Equilibrium/equilibria temperature changes

Let us consider a solution of three substances A, B and C which do not react together, and suppose the solution is in equilibrium with one of the solid components. Then c = 3, r = 0, = 2 whence — 3 and the system is trivariant. We can thus consider the pressure and composition of the solution (p, Xj, x ) and see how the equilibrium temperature changes with these variables. Let us take the pressure as constant,... 

When two objects at different temperatures are brought into contact, heat flows from the hotter to the colder body (Figure 1-18) this continues until the two are at the same temperature. We say that the two objects are then in thermal equilibrium. The temperature change that occurs for each object depends on the initial temperatures and the relative masses and specific heats of the two materials. 

I See the Saunders Interactive General Chemistry CD-ROM, Screen 16.12, Disturbing a Chemical Equilibrium (2) Temperature Changes. 

Since the earth has temperature, it emits radiant energy known as thermal radiation or planetary infrared radiation. Satellites have measured an average radiant emission from the earth of about 240 watts per square meter. This is the radiation a black body gives off if its temperature is about -19°C (-3°F). This is also the same energy rate as the solar constant averaged over the earth s surface minus the 30% reflected radiation. Thus, the amount of radiation emitted by the earth is closely balanced by the amount of solar energy absorbed. Because the earth is in this state of radiation equilibrium, its temperature changes relatively slowly from year to year. 

To reestablish equilibrium, a temperature change ATe results, which can be related to AFnet by a parameter Xq... 

Final temperature of the calorimeter at constant heat production rate Equilibrium temperature change... 

Perturbation or relaxation techniques are applied to chemical reaction systems with a well-defined equilibrium. An instantaneous change of one or several state fiinctions causes the system to relax into its new equilibrium [29]. In gas-phase kmetics, the perturbations typically exploit the temperature (r-jump) and pressure (P-jump) dependence of chemical equilibria [6]. The relaxation kinetics are monitored by spectroscopic methods. 

The previous subsection described single-experiment perturbations by J-jumps or P-jumps. By contrast, sound and ultrasound may be used to induce small periodic perturbations of an equilibrium system that are equivalent to periodic pressure and temperature changes. A temperature amplitude 0.002 K and a pressure amplitude 5 P ss 30 mbar are typical in experiments with high-frequency ultrasound. Fignre B2.5.4 illustrates the situation for different rates of chemical relaxation with the angular frequency of the sound wave... 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... 

It follows that the position of thermodynamic equilibrium will change along the reactor for those reactions in which a change of tire number of gaseous molecules occurs, and therefore that the degree of completion and heat production or absorption of the reaction will also vaty. This is why the external control of the independent container temperature and the particle size of the catalyst are important factors in reactor design. 

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

The solution then follows along the same lines as for TCR if the temperature and pressure are known then 7, S and the resulting mole fractions can be determined from the equilibrium constants. The temperature change between inlet and outlet is now likely to be higher than in the TCR reactions, so the determination of the A, s as functions of a single mean temperature for the reaction is more difficult. 

Another technique that can be used to account for the presence of liquids is to assume that the water and oil in the stream pass through the choke with no phase change or loss of temperature. The gas is assumed to cool to a temperature given in Figure 4-8. The heat capacity of the liquids is then used to heat the gas to determine a new equilibrium temperature. 

The effect of a temperature change on solubility equilibria such as these can be predicted by applying a simple principle. An increase in temperature always shifts the position of an equilibrium to favor an endothermic process. This means that if the solution process absorbs heat (AHsoin. > 0), an increase in temperature increases the solubility. Conversely, if the solution process is exothermic (AH < 0), an increase in temperature decreases the solubility. 

The equilibrium constant for this system, like all equilibrium constants, changes with temperature. At 100°C, K far the N204-N02 system is 11 at 150°C, it has a different value, about 110. Any mixture of N02 and N204 at 100°C will react in such a way that the ratio (Eno /EnjO, becomes equal to 11. At 150°C, reaction occurs until this ratio becomes 110. 

Le Chatelier s principle A relation stating that when a system at equilibrium is disturbed it responds in such a way as to partially counteract that change, 337-338 buffers and, 385 compression effects, 339-340 expansion effects, 339-340 precipitation equilibrium, 442 reaction conditions, 348q temperature changes, 340 Lead, 2,501 Leclanch cell, 500 Leucine, 622t... 

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