The Variation of Vapor Pressure with Temperature

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. 

When the temperatnre increases, the proportion of molecules with energy in excess of the cohesive energy also increases, and an excess vapor pressnre is observed. The Clansins-Clapeyron eqnation describes the variation of vapor pressure with temperature as follows ... 

In this experiment the variation of vapor pressure with temperature will be measured and used to determine the molar heat of vaporization. 

These equations may be utilized for various purposes for example, if the variation of boiling point with pressure or, what is the same thing, the variation of vapor pressure with temperature, is known, it is possible to calculate the heat of vaporization. Alternatively, if the latter is available, it is possible to determine dT/dP or dp/dT, for the rate of change of boiling point or of vapor pressure, respectively. 

Figure 11.40(a) shows the phase diagram of water. The graph is divided into three regions, each of which represents a pure phase. The line separating any two regions indicates conditions under which these two phases can exist in equilibrium. For example, the curve between the liquid and vapor phases shows the variation of vapor pressure with temperature. (Compare this curve with Figure 11.35.) The other two curves similarly indicate conditions for equilibrium between ice and liquid water and between ice and water vapor. (Note that the solid-liquid boundary line has a negative slope.) The point at which all three curves meet is called the triple point, which is the only condition under which all three phases can be in equilibrium with one another. For water, this point is at 0.01°C and 0.006 atm.

The values in this table were measured either by calorimetric techniques or by application of the Claperyon equation to the variation of vapor pressure with temperature. See Reference 1 for a discussion of the accuracy of different experimental techniques and methods of estimating enthalpy of vaporization at other temperatures. Several of the references present empirical techniques for correlating enthalpy of vaporization with molecular structure. 

You might have noticed that the plots of the variation of vapor pressure with temperature shown in Figure 11.24 have a distinct shape Each curves sharply upward to a higher vapor pressure with increasing temperature. The relationship between vapor pressure and temperature is given by an equation called the Clausius-Clapeyron equation ... 

We noted earlier that the vapor pressure of a substance depends on temperature. The variation of vapor pressure with temperature of some hquids was given in Figure 11.7. 

The Variation of Vapor Pressure with Temperature Solve the vapor pressure equation for two temperatures P2 at T2 and P at T )... 

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