Chemical equilibrium: Difference between revisions
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:<math>\Delta_rG^\ominus = -RT \ln K_\mathrm{eq}</math> | :<math>\Delta_rG^\ominus = -RT \ln K_\mathrm{eq}</math> | ||
where ''R'' is the [[universal gas constant]] and ''T'' the [[temperature]]. | where ''R'' is the [[universal gas constant]] and ''T'' the [[temperature]] (In Kelvin). | ||
When the reactants are [[Solution (chemistry)|dissolved]] in a medium of high [[ionic strength]] the quotient of [[activity coefficient]]s may be taken to be constant. In that case the '''concentration quotient''', ''K''<sub>c</sub>, | When the reactants are [[Solution (chemistry)|dissolved]] in a medium of high [[ionic strength]] the quotient of [[activity coefficient]]s may be taken to be constant. In that case the '''concentration quotient''', ''K''<sub>c</sub>, | ||
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Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant. | Obtaining the value of the standard Gibbs energy change, allows the calculation of the equilibrium constant. | ||
[[File:Diag eq.svg|thumb | [[File:Diag eq.svg|thumb]] | ||
===Addition of reactants or products=== | ===Addition of reactants or products=== | ||
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:<math>K_\mathrm{c}=\frac \mathrm{[CO_2]} \mathrm{[CO]^2}</math> | :<math>K_\mathrm{c}=\frac \mathrm{[CO_2]} \mathrm{[CO]^2}</math> | ||
==Multiple | == Equilibria Among Multiple Reactions== | ||
Consider the case of a dibasic acid H<sub>2</sub>A. When dissolved in water, the mixture will contain H<sub>2</sub>A, HA<sup>−</sup> and A<sup>2−</sup>. This equilibrium can be split into two steps in each of which one proton is liberated. | Consider the case of a dibasic acid H<sub>2</sub>A. When dissolved in water, the mixture will contain H<sub>2</sub>A, HA<sup>−</sup> and A<sup>2−</sup>. This equilibrium can be split into two steps in each of which one proton is liberated. | ||
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The effect of changing temperature on an equilibrium constant is given by the [[van 't Hoff equation]] | The effect of changing temperature on an equilibrium constant is given by the [[van 't Hoff equation]] | ||
:<math>\frac {d\ln K} {dT} = \frac{\Delta H_\mathrm{m}^\ominus} {RT^2}</math> | :<math>\frac {d\ln K} {dT} = \frac{\Delta H_\mathrm{m}^\ominus} {RT^2}</math> | ||
Thus, for [[ | Thus, for [[exothermic]] reactions (Δ''H'' is negative), ''K'' decreases with an increase in temperature, but, for [[endothermic]] reactions, (Δ''H'' is positive) ''K'' increases with an increase in temperature.<ref>{{cite book|first1=Peter |last1=Atkins |first2=Julio |last2=De Paula |title=Atkins' Physical Chemistry |url=https://archive.org/details/atkinsphysicalch00pwat |url-access=registration |edition=8th |publisher=W. H. Freeman |date=2006 |isbn=0-7167-8759-8 |page=212}}</ref> An alternative formulation is | ||
:<math>\frac {d\ln K} {d(T^{-1})} = -\frac{\Delta H_\mathrm{m}^\ominus} {R}</math> | :<math>\frac {d\ln K} {d(T^{-1})} = -\frac{\Delta H_\mathrm{m}^\ominus} {R}</math> | ||
At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of ''K'' with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way. | At first sight this appears to offer a means of obtaining the standard molar enthalpy of the reaction by studying the variation of ''K'' with temperature. In practice, however, the method is unreliable because error propagation almost always gives very large errors on the values calculated in this way. | ||