Calorimetry calculation

Worked Example 8.5 shows how specific heats are used in calorimetry calculations. 

Knowledge Required (1) The principles of heat flow. (2) The meaning of the term specific heat. (3) The methods for carrying out calorimetry calculations. 

Table 4.5, for a number of substances, gives the values found by calorimetry, calculated using Planck s hypothesis, and the absolute values found by spectroscopic measurements, independent of Planck s hypothesis. We can see two distinct categories of molecules ... 

The cure of novolaks with hexa has been studied with differential scanning calorimetry (dsc) and torsional braid analysis (tba) (46) both a high ortho novolak and a conventional acid-cataly2ed system were included. The dsc showed an exothermic peak indicating a novolak—hexa reaction ca 20°C higher than the gelation peak observed in tba. Activation energies were also calculated. 

The metabolic rate can be measured in several ways. When no external work is being performed, the metabolic rate equals the heat output of the body. This heat output can be measured by a process called direct calorimetry. In this process, the subject IS placed m an insulated chamber that is surrounded by a water jacket. Water flows through the jacket at constant input temperature. The heat from the subject s body warms the air of the chamber and is then removed by the water flowing through the jacketing. By measuring the difference between the inflow and outflow water temperatures and the volume of the water heated, it is possible to calculate the subject s heat output, and thus the metabolic rate, in calories. 

In recent years, fluorine bomb calorimetry has been used effectively. A number of substances that will not burn in oxygen will burn in fluorine gas. The heat resulting from this fluorine reaction can be used to calculate AfH°m. For example, Murray and 0 Hare have reacted GeS2 with fluorine and measured ArH°. The reaction is... 

Calculate energy changes from calorimetry data and write a thermochemical equation (Examples 6.4 and 6.7). 

Volume, pressure, temperature, and amounts of substances may change during a chemical reaction. When scientists make experimental measurements, however, they prefer to control as many variables as possible, to simplify the interpretation of their results. In general, it is possible to hold volume or pressure constant, but not both. In constant-volume calorimetry, the volume of the system is fixed, whereas in constant-pressure calorimetry, the pressure of the system is fixed. Constant-volume calorimetry is most often used to study reactions that involve gases, while constant-pressure calorimetry is particularly convenient for studying reactions in liquid solutions. Whichever type of calorimetry is used, temperature changes are used to calculate q. 

In our world, most chemical processes occur in contact with the Earth s atmosphere at a virtually constant pressure. For example, plants convert carbon dioxide and water into complex molecules animals digest food water heaters and stoves bum fiiel and mnning water dissolves minerals from the soil. All these processes involve energy changes at constant pressure. Nearly all aqueous-solution chemistry also occurs at constant pressure. Thus, the heat flow measured using constant-pressure calorimetry, gp, closely approximates heat flows in many real-world processes. As we saw in the previous section, we cannot equate this heat flow to A because work may be involved. We can, however, identify a new thermod mamic function that we can use without having to calculate work. Before doing this, we need to describe one type of work involved in constant-pressure processes. 

How do we determine the energy and enthalpy changes for a chemical reaction We could perform calorimetry experiments and analyze the results, but to do this for every chemical reaction would be an insurmountable task. Furthermore, it turns out to be unnecessary. Using the first law of thermodynamics and the idea of a state function, we can calculate enthalpy changes for almost any reaction using experimental values for one set of reactions, the formation reactions. 

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. 

This equation is used in calculating heats of solvation of electrolytes. The heat of solution can be determined highly accurately by calorimetry (with an error of <0.1%). This heat is relatively small, and the values are between 100 and +40kJ/mol. Different methods exist to calculate the breakup energies approximately on the basis of indirect experimental data or models. Unfortunately, the accuracy of these calculations is much lower (i.e., not better than 5%). 

Calorimetry. Radioactive decay produces heat and the rate of heat production can be used to calculate half-life. If the heat production from a known quantity of a pure parent, P, is measured by calorimetry, and the energy released by each decay is also known, the half-life can be calculated in a manner similar to that of the specific activity approach. Calorimetry has been widely used to assess half-lives and works particularly well for pure a-emitters (Attree et al. 1962). As with the specific activity approach, calibration of the measurement technique and purity of the nuclide are the two biggest problems to overcome. Calorimetry provides the best estimates of the half lives of several U-series nuclides including Pa, Ra, Ac, and °Po (Holden 1990). 

Table II. Selective Solvent Extraction, Calculated Mc PDMAAm, and Differential Scanning Calorimetry Data...

Kujawa and Winnik [209] reported recently that other volumetric properties of dilute PNIPAM solutions can be derived easily from pressure perturbation calorimetry (PPC), a technique that measures the heat absorbed or released by a solution owing to a sudden pressure change at constant temperature. This heat can be used to calculate the coefficient of thermal expansion of the solute and its temperature dependence. These data can be exploited to obtain the changes in the volume of the solvation layer around a polymer chain before and after a phase transition [210], as discussed in more detail in the case of PVCL in Sect. 3.2.2. 

Data from indirect calorimetry can also be used to determine a respiratory quotient. Values greater than 1 suggest overfeeding, whereas values less than 0.7 suggest a ketogenic diet, fat gluconeogenesis, or ethanol oxidation. Respiratory quotient (RQ) is calculated as follows ... 

In differential scanning calorimetry, the selected chemical reaction is carried out in a cmcible and the temperature difference AT compared to that of an empty crucible is measured. The temperature is increased by heating and from the measured AT the heat production rate, q, can be calculated (Fig. 3.19). Integration of the value of q with respect to time yields measures of the total heats... 

Phosphorus trifluoride has been used as a reactant gas in calorimetry to act as a fluorine acceptor rather than donor. The heats of formation of xenon fluorides have been calculated from the reaction heats (137) ... 

RR R"C3B2Me2)Ni](RR R"C3B2Me2) Ni(RR R"C3B2Me2) Theoretical studies Molecular and electronic structure calculations Triple-decker sandwiches S, EXAFS, thermogravimetry, differential calorimetry, electrical conductivity 44... 

Testing includes screening (e.g., literature research, mixing calorimetiy, thermodynamic calculations, estimation of heats of reaction, DSC, flash point calculations), quantitative assessment (e g., accelerated rate calorimetry, specialized calorimetry), and scaleup (vent size packaging [VSP], modeling, reaction calorimetry). 

In this chapter, you learned about thermochemistry, the heat changes accompanying chemical reactions. You learned about calorimetry, the technique used to measure these heat changes, enthalpies, and the types of heat capacities that we can use in thermochemistry calculations. Finally, you learned about Hess s law and how we can use it to calculate the enthalpy change for a specific reaction. 

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