Entropy is important in determining equilibrium constants

The answer is due to entropy, a measure of disorder. Even when there is a difference in energy between the starting materials and products in an equilibrium, you still get some of the less stable components. Put simply, having a mixture of components is favourable because a mixture has higher entropy than a pure compound, and equilibria tend to maximize overall entropy. This may be quite a new concept to you, so we will now work our way stepwise through these ideas. 

To do this we need to introduce our second equation. The free energy of a reaction, AG, is related to two other quantities, the enthalpy of reaction, AH, and the entropy of reaction, AS, by the equation  

Entropy, S, is a measure of the disorder in the system, so AS represents the entropy difference—the change in disorder—between the starting materials and the products. More disorder gives a positive AS less disorder a negative AS. 

AS is positive (and hence -TAS is negative), i.e. the reaction becomes more disordered. 

Of course, we can still get a negative AG from an endothermic reaction (i.e. from a positive AH) but only if the reaction products are more disordered than the starting materials likewise a reaction which becomes more ordered as it proceeds can still be favourable, but only if it is exothermic to compensate for the loss of entropy. 

Even when there is a difference in energy between the two states, we still get some of the less stable state. This is because of entropy. Why we get the mixture of states is purely down to entropy—there is greater disorder in the mixture of states, and it is to maximize the overall entropy that the equilibrium position is reached. 

The equation AG° - AIT - TA5° tells us that how ACT1 varies with temperature depends mainly on the entropy change for the reaction (AS°). We need these terms to explain the temperature dependence of equilibrium constants and to explain why some reactions may absorb heat (endothermic) while others give out heat (exothermic). 

Entropy dominates equilibrium constants in the difference between inter- and intramolecular reactions. In Chapter 6 we explained that hcmiacetal formation is unfavourable because the C=0 double bond is more stable than two C-0 single bonds. This is clearly an enthalpy factor depending simply on bond strength. That entropy also plays a part can be clearly seen in favourable intramolecular hemiacetal formation of hydroxyaldehydes. The total number of carbon atoms in the two systems is the same, the bond strengths are the same and yet the equilibria favour the reagents (MeCHO + EtOH) in the inter- and the product (the cyclic hemiacetal) in the intramolecular case. 

In Chapter 8 we saw how increasing the number of electronegative substituents on a carboxylic acid decreased the acid s pKa, that is, increased its acidity. Acid strength is a measure of the equilibrium constant for this simple reaction. 

There is some discussion of entropy in related reactions in Chapter 6. 

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It is clear that the equilibrium constants for these activated complexes, which may have a life of only about 10 13 second, can not be determined by direct experimental means. Sometimes important conclusions may be drawn without even attempting to calculate this equilibrium constant—making the necessary estimates from considerations of entropy, or comparing different reactions in such a way that this term cancels out. Again in using activities instead of concentrations one can arbitrarily specify standard states for reactions in different phases in such a way as to simplify the calculations. 

NBS scale (which will be referred to here as the 1984 scale ) is seriously out of date, missing information on about 900 compounds. In addition, since 1991 several important publications (both experimental and theoretical) have presented data indicating that portions of the thermochemical scale, as evaluated in 1984, are in need of re-evaluation. Furthermore, recent publications from two laboratories (Mautner and Sieck at the National Institute of Standards and Technology, and Szulejko and McMahon at the University of Waterloo) provided extensive data sets in which equilibrium constants had been determined as a function of temperature, i.e. experimental entropy change determinations had become available. 

In the years following Berzelius, a number of further examples of catalytic action were discovered, but scientific appreciation of their mode of action had to await the arrival of experimental and theoretical techniques for the study of reaction rates. It then became possible for F.W. Ostwald to define a catalyst as a substance that increases the rate at which a chemical system approaches equilibrium, without being consumed in the process. This handy form of words encapsulates the essential truth of the catalytic effect, and has stood the test of time it carries with it a number of important implications that we should now explore. The first of these is that the position of equilibrium attained in a catalysed reaction is exactly the same as that which would ultimately be arrived at in its absence this must be so because the equilibrium constant K is determined by the Gibbs free energy of the process, and this in turn is fixed by the enthalpy and entropy changes, thus ... 

The constant of integration in Eq. (1.13) cannot be determined by thermodynamics. It is of no practical importance when we are considering the gas by itself, for in all cases we have to differentiate the entropy, or take differences, in our applications. But when wc come to the equilibrium of different phases, as in the problem of vapor pressure, and to chemical equilibrium, we shall find that the constant in the entropy is of great importance. Thus it is worth while devoting a little attention to it here. There is one piece of information which we can find about it from thermo-... 

We have now acquired all the tools with which to perform one of the most practical calculations of chemical thermodynamics determining the equilibrium constant for a reaction from tabulated data. Example 13-10, which demonstrates this application, uses thermodynamic properties of ions in aqueous solution as well as of compounds. An important idea to note about the thermodynamic properties of ions is that they are relative to H" (aq), which, by convention, is assigned values of zero for AfH°, AfG°, and S°. This means that entropies listed for ions are not absolute entropies, as they are for compounds. Negative values of S° simply denote an entropy less than that of H (aq). 

Free energy, G = H — TS, is a state function that indicates whether a reaction is spontaneous or nonspontaneous. A reaction at constant temperature and pressure is spontaneous if AG < 0, nonspontaneous if AG > 0, and at equilibrium if AG = 0. In the equation AG = AH — TAS, temperature is a weighting factor that determines the relative importance of the enthalpy and entropy contributions to AG. 

Equation 2.2-8 indicates that the internal energy U of the system can be taken to be a function of entropy S, volume V, and amounts nt because these independent properties appear as differentials in equation 2.2-8 note that these are all extensive variables. This is summarized by writing U(S, V, n ). The independent variables in parentheses are called the natural variables of U. Natural variables are very important because when a thermodynamic potential can be determined as a function of its natural variables, all of the other thermodynamic properties of the system can be calculated by taking partial derivatives. The natural variables are also used in expressing the criteria of spontaneous change and equilibrium For a one-phase system involving PV work, (df/) 0 at constant S, V, and ,. ... 

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