Enthalpy constant-volume calorimetry

Equation can also be used to calculate the standard enthalpy of formation of a substance whose formation reaction does not proceed cleanly and rapidly. The enthalpy change for some other chemical reaction involving the substance can be determined by calorimetric measurements. Then Equation can be used to calculate the unknown standard enthalpy of formation. Example shows how to do this using experimental data from a constant-volume calorimetry experiment combined with standard heats of formation. 

Bomb" combustion calorimetry or constant-volume calorimetry is a technique that dates back to Lavoisier178 (Fig. 11.76), is now mostly relegated to undergraduate teaching laboratories and is in bad need of a renaissance. It measures the internal energy of combustion AEc, which is easily converted to AHc, and then converted to standard enthalpies of formation AHf s.is- In a typical "macro" experiment, with commercially available equipment, a very carefully measured mass m (-2.0 g) of a sample of molar mass M g/mol and... 

If a calorimetry experiment is carried out under a constant pressure, the heat transferred provides a direct measure of the enthalpy change of the reaction. Constant-volume calorimetry is carried out in a vessel of fixed volume called a bomb calorimeter. Bomb calorimeters are used to measure the heat evolved in combustion reactions. The heat transferred under constant-volume conditions is equal to A Corrections can be applied to A values to yield enthalpies of combustion. 

This section reviews calorimetry [69-71] the measurement for a "system" (=sample+container) of (1) the "latent" enthalpy AH, (2) the internal energy AE, (3) the heat capacity at either constant pressure, CP = dH/dT, or (4) the heat capacity at constant volume Cv = dE/dT. All these measurements require careful control of the initial and final states, along with reliable temperature measurements for the system relative to its surroundings. Around room... 

The measurement of heat capacity and related quantities is known as calorimetry. Most often the constant-pressure heat capacity is measured some instruments measure the constant-volume heat capacity Cy. Often, what is actually measured is not the derivatives Cp and Cy but an energy change divided by a small but finite temperature change. In some cases, the original enthalpy increment data may be more useful than the approximate heat capacities derived from them. In addition to the lUPAC books referenced in Section 1.8.1, the monograph of Flemminger and Flohne... 

The heat capacity and transition enthalpy data required to evaluate Sm T ) using Eq. 6.2.2 come from calorimetry. The calorimeter can be cooled to about 10 K with liquid hydrogen, but it is difficult to make measurements below this temperature. Statistical mechanical theory may be used to approximate the part of the integral in Eq. 6.2.2 between zero kelvins and the lowest temperature at which a value of Cp,m can be measured. The appropriate formula for nonmagnetic nonmetals comes from the Debye theory for the lattice vibration of a monatomic crystal. This theory predicts that at low temperatures (from 0 K to about 30 K), the molar heat capacity at constant volume is proportional to Cv,m = aT, ... 

Calorimetry is the measurement of heat changes as the temperature of a substance is varied. In a calorimeter in which the sample is held at constant volume, changes in internal energy are detected. If the pressure is constant, then enthalpy changes are measured. In the latter (more usual) experiment, phase transitions are characterized by finite enthalpy changes if they are first order or changes in the gradient of enthalpy with temperature if they are second order (Fig. 1.4). 

I continue to feel that the study of the volume changes in protein reactions is sorely neglected. They may be determined by dilatometry and by the effects of pressure on protein equilibrium constants. The results complement the results of the determination of enthalpy changes as measured by calorimetry and the effects of temperature on equilibrium constants. Much useful insight at the molecular level can be obtained from a knowledge of volume changes... 

Thermal properties are measured by some form of calorimetry, an exacting experimental procedure in which some kind of reaction is carried out, such as dissolution of a solid phase, and the heat (q) released or absorbed is measured. If the reaction occurred at constant pressure, the measured is a AH, and if not, it is fairly easily converted into a AH. Entropy can also be measured by calorimetry, though of a different type, and combining the enthalpy and entropy measurements gives AG numbers. Values of AG° can also be obtained by other methods, to be discussed in later chapters. All these quantities are related to the heat capacity, which turns out to be a very fundamental and important parameter. If pressure changes are important, then the volume or density is also required. 

As the temperature of a crystalline polymer increases, the phase transition is achieved when the crystallinity is dissolved. This process is known as fusion and is investigated by X-ray diffraction, specific volume, double refraction or calorimetry measurements. Using this last test, it is quite easy to identify the melting point, because this process is accompanied by an increase in enthalpy (heat absorption at constant pressure) (Fig. 2.22). 

The goal of thermodynamics is to establish basic functions of state, the most important of which (for differential scanning calorimetry) are U, internal energy H, enthalpy p, pressure V, volume S, entropy and Cp, heat capacity at constant pressure. 

---