats. If the variation of the equilibrium heat of fusion, vaporization or transition with temperature is required, equation (12.7) must be modified, as will be seen in 271. 

The variation with temperature of the electrode potentials for pure water vapor and pure carbon dioxide at standard pressure is shown in Figure 25-1. 

Since the total pressure of the vapor-liquid system is constant, the equilibrium constant, Ki, has the same temperature dependence as the vapor pressure, P9. This variation with temperature may be quite large and can significantly complicate temperature-dependent calculations. 

Reaction 1 is highly exothermic. The heat of reaction at 25°C and 101.3 kPa (1 atm) is ia the range of 159 kj/mol (38 kcal/mol) of soHd carbamate (9). The excess heat must be removed from the reaction. The rate and the equilibrium of reaction 1 depend gready upon pressure and temperature, because large volume changes take place. This reaction may only occur at a pressure that is below the pressure of ammonium carbamate at which dissociation begias or, conversely, the operating pressure of the reactor must be maintained above the vapor pressure of ammonium carbamate. Reaction 2 is endothermic by ca 31.4 kJ / mol (7.5 kcal/mol) of urea formed. It takes place mainly ia the Hquid phase the rate ia the soHd phase is much slower with minor variations ia volume. 

Fig. 8. Variation of vapor pressure with temperature for gas turbine fuels (14). To convert kPa to psi, divide by 6.9.

Notwithstanding their very low vapor pressure, their good thermal stability (for thermal decomposition temperatures of several ionic liquids, see [11, 12]) and their wide operating range, the key property of ionic liquids is the potential to tune their physical and chemical properties by variation of the nature of the anions and cations. An illustration of their versatility is given by their exceptional solubility characteristics, which make them good candidates for multiphasic reactions (see Section 5.3.4). Their miscibility with water, for example, depends not only on the hydrophobicity of the cation, but also on the nature of the anion and on the temperature. 

FIGURE 7.25 The variation of the (molar) Gibbs free energy with temperature for three phases of a substance at a given pressure. The most stable phase is the phase with lowest molar Gibbs free energy. We see that, as the temperature is raised, the solid, liquid, and vapor phases in succession become the most stable. 

Since we did not measure the conversion during the experiment, we computed the equilibrium vapor pressure at the average solution temperature. We believe that, for safety design, the equilibrium vapor pressure is an adequate estimate of the styrene vapor pressure. For example, even at a 50% conversion, the difference is only 10 at the experimental temperatures. Figures 6, 7 and 8 compared the observed pressures with the computed total pressures. The latter were based on the equilibrium vapor pressure. As expected, there were increasing variations in Tests 1, 2 and 3 respectively because of their higher initial conversions. From these figures we can verify that our pressure and temperature measurements were in phase with respect to time. 

It is of interest to consider the variation of vapor pressure with temperature. The vapor pressure of a liquid is constant at a given temperature. It increases with increasing temperature upto the critical temperature of the liquid. The liquid is completely in the vapor state above the critical temperature. The variation of the vapor pressure with temperature can be expressed mathematically by the Clapeyron-Clausius equation. Clausius modified the Clapeyron equation in the following manner by assuming that the vapor behaves like an ideal gas. 

The variation in the vapor pressure of a pure metal with temperature is usually approximated by the relationship... 

All partitioning properties change with temperature. The partition coefficients, vapor pressure, KAW and KqA, are more sensitive to temperature variation because of the large enthalpy change associated with transfer to the vapor phase. The simplest general expression theoretically based temperature dependence correlation is derived from the integrated Clausius-Clapeyron equation, or van t Hoff form expressing the effect of temperature on an equilibrium constant Kp,... 

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