Freezing enthalpy changes

Vaporization and condensation are opposite processes. Thus, the enthalpy changes for these processes have the same value but opposite signs. For example, 6.02 kJ is needed to vaporize one mole of water. Therefore, 6.02 kJ of energy is released when one mole of water freezes. 

Nagaoka s equation (Nagaoka et al, 1955) is an extension of Plank s model and takes into account the time required to reduce the temperature from an initial temperature T, above the freezing poinf. The lafenf heat of fusion in equafion 3.3 is replaced by the total enthalpy change A/i which includes the sensible heat which must be removed in reducing the temperature from an initial T and in addition an empirical correction factor is included. Thus... 

They thus have time to react and approach their low-pressure composition before the equilibria freeze. Both heats refer to the same standard temperature, e.g. 298°K, and can be corrected to give the standard enthalpy change on formation of the respective set of products from the explosive... 

We saw in Section 8.5 that an enthalpy change is often called a heat of reaction because it is a measure of the heat flow into or out of a system at constant pressure. If the products have more enthalpy than the reactants, then heat has flowed into the system from the surroundings and AH has a positive sign. Such reactions are said to be endothermic (endo means "within," so heat flows in). The reaction of 1 mol of barium hydroxide octahydrate with ammonium chloride, for example, absorbs 80.3 kj from the surroundings (AH° = +80.3 kj). The surroundings, having lost heat, become so cold that water freezes around the outside of the container (Figure 8.6). 

The enthalpy change associated with freeze of water at 273K is -d.OkJmol 1. The heat capacity (Cp) for water is 75.3Jmor K I and for ice 37.6Jmol 1K 1. Calculate the... 

Another important equation, the Gibbs-Helmholtz equation, is derived from the Maxwell relations. A chemist may use this equation to determine the enthalpy change in a reaction, and a pharmaceutical scientist may use it to calculate colligative properties (i.e., freezing point depression and boiling point elevation). The expression for free energy with respect to temperature at constant pressure is given by Equation (1.105) ... 

By taking the slope of the plot of AG/T vs. 1/T, one can determine the enthalpy change for a reaction. The equilibrium constants at different temperatures under constant pressure, freezing point depression, and boiling point elevation may be calculated from Equation (1.116), as will be discussed in Chapter 3. 

K), the adiabatic temperature for complete conversion in a chemical reactor would be around 2400 K. The external resistance R x "freezes the reactor, both by reducing the rate of the reaction and by allowing only a portion of the reaction enthalpy change (-AH°) to be converted into heat. 

Enthalpy changes accompany such processes as the dissolution of a solute, the formation of micelles, chemical reaction, adsorption onto solids, vaporisation of a solvent, hydration of a solute, neutralisation of acids and bases, and the melting or freezing of solutes. 

Let us first examine what thermodynamics predicts when this process occurs at the ordinary freezing point of water under atmospheric pressure, 273.15 K. The measured enthalpy change (the heat absorbed at constant pressure) is... 

The reverse processes, condensing and freezing, have enthalpy changes of the same magnitude but opposite sign ... 

The three states of water are so common because they all are stable under ordinary conditions. Carbon dioxide, on the other hand, is familiar as a gas and a solid (dry ice), but liquid CO2 occurs only at external pressures greater than 5 atm. At ordinary conditions, solid CO2 becomes a gas without first becoming a liquid. This process is called sublimation. Freeze-dried foods are prepared by sublimation. The opposite process, changing from a gas directly into a solid, is called deposition—you may have seen ice crystals form on a cold window from the deposition of water vapor. The heat of sublimation (Aff°ubi) is the enthalpy change when 1 mol of a substance sublimes. From Hess s law (Section 6.5), it equals the sum of the heats of fusion and vaporization ... 

Figure 12.2 Phase changes and their enthalpy changes. Each type of phase change is shown with its associated enthalpy change. Fusion (or melting), vaporization, and sublimation are endothermic changes (positive AH°), whereas freezing, condensation, and deposition are exothermic changes (negative AH°).

Similarly, if you freeze water at 272 K, the enthalpy change is now -6008kJmol", and... 

Enthalpy changes also accompany physical transformations such as vaporization, freezing, and sublimation. 

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