Note: I can't emphasize enough the fact that you need to be reading this in the book also. For example I spent all of Thursday on section 5.3 with the phase transitions. I spent a good deal of time on the partial derivative things described again on page 157. I spent a lot of time deriving the equation the fully describes the depth at which phase transitions occur. And of course I mentioned a number of times that the phase of a substance with the lower Gibbs free energy is the more stable one at some given T and P (think figure 51.5 here). Then there's that Clausius-Clapeyron equation starting on page 172.

1. problem 5.28
    
2. I worked something like problem 5.28 in class, where I only took into account how the pressure affects the Gibbs free energy of the calcite-aragonite transition. Now, let's do this right: Find the depth z=Δz below Earths' surface at which CaCO₃ will switch from one form to another. Use the temperature gradient of 15K/km, and take the average density of Earth to be 4,500 kg/m³. With your calculations, you should carry your significant figures through since you do have data in the back of the book to 6 sig. figs. However, in the end, you should only have about 2 sig. figs. for your depth. Be careful of your signs on your temperature and pressure gradients. And yes, you should be sure to either show your work or turn in a neat copy of the spreadsheet you created to calculate this.
    
3. Part of the overall air pressure that we experience is due to the water vapor that is in the air. This is the so-called "partial pressure" of the water vapor, since it forms a part of the overall vapor pressure. The ratio of the partial pressure of water vapor when the air is unsaturated with water to when the air is saturated with water is called the "relative humidity;" e.g., when the air is only holding 60% of the water vapor that it could possibly hold, the relative humidity is 60%. This vapor-holding capacity is dependent on the temperature and pressure of the atmosphere, as you well know from experience. The "dew point" temperature is the temperature at which the relative humidity would be 100%; note that when the dew point temperature is less than the actual temperature, then the relative humidity is less than 100%.
   
   It's time to use the Clausius-Clapeyron equation to investigate this situation. Treat the water vapor as an ideal gas like we did in class.
   
   In class, we started to draw the line between the liquid and gaseous phases of water. Look at the data in Figure 5.11: you have the temperature and pressure of the triple point of water: T_TP=0.010⁰C=273.16K and P_TP=0.00612bar=0.00612bar*(1.000atm/1.013bar)=0.00604atm.
   
   (a) Use the data in Figure 5.11 to construct the plot the liquid-vapor boundary for water for the temperatures 5.0^oC, 10.0^oC, 15^oC, etc., every 5.0^oC al the way up to 40.0^oC. Note that the heat of vaporization "L" changes over this temperature range. Use linear interpolation to find the correct values between those given for 0.010^oC, 25.0^oC and 50.0^oC. For those of you uninitiated to this little physics tool, "linear interpolation" means that if L=5.0kJ/mol at 0.0^oC, and L=15.0kJ/mol at 25.0^oC, then the value for L at 15.0^oC would be (15/25) of the way between 5.0kJ/mol and 15.0kJ/mol; e.g., L(15.0^oC)=5.0kJ/mol+(15/25)*(15.0kJ/mol-5.0kJ/mol)=5.0kJ/mol+6.0kJ/mol=11.0kJ/mol.
   
   (b) Suppose that on a certain summer day the temperature is 30.0^oC. What is the dew point temperature if the relative humidity is 90%? If you're not sure how to do this, then ask me and I'll go over this explicitly early next week. This is a practical, everyday application of this material.
    
4. problem 5.48. Note, you really need to read through the section in chapter 5 that talks about the physical nature of the van der Waals equation of state. 
    
5. The van der Waals parameters for methane are a=2.300 atm L²/mol² and b=0.0430 L/mol. Find (P, V, T) of the critical point for methane. Be careful of your units.

That's all for homework #5.

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