Enthalpy Changes For Phase Transitions

Estimate the heat of fusion or heat of vaporization from empiricai for-muias, or iook up the vaiue in a reference tabie. 

Estimate the heat of vaporization from the Clausius-Ciapeyron equation or the Othmer piot. 

Calculate an enthalpy change of a substance including the phase transitions. 

Heat of fusion Heat of vaporization Heat of condensation Heat of sublimation Solid to liquid Liquid to vapor Vapor to liquid Solid to vapor 

You can see from the chart for n-butane (Fig. 4.9) that the heats of vaporization (and 

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Enthalpy Changes for Phase Transitions of Rare-Earth lodates84... 

The enthalpy change for the transition from a crystal phase to a hquid phase. 

Although there are other ways, one of the most convenient and rapid ways to measure AH is by differential scanning calorimetry. When the temperature is reached at which a phase transition occurs, heat is absorbed, so more heat must flow to the sample in order to keep the temperature equal to that of the reference. This produces a peak in the endothermic direction. If the transition is readily reversible, cooling the sample will result in heat being liberated as the sample is transformed into the original phase, and a peak in the exothermic direction will be observed. The area of the peak is proportional to the enthalpy change for transformation of the sample into the new phase. Before the sample is completely transformed into the new phase, the fraction transformed at a specific temperature can be determined by comparing the partial peak area up to that temperature to the total area. That fraction, a, determined as a function of temperature can be used as the variable for kinetic analysis of the transformation. 

Enthalpies of phase transitions are reported in kilojoules per mole. The enthalpy change for a reverse reaction is the negative of the enthalpy change for the forward reaction. Enthalpy changes can be added to obtain the value for an overall process. 

The heating curve of a substance shows how its temperature changes as energy is supplied as heat at a constant rate. The curve contains a lot of useful information about a substance, including the temperature and enthalpy of each phase transition and the heat capacity of each phase. Simple laboratory heaters can be used to obtain a crude estimate of a heating curve. However, for accuracy, one of two related techniques is normally used. 

Figure 4.10 Enthalpy change for water at 1 atmosphere showing the phase transitions.

We shall proceed as in Example 4.31 to add the known chemical equations and the phase transitions to yield the desired cheimcal equation and carry out the operations on the enthalpy changes. For reaction A, AH = S A ff/products 2 ff/ teactants. 

The other common category of calorimetry is differential methods, in which the thermal behavior of the substance being measured is compared to that of a reference sample whose behavior is known. In differential scanning calorimetry (DSC), the instrument measures the difference in power needed to maintain the samples at the same temperature. In differential thermal analysis (DTA), the samples are heated in a furnace whose temperature is continuously changed (usually linearly), and the temperature difference between the sample and the reference sample as a function of time can yield thermodynamic information. DSC and DTA are most commonly used for determining the temperature of a phase transition, particularly for transitions involving solids. In addition, DSC experiments can yield values for the enthalpy of a phase transition or the heat capacity. Commercial DSC and DTA instruments are available. 

At the critical point the difference between liquid and vapour volumes approaches zero, suggesting that the energy needed for phase transition, in other words the enthalpy of vaporisation, should diminish to zero. The above observation illustrates in a simple manner the link between the PVT behaviour of a fluid and the energy implied in its physical changes. 

The polymorphism of calcium carbonate is still not completely understood despite its very long history and the appearance of many published studies. In addition to calcite, aragonite and vaterite, non-crystalline forms of CaCOs of biolo cal origin exist. An account of the relationships between these solid phases has appeared recently [39] together with a summary of thermodynamic and kinetic data for the transformations of the metastable polymorphs aragonite and vaterite to the stable calcite. These authors describe the preparation of non-crystalline calcium carbonate and report preliminary values of the transition temperature and enthalpy change for its crystallization to calcite. The DSC method, siq)ported by TG and PXRD, was used in this study. 

Solution This problem is very similar to Example 2.1 . where we calculated the enthalpy changes for the same conditions. The normal boiling point of toluene is = 383.79 K therefore, in both cases we are dealing with a phase transition. The vapor phase will be treated as an ideal gas. Both the ideal-gas heat and liquid-phase heat capacities are given by the pol)momial function... 

Log Kf—can all be reduced to Cp j over the relevant temperature range and S° and AfH° at one specific temperature (usually, but not necessarily, 298 K). (If the temperature range involves phase transitions, one must know in addition the appropriate enthalpy change for vaporization, AH for sublimation or A/f for melting.) All the other... 

So far we have considered enthalpy changes for simple physical processes such as temperature changes and phase transitions. But the importance of chemistry to the energy economy arises from the fact that there are enthalpy changes in chemical reactions as well. This enthalpy change is commonly referred to as the heat of reaction. Because many reactions are carried out under constant pressure conditions, this term is sensible, even if slightly imprecise. 

Retention in chromatography is controlled by thermodynamic equilibria. The partition ofthe analyte between the mobile and the stationary phase is in control of the retention factor. This partition can be described by the laws of reversible thermodynamics. Therefore, we also borrow the thermodynamic description of the temperature dependence of equilibria. This is the so-called van t Hoff equation, which is the quantitative expression of the Le Chatelier principle. According to this, the temperature dependence of the retention factor k can be described by 2.9, with R being the general gas constant, AH° the molar enthalpy (heat tone) related to the transition of the analyte from mobile to stationary phase, AS° the molar entropy change for this transition, andj( the so-called phase ratio of the packed stationary phase in the column. 

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