5 Thermodynamics & Kinetics-Clausius-Clapeyron Equation, Lecture notes of Chemistry

Download 5 Thermodynamics & Kinetics-Clausius-Clapeyron Equation and more Lecture notes Chemistry in PDF only on Docsity! 5.60 Spring 2007 Lecture #19 page 1 Clausius-Clapeyron Equation Let’s revisit solid-gas & liquid-gas equilibria. We can make an approximation: >> ∆ ∆ ≈gas solid liquid gas vapsubl, , V V V V V V We can ignore the molar volume of the condensed phase compared to the gas. Taking the Clapeyron equation (exact), e.g. for solid-gas eq. and using the approximation above: ∆ ∆ ∆ = = ≈ ∆ ∆ subl subl subl gas subl subl S H Hdp dT V T V TV Assuming an ideal gas, =gas RTV p ⇒ ∆ ∆ = =subl subl 2 2 ln p H Hdp dp p d p dT RT dT dT RT = This is the Clausius-Clapeyron Equation for liq-gas, replace ∆ subH with ∆ vapH i.e. ∆ ∆ = =vap vap 2 2 ln p H Hdp pdp d p dT RT dT dT RT = The Clausius-Clapeyron equation relates the temperature dependence of the vapor pressure of a liquid or a solid to ∆ vapH or ∆ subH (respectively). 5.60 Spring 2007 Lecture #19 page 2 We can make another approximation: Assuming ∆ sublH independent of T, 2 2 1 1 subl subl subl2 2 1 2 1 2 1 1 1 1 ln p T p T H Hdp p T TdT p R T p R T T R TT ⎛ ⎞ ⎛∆ ∆ − = = − − =⎜ ⎟ ⎜ ⎝ ⎠ ⎝ ∫ ∫ 1 2 H ⎞∆ ⎟ ⎠ This is the Integrated Clausius-Clapeyron Equation (for liq-gas, replace ∆ subH with ∆ vapH ) i.e. ∆ ∆⎛ ⎞ ⎛ − ⎞ − =⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ vap vap2 2 1 1 2 1 1 2 1 1H H T T T T R TT = −ln p p R In practice this is how you determine vapor pressure over a liquid or solid as a function of T. Clausius-Clapeyron problems have the two following forms: 1. You know (T1,p1) and (T2,p2) for s-g or ℓ-g coexistence and want to know ∆ subH or ∆ vapH 2. You know (T1,p1) and ∆ subH or ∆ vapH for s-g or ℓ-g coexistence and want to know (T2,p2) (coexistence). This allows you, for example, to calculate that the boiling point in Denver is 97°C. 5.60 Spring 2007 Lecture #19 page 5 Another example: RDX (1,3,5-trinitro-1,3,5-triazacyclohexane) is widely used in military applications, including high explosives and rocket and gun propellants. It is also a common ingredient of commercial and military plastic explosives, including C-4 and Semtex, and is often employed for illicit or criminal purposes. It is a white solid with a melting point in the pure state of 204 ∞C (481 K). Designing reliable detectors for the presence of RDX requires having an accurate knowledge of its vapor pressure as a function of temperature. Literature data have been reviewed in a recent DOT/TSA report, “Vapor Pressure Data Base for Explosives and Related compounds,” by J. C. Wormhoudt (Oct. 2003). Vapor pressure data for RDX are shown in the diagram. The vapor pressure data are well described by the Clausius-Clapeyron equation to within ±95% confidence limits. Note that the vapor pressure of RDX at 300 K (at which, for example, an explosives detector at an airport security screening station would have to operate is only 10-11 bar. Note also that since all reported data are for temperatures less than 450 K the process represented by these data is actually sublimation rather than evaporation from the liquid phase. 5.60 Spring 2007 Lecture #19 page 6 0- ! \ 24 p~ 10° Torr | a4 ~10™ bar i (10 parts per trillion!) | ge i 5 6-4 i 3 3 i a @ RDX Data Points { 10-4 —— Clausius-Clapeyron Fit to All Data j — 95% Confidence Limits | —— 95% Prediction Limits 124 ms: T T T T T T T T 24 2.6 28 3.0 3.2 34 3.6 3.8 1O00/TCRY 400K 300K = 3.3