# Using The Clausius-Clapeyron Equation

## Clausius-Clapeyron Equation

:
Applications :
1. Plot Ln P* vs. 1/T(K) and use the slope to determine .

2. Linearly interpolate on Ln P* vs. 1/T(K) to determine P* at an intermediate T.

3. Correlate { P*,T } data by fitting it to an equation in terms of Ln P* vs. 1/T(K) .
Use this equation to predict P* at any T.

The Antoine Equation:

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### Ch 3, Lesson E, Page 12 - Using The Clausius-Clapeyron Equation

• Well, if you found a table of vapor pressure – temperature data and you plotted the natural log of the vapor pressure vs 1/T (Kelvin) you could estimate ΔHvap from the slope.
• That’s cool.  Remember that ΔHvap is not really constant over a wide range of temperatures.
• Let’s say I told you the vapor pressure of a chemical at 50oC and at 100oC, but you needed the vapor pressure at 65oC.  What would you do ?
• You probably would use the linear interpolation technique that I taught you back in chapter 2.  That wouldn’t be an awful thing to do, but it is not the best way to go.  Why ?
• Well, the Clausius-Clapeyron Equation tells us that P* vs T is NOT linear !  So, linear interpolation is NOT accurate !  Oops
• The good news is that that the Clausius-Clapeyron Equation tells us that the natural log of P* vs 1/T(Kelvin) IS linear !
• So, we need to setup a linear interpolation table using Ln(P*) vs 1/T(Kelvin) !
• That will yield the best estimate of the vapor pressure at 65oC.
• This is only accurate over a range of temperatures for which the ΔHvap is approximately constant, right ?  Remember our assumptions in the development of the Clausius-Clapeyron Equation.
• If you really want to accurately correlate vapor pressure data, you definitely want to use the natural log of P* and 1/T(Kelvin), but the equation is not necessarily linear because we know that ΔHvap is not really a constant.
• The most popular simple correlation for vapor pressure is called the Antoine Equation.
• This is an extremely useful equation and you will find values of the constants A, B and C tabulated in a wide variety of reference books as well as in the NIST WebBook.