13. Liquids, Solids & Intermolecular Forces
Clausius-Clapeyron Equation
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Now the Clausius Clapeyron equation can be changed into different forms. The first one we're going to talk about is the linear form of it. We're gonna say we use this form of the equation when a plot of the natural log, which is ln of pressure versus inverse temperature is given. So if we talk about this, we can look at it in terms of our graph here. And anytime we do a plot, remember a plot is always of y versus x. Here our y is l and p, which is why it's on the y axis, And then inverse temperature just means 1 over t, that represents our x, so that's why it's here on the x axis. So we have inverse of the, pressure and then we have inverse temperature, 1 over t. Basically, we're gonna use the line form of the Clausius Clapeyron equation to help us determine the enthalpy of vaporization, which is delta h vape. And that's connected to the idea of our slow intercept form of the straight line, which is y equals mx plus b. So again, our y axis has l and p, our x has one over t. Here with this information we can find our slope which equals rise over run, which remember is change in your y divided by change in your x. Here our linear form of the Clausius Clapeyron equation becomes lnp equals negative delta h vape over r times 1 over t plus c. Again, this is related to the slope intercept form of a straight line, so this would be y equals m x plus b. M represents our slope, which represents negative delta h big over r. Now r itself, remember, is our gas constant. It's 8.314 with the units of joules over moles times Kelvin. Pressure here is p is our vapor pressure and it's in units of Torr or millimeters or mercury. When we talk about our delta h of vape, that's our enthalpy of vaporization, here it's customarily in joules per mole. Sometimes you might see it in kilojoules per mole, but just make sure units match. The units of r are in joules, so that's why we tend to see delta h of vape in joules. Now we can also say our temperature here is temperature in Kelvin, and then c is just the constant of a substance. Now again, when it comes to the linear form of the Clausius Clapeyron equation, the most important part is this portion here in blue. This portion here helps us to link together the concept of slope and our enthalpy of vaporization. So keep that in mind when we're given the plot of temperature, and they're asking us to determine either the slope or the enthalpy of vaporization.
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