A Summary of Different Methods Used to Measure Vaporization Enthalpies BG Bourdon gauge C calorimetric determination GCgas chromatography GCCgas chromatography-calorimetry CGCcorrelation gas chromatography DM diaphram manometer DSCdifferential scanning calorimeter EBebullometry GS gas saturation, transpiration HGHeise gauge

HSA head space analysis I isoteniscope IPM inclined piston manometry ME Mass effusion-Knudsen effusion MG McLeod gauge MM mercury manometer OMoil manometer RG Rodebush gauge SGspoon gauge STGstrain gauge T tensimeter TE torsion effusion UVultraviolet absorption A Summary of Different Methods Used to Measure Vaporization Enthalpies (continued)

TBthermobalance TGA thermal gravimetric analysis TPTDtemperature programmed thermal desorption particle beam mass spectrometry TRMthermoradiometric method TSGC temperature scanning gas chromatography UVultraviolet absorption HSA V viscosity gauge VG MKS Baratron Vacuum Gauge

1. Measurement of vapor pressure as a function of temperature - using a manometer 2. Knudsen effusion P =  m(2  RT/mw) 1/2 /  t AK c K c = 8r/(3l +8r) where: P = pressure;  m = mass loss from cell;  t = period of time; A = area of opening mw = molecular weight; T = temperature (K) r = radius of opening; l = thickness of opening Measurement of Vaporization Enthalpies

3. Calvet calorimeter 4. Transpiration 5. Head space analysis 6. Correlation gas chromatography

Correlation gas chromatography

What is t a ? t a is the adjusted retention time t i - t nrr t i = retention time of i th component t nrr = retention time of a non retained reference What does t a measure?

For a pure component, a plot of ln (vapor pressure) vs 1/T over a narrow temperature range results in a straight line. The slope of the line is equal to -  g l H m (T m ), the enthalpy of vaporization. A plot of ln (1/ t a ) vs 1/T over a narrow temperature range results in a straight line. What does the slope measure?

Enthalpy of Transfer Determination for Tetradecane ln(1/t a ) = -  g sln H m (T m )/R + intercept  g sln H m (T m ) * J mol -1 = kJ mol -1

What is  sln g H m (T m ) ? What does it measure? Solute on stationary phase of column  gas phase Thermochemical cycle: Vapor  pure liquid  solution on the capillary column  sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m )

Characteristics of capillary gas chromatographs with FID detectors Typical sample sizes ~ microgram quantities solids or liquids are in “solution” or adsorbed; concentrations are low and too dispersed for crystallization temperatures are also high for crystals to form

Equations for the temperature dependence of ln(1/t a ) for C 14 to C 20 :

 l g H m ( K) = (1.436  0.019)  sln g H m (T m ) – (4.54  0.35); r 2 =

Why does  l g H m ( K) correlate with  sln g H m (T m ) in a linear fashion?  g sln H m (T m ) =  g l H m (T m ) +  sln H m (T m ) We know that  g l H m ( K)  4.69 (n C -n Q ) However T = K is an arbitrary temperature  g l H m (T m ) = A T (n C ) + B T where A is some constant and B is a variable but small in magnitude Lets assume for the moment that  sln H m (T m ) = A sln (n C ) + B sln where B is a variable but small in magnitude The slope of the line from the correlation is given by: slope =  l g H m ( K) /  sln g H m (T m )

slope = [A 298 (n C ) + B 298 ]/{[A T (n C ) + B T ]+ A sln (n C ) + B sln } slope = [A 298 (n C ) + B 298 ]/{(A T + A sln )(n C ) + (B T + B sln )} let A’ = (A T + A sln );B’= (B T + B sln ) slope =/[A 298 (n C ) + B 298 ]/{(A’)(n C ) + (B’)} if = (A’)(n C ) > B’ and A 298 > B 298 then slope = (A 298 )/(A’) = constant

Table 4. Parameters of the Cox Equation. T b A o 10 3 A A 2 tetradecane pentadecane hexadecane heptadecane octadecane nonadecane eicosane Cox Equation ln (p/p o ) = (1-T b /T)exp(A o +A 1 T +A 2 T 2 ) Ruzicka, K.; Majer, V. “Simultaneous treatment of vapor pressures and related thermal data between the triple point and normal boiling temperatures for n- alkanes C 5 -C 20, ” J. Phys. Chem. Ref. Data 1994, 23, 1-39.

 H v (298)  H v (lit) (449)  H sln v  H sln tetradecane pentadecane hexadecane heptadecane octadecane nonadecane eicosane

 l g H m (T)/ kJ mol -1 = 3.816n C  sln H m (T)/ kJ mol -1 = n C +1.08

 l g H m (449 K) / kJ mol -1 = 3.82n C  sln H m (449 K) / kJ mol -1 = -0.35n C  l g H m ( K) / kJ mol -1 = 4.98n C  l g H m ( K)/  sln g H m (449 K) = (4.98n C +1.88)/(3.82n C n C +1.08)  l g H m ( K)/  sln g H m (449 K)= 4.98/(3.47) =  l g H m ( K) /  sln g H m (T m ) = (1.436  0.019)