Temperature standard enthalpy change, equilibrium

Both the integrated and differential forms show that a plot of log K against 1/T should yield a straight line with a slope equal to -AH0/2.303 R. Thus, a measured value of AH0 can be employed to calculate the equilibrium constant at temperatures other than that for which it is given. Conversely, it is possible to use measurements of the equilibrium constant at a number of temperatures to evaluate the standard enthalpy change for the reaction. 

We may summarize the optimum pH s of the coagulants obtained in the previous examples alum = 5.32, ferrous = 11.95, and ferric = 8.2. The problem with these values is that they only apply at a temperature of 25°C. If the formulas for the determination of these pH s are reviewed, they will be found to be functions of equilibrium constants. By the use of the Van t Hoff equation, values at other temperatures for the equilibrium constants can be found. These, however, as mentioned before, also need the value of the standard enthalpy change, AH298, as discussed in the chapter on water stabilization. For the aforementioned coagulants, no values of the enthalpy change are available. Thus, until studies are done to determine these values, optimum pH values must be determined using the jar test. 

This table also gives the standard enthalpy change for the reaction, Af/°. With the help of the values, the equilibrium constant valid for a temperature other than 25°C can be calculated on the basis of the thermodynamic relation... 

AH - standard enthalpy change of interaction, AS -K - equilibrium constants at two different temperatures T),... 

Relate the change in the equilibrium constant of a reaction with temperature to its standard enthalpy change (Section 14.7, Problems 59-70). 

A system with an equilibrium constant of 5 x 10 Lmol at 25°C is subjected to a temperature jump of 5°C. Calculate the new equilibrium constant given that the standard enthalpy change for the reaction is lOkJmol. ... 

Here AH is the standard enthalpy change of reaction AS the standard reaction entropy change R the gas constant T the temperature /(eq the equilibrium constant for the reaction, given simply by the product of concentrations (activities in reality) of all the products to the power of their stoichiometric coefficients over the same product for reactants m the number of products / / the forward rate constant kr the reverse rate constant n, the stoichiometric coefficient of species i and 1 the number of reactants. A AG value below zero indicates a reaction with an equilibrium point where there is an excess of products over reactants, a... 

Standard enthalpy change values, Aff°, for reactions are most commonly used in water chemistry to determine the effect of temperature on the position of equilibrium. A useful expression in this regard is due to Van t Hoff, which states that... 

Analyze We are asked to determine the standard enthalpy change of a reaction and how the equilibrium constant for the reaction varies with temperature. 

The relationship between the temperature of a reaction, its standard enthalpy change, and the equilibrium constant at that temperature can be expressed as the following linear equation ... 

Plan We can use standard enthalpies of formation to calculate AH for the reaction. We can then use Le ChateUer s principle to determine what effect temperature will have on the equilibrium constant. Recall that the standard enthalpy change for a reaction is given by the sum of the standard molar enthalpies of formation of the products, each multipUed by its coefficient in the balanced chemical equation, less the same quantities for the reactants. At 25 C, AHj for NH3( ) is —46.19 kj/mol. The AHJ values for H2(g) and N2(g) are zero by definition, because the enthalpies of formation of the elements in their normal states at 25 C are defined as zero (S tion 5.7). Because 2 mol of NH3 is formed, the total enthalpy change is... 

The formation of NO from N2 and O2 provides another interesting example of the practical importance of changes in the equilibrium constant and reaction rate with temperature. The equilibrium equation and the standard enthalpy change for the... 

Most ion/molecule equilibrium studies have been devoted also to the derivation of extensive scales of BDEs. From the temperature dependence of the equilibrium constants (Van t Hoff equation), enthalpy changes have been obtained. The BDEs are defined as the standard enthalpy changes at 0 K for the reaction (Eq. 1.6). These can be calcnlated using Kirchhoff s equation ... 

Using this expression, we can estimate the values of equilibrium constants at different temperatures, knowing the standard enthalpy change. Or, we can estimate the standard enthalpy change knowing the equilibrium constant at two different temperatures, rather than plotting data as suggested by equation 5.19. 

For a reaction whose standard enthalpy change is -100.0 kJ, what temperature is needed to double the equilibrium constant from its value at 298 K What temperature is needed to increase the equilibrium constant by a factor of 10 What if the standard enthalpy change were -20.0 kJ ... 

K is termed the equilibrium constant and it relates the activities (or concentrations under ideal conditions) of products and reactants when equilibrium has been attained at a given temperature. AG° may as in Eq. 3.1 be expressed in terms of the standard enthalpy change, AH°, and entropy change, AS° ... 

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

Heat effects accompanying chemical reaction influence equilibrium constants and compositions as well as rates of reaction. The enthalpy change of reaction, AHr, is the difference between the enthalpies of formation of the participants. It is positive for endothermic reactions and negative for exothermic ones. This convention is the opposite of that for heats of reaction, so care should be exercised in applications of this quantity. Enthalpies of formation are empirical data, most often known at a standard temperature, frequently at 298 K. The Gibbs energies of formation, AGfl likewise are empirical data. 

The equilibrium concentration of the ions A- and B- participating in the equlibrium can be directly observed by mass spectrometry. Thus, the free-energy change can be derived from the equilibrium constant, since the concentrations of the neutral species are known in advance. Similarly, by measuring the temperature dependence of the equilibrium constants, the associated enthalpy and entropy can be obtained from van t Hoff plots. By measuring a series of interconnecting equlibria, an appropriate scale can be established. The primary standard in such work has frequently been SO2 whose electron affinity is well established by electron photodetachment36. 

Figure 2-8 The equilibrium constant of Reaction 2-79 as a function of temperature in InK versus lOOO/T plot. The rough straight line means that the standard state enthalpy change of Reaction 2-79 is constant. Solid circles are 1-atm data from Zhang et al. (1997a) and open circles are 500-MPa data from Zhang (unpublished data).

Equation (3.10.5) or (3.10.7) is the fundamental relation of interest, the van t Hoff equation it is evident that from the enthalpy change accompanying a unit advancement of the reaction of interest under standard conditions, one can obtain the rate of change of the equilibrium constants Kq with alterations in temperature. 

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