Equilibrium constants vary with temperature

We have said that the equilibrium constant is a constant only so long as the temperature does not change. Exactly how the equilibrium constant varies with temperature depends on whether the reaction is exothermic or endothermic. If the reaction is exothermic (that is, gives out heat) then at higher temperatures the equilibrium constant will be smaller. For an endothermic reaction, as the temperature is increased, the equilibrium constant increases. Putting our all important equations AG° = -RTlnKand AG° = AH° - 2AS° together we see that -/ T]n K = AH° - 7A.S°. If we divide throughout by -R Twe have 

The equilibrium constant Kcan be divided into enthalpy and entropy terms but it is the enthalpy term that determines how K varies with temperature. Plotting In K against 1/T would give us a straight line with slope - AtPIR and intercept AS0. Since T (the temperature in Kelvin) is always positive, whether the slope is positive or negative depends on the sign of AH° if it is positive then, as temperature increases, InK (and hence K) increases. In other words, for an endothermic reaction (AHpositive), as Tincreases, K([products]/[reactants]) increases which in turn means that more products must be formed. 

Making reactions go faster the real reason reactions are heated 

You may well be familiar with a rule that helps to predict how a system at equilibrium responds to a change in external conditions—Le Chatelier s principle. This says that if we disturb a system at equilibrium it will respond so as to minimize the effect of the disturbance. An example of a disturbance is adding more starting material to a reaction mixture at equilibrium. What happens More product is formed to use up this extra material. This is a consequence of the equilibrium constant being, well... constant and hardly needs anybody s principle. 

Simple dimerization reactions will favour the dimer at low temperatures and the monomer at high temperatures. Two monomer molecules have more entropy than one molecule of the dimer. An example is the dimerization of cyclopentadienp. On standing, cyclopentadiene dimerizes and if monomeric material is needed the dimer must be heated and the monomer used immediately. If you lazily leave the monomer overnight and plan to do your reaction tomorrow, you will return in the morning to find dimer. 

This idea becomes even more pointed when we look at polymerization. Polyvinyl chloride is the familiar plastic PVC and is made by reaction of large numbers of monomeric vinyl chloride molecules. There is, of course, an enormous decrease in entropy in this reaction and any polymerization will not occur above a certain temperature. Some polymers can be depolymerized at high temperatures and this can be the basis for recycling. 

We have said (p. 245) that the equilibrium constant is a constant only as long as the temperature does not change. We can work out exactly how the equilibrium constant varies with temperature by putting our two all-important equations AG = -RTlnK and AG = AH-TAS together to make 

Notice that the equation above also tells us that enthalpy becomes a less important contributor to the equilibrium constant as temperature increases, so the higher the temperature, the more important is the entropy term. This fact means that some reactions favour one side of the equilibrium at low temperature but the other at high temperature. Here is an example the dimerization of cyclopentadiene. You will meet the mechanism of this reaction in Chapter 34, but for 

Everything decomposes at a high enough temperature eventually, giving atoms. This is because the entropy for lots of particles all mixed up is much greater than that of fewer larger particles. 

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We have already seen (p. 56) that the Ka, and hence pKa, value for an acid is not an intrinsic attribute of the species itself, because it varies from one solvent to another the value depending on the overall system of which the acid is a constituent. Values are normally quoted for aqueous solution, unless otherwise specified, because most data are available for that solvent. Most values are also quoted as at 25°, again because most data were obtained at this temperature. A constant temperature has to be specified as Ka, an equilibrium constant, varies with temperature. We have been concerned above with the relative... 

How the equilibrium constant varies with temperature can be of importance. Consider first the simple derivative... 

For ACj, = 0, the equilibrium constant varies with temperature according to the relation... 

K is known as the equilibrium constant and in this case it has the value 2000. An equilibrium constant greater than unity suggests that equilibrium lies to the right-hand side and the forward reaction is favoured. Equilibrium constants vary with temperature, but not with concentration if the concentrations have been correctly expressed in terms of activities. 

To express how the reaction equilibrium constant varies with temperature, we separate the variables and integrate ... 

Equation (4.550) also allows one to determine how the equilibrium constant varies with temperature. With Equation (4.547), Equation (4.550) implies that... 

From Le Chatelier s principle we know that for exothermic reactions, the equilibrium shifts to the left (i.e K and A, decrease) as the temperature increases. Figures C-1 and C-2 show how the equilibrium constant varies with temperature for an exothermic reaction and for an endothermic reaction, respectively. 

At 25°C, Kyj = lO mop dm corresponding to piif = 14 at 25°C. Like most other equilibrium constants varies with temperature (see Section 2.9 and Worked Problem 2.4). 

P25.32 Equilibrium constants vary with temperature according to the van t Hoff equation [7.25] which can be written in the form... 

The way in which equilibrium constants vary with temperature is a matter of considerable importance in thermodynamics. It leads us to a very convenient - v GG-experimental procedure for measuring enthalpy changes in chemical reactions. -... 

Equation 3.50, known as the van t Hoff equation, expresses how the equilibrium constant varies with temperature. Equation 3.50 can be integrated between two temperatures to give... 

Unlike changes in the concentrations of reactants or products, in which the equilibrium constant is unaffected, a temperature shift also changes the vahie of the equilibrium constant. (As for rate constants, we are again confronted with a constant that varies as a function of temperature ) The fact that equilibrium constants vary with temperature, however, is important in the way chemical reactions occur in industrial processes. Often, high temperatures are required for... 

Equilibrium constant K, K) (12.3) The ratio of concentrations of products to those of reactants each concentration is raised to a power that matches its stoichiometric coefficient in the balanced chemical equation. Equilibrium constants vary with temperature. 

In equations (4 18) and (4 19) Kp and Kf necessarily refer to the temperature T and so also do the /e s. The extent to which the equilibrium constant varies with temperature is readily obtained in terms of the heat of reaction. 

Second, equilibrium constants vary with temperature. Table 15.2 gives values of Kc for methanation at various temperatures. Note that Kc equals 4.9 X 10 at 298 K. Therefore, an equilibrium mixture at room temperature is mostly methane and... 

This expression can tell us how the equilibrium constant varies with temperature at constant pressure by taking the first derivative with respect to temperature. From Equations 5.42 and 5.43,... 

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