Clausius-Clapeyron equation integrated form

Two estimates will be made using vapor pressure data from the CRC Handbook [63] and the integrated form of Clausius-Clapeyron equation ... 

It is possible, however, to simplify the calculation of the energy transfer by assuming that the vapor phase is always a saturated vapor. O Connor (Ol) has shown that the rate of approach of a superheated vapor to saturated conditions is extremely rapid when the superheated vapor is in direct contact with its liquid phase. If the vapor phase is assumed to be saturated, the temperature of the phase can be calculated from an integrated form of the Clausius-Clapeyron equation instead of from the vapor-phase energy-transfer equation. 

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,... 

The form of the Clausius-Clapeyron equation in Equation (5.5) is called the integrated form. If pressures are known for more than two temperatures, an alternative form may be employed ... 

We employ the integrated form of the Clausius-Clapeyron equation when we know two temperatures and pressures, and the graphical form for three or more. 

One of the critical issues in vapor pressure methods is the choice of the procedure to calculate the vaporization enthalpy. For instance, consider the vapor pressures of ethanol at several temperatures in the range 309-343 K, obtained with a differential ebulliometer [40]. The simplest way of deriving an enthalpy of vaporization from the curve shown in figure 2.4 is by fitting those data with the integrated form of the Clausius-Clapeyron equation [1] ... 

What would be the form of the integrated Clausius-Clapeyron equation if the heat capacity of the vapor were given by the equation... 

Equation (7.35c) is known as the Clausius-Clapeyron equation, which may also be expressed in integrated form... 

Equation (11) is an integrated form of Clausius-Clapeyron equation. If the integration is carried out indefinitely (without limits) then we can write the vapour-pressure equation (9) as,... 

Calculate the number n of moles of HCl in the solution dispensed. Give S and 5 for the initial and final volumes, and give a limit of error (95 percent confidence) for n. The heat of vaporization of a liquid may be obtained from the approximate integrated form of the Clausius-Clapeyron equation. 

Solids Below the triple point, the pressure at which the solid and vapor phases of a pure component are in equilibrium at any given temperature is the vapor pressure of the solid. It is a monotonic function of temperature with a maximum at the triple point. Solid vapor pressures can be correlated with the same equations used for liquids. Estimation of solid vapor pressure can be made from the integrated form of the Clausius-Clapeyron equation... 

In order to extend the method of calculating ideal solubilities of gases to temperatures above the critical point, when the liquid cannot exist and direct determination of the vapor pressure is not possible, it is necessary to estimate a hypothetical vapor pressure by suitable extrapolation. This is best done with the aid of the integrated form of the Clausius-Clapeyron equation. If the vapor pressures at any two temperatures are known, the hypothetical value at a temperature above the critical point may be evaluate on the assumption that the heat of vaporization remains constant. 

Use the definite integral form of the Clausius-Clapeyron equation [Solution to Exercise 4.8(b)]. /pi AvapH ( I 1 ... 

One such method uses a linear relation between temperature and the molar heat of vaporization which is estimated using the Kistiakowsky Constant. The integrated form of the Clausius-Clapeyron equation may be expressed... 

The equation of Clausius and Clapeyron in integrated form for the dependence of the vapor pressure p on temperature T reads as... 

We can estimate the position of the liquidus assuming that our mixture forms an ideal solution, hence it obeys Raoult s law. From the Clausius-Clapeyron equation with some integration and algebraic manipulation we can obtain... 

Over a limited temperatme range around an equilibrium condition (po,Tb), where AH a constant, an integrated form of the Clausius-Clapeyron equation apphes... 

Solution As known, the integrated form of Clapeyron-Clausius equation is,... 

Integrated Form of Clapeyron-Clausius Equation for Uquid=Gas Equilibrium... 

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