Vapor Pressure Project: The vapor pressure, P, in millimeters of mercury (mm Hg), of a

Chapter 7, Problem 10

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Vapor Pressure Project: The vapor pressure, P, in millimeters of mercury (mm Hg), of a liquid or a solid (Figure 7-3p) increases as thetemperature increases. The rate of change ofthe vapor pressure, dP/dT, is directlyproportional to P and inversely proportional tothe square of the Kelvin temperature, T. Inphysical chemistry you will learn that thisrelationship is called the Clausius-Clapeyronequation.Figure 7-3pa. Write a differential equation that expressesdP/dT in terms of P and T. Integrate theequation, then solve for P in terms of T .b. The table shows the vapor pressure fornaphthalene (mothballs, C10H8) from an oldedition of Langes Handbook of Chemistry.Use the data for 293 K (20C) and 343 K(70C) to find the two constants in theequation you wrote in part a. You may solvethe system of simultaneous equations eitherin their logarithmic form or in theirexponential form, whichever is more convenient. Dont be afraid of largenumbers! And dont round them off!C K mm Hg10 283 0.02120 293 0.05430 303 0.13340 313 0.32050 323 0.81560 333 1.8370 343 3.9580 353 7.4 (melting point)90 363 12.6100 373 18.5110 383 27.3200 473 496.5c. How well does your function fit the actualdata? Does the same equation fit well abovethe melting point? If so, give information tosupport your conclusion. If not, find anequation that fits better above the meltingpoint. Do any other types of functionsavailable on your grapher seem to fit thedata better than the function from theClausius-Clapeyron equation?d. Predict the boiling point of naphthalene,which is the temperature at which the vaporpressure equals atmospheric pressure, or760 mm Hg.e. What extensions can you think of for thisproject?

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