View source for General Chemistry/Systems seek chemical equilibrium

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'''Chemical equilibrium''' is the state in which a chemical reaction proceeds at the same rate as its reverse reaction.  When this condition is met, there is no change in the proportions of the various compounds involved, and the reaction ceases to progress. A common example given is the [[w:Haber process|Haber-Bosch process]], in which hydrogen and nitrogen combine to form ammonia. Equilibrium is reached when the rate of production of ammonia equals its rate of decomposition. [[w:Le Chatelier's principle]] describes qualitative predictions that can be made about chemical equilibrium.


Without energy input chemical reactions always proceed towards equilibrium.  For a reaction 

:<math>kA + mB \leftrightarrow nC + pD</math>

equilibrium occurs when

:<math>\frac{\left[A\right]^k \left[B\right]^m} {\left[C\right]^n \left[D\right]^p} = K</math>

where K is a constant called the equilibrium constant.  The left side of the equation is called the mass action expression and is denoted Q for a generic state (not necessarily in equilibrium).  For a single-step reaction, this can easily be derived just by considering the kinetics involved.  Unlike rate equations, though, it still holds for multi-step reactions since the expressions for each step just multiply together.  This, by the way, also gives us the relationship between equilibrium and temperature:

:<math>K_T = K_\infty e^{-\frac{\Delta E}{RT}}</math>

where ''&Delta;E'' is the difference in energy per mole between reactants and products, ''e'' is the base of the natural logarithm, and ''R'' is the molar gas constant.  The constant is mainly influenced by entropy change, but that's a little more complicated - whereas energy is roughly constant against concentration, entropy varies logarithmically so we have to refer back to a particular state.  The relationship makes the most sense in terms of the free energy difference, &Delta;F* = &Delta;E - T&Delta;S*, which represents the total work that can be done by the system as it develops.  At equilibrium &Delta;F = 0, which gives us

:<math>\Delta F^* = RT \ln {\left(\frac{Q^*}{K}\right)}</math>

Very often we consider the standard state, where Q = 1 in appropriate units, which can then be neglected.  Note that all this applies to a reaction at constant temperature only.  For a reaction at constant pressure (which is actually somewhat more typical) you would use the Gibbs free energy, &Delta;G* = &Delta;H - T&Delta;S*, where &Delta;H is the change in enthalpy.

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