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Chemical Equilibrium

A central idea used to predict how chemicals react to form products, is the concept of chemical equilibrium. Chemical equations show reactants with arrows transform into products. However, many reactions do not completely transform all the reactants into products.




Many reactions result in a mixture of reactants and products. Reactions undergo the reverse reaction where products transform into reactants, Figure 1.





SO2+O2 equilibrium reaction
Figure 1: Equilibrium between reactants and products results in a mixture of both reactants and products.




When a mixture of reactants and products cease any meaningful change in composition, the reaction has reached equilibrium. The ratio of concentrations of reactants to products gives an equilibrium constant, Keq.



A brief note on the term equilibrium bears mentioning.




Many students get confused when they think the term equilibrium comes from the root word “equal”. This causes them to mistakenly believe reactions have an “equal amount of reactants and products”.




However the term equilibrium comes from the term “equilibrate”; which is closer in meaning to a calibration point. In this case, the calibration point means when the concentration of reactants to products has reached the correct ratio.



It’s easier to understand chemical equilibrium if you start with how a physical equilibrium works.




Physical Equilibrium




Physical equilibrium refers to how a substance establishes a steady state between two phases. Water exists at the same time as water and vapor. At room temperature, although water appears to exist only in the liquid state, in reality there is a significant amount of water vapor near the liquid water.




vapor liquid equilibrium
Figure 2: Equilibrium of water between the vapor and liquid state


Water molecules leave the liquid state to become water vapor molecules.  Slow moving water molecules in the gaseous state get captured by the intermolecular forces in the liquid state. Both  occur at cross purposes to each other, Figure 2.



This dance from vapor to liquid and liquid to vapor continues indefinitely.  When the rate of water molecules liberated from liquid state into the gas state equals the rate of water molecules captured by liquid from the vapor state, there is no observable overall change. This state is dynamic equilibrium, Figure 3.








Water vapor equilibrium equation
Figure 3: Schematic representation of water molecules in equilibrium water molecules in the vapor state.

Chemical Equilibrium




Chemical equilibrium results from reactants converted to products while products transform back into reactants. This results from the mass action equation. The ratio of products to reactants fixes the point when the concentration of reactants and products ceases any change. The rate of the forward reaction equals the rate of the backward reaction.



The equilibrium constant Keq in its most basic form is expressed by equation (1), the ratio of products to reactants.





\LARGE{K_c = \frac{products}{reactants}}               (1)


If you use a generic reaction where reactants A + B turn into products C + D, it can expressed as chemical equation (2).



\LARGE{a A + b B\longrightarrow c C + d D}           (2)



This gives the mass action equation (3). The coefficients in the stoichiometric equation provides an exponent for the equilibrium concentrations.





\LARGE{K_{eq}=\frac{[C]^c[D]^d}{[A]^a[B]^b}}     (3)


If a reaction has a coefficient between Keq = 1 x 10-3  to Keq = 1 x 103, then the reaction is considered reversible.



In the case where Keq > 1 x 103 then the reaction is considered to be practically irreversible.



Reactions with Keq < 1 x 10-3 , the reaction is categorized as not proceeding to any great extent.




Acid-base reactions and other equilibrium mixtures however,with very small equilibrium constants still have importance.




Reversible Reactions




Reversible equilibrium occurs when products and reactants coexist. Note for example the equilibria of weak acids. You  find reversible equilibria provided by examples of gaseous mixtures like in equation (4).



\LARGE{N_2O_4\rightleftharpoons NO_2 + NO_2}           (4)


Practically Irreversible Reactions



Some reactions are technically reversible, but not reversible in the real world. This means they have an equilibrium constant considerably greater than 1 x 106. That makes the proportion of product to reactant more than one million molecules of products compared to reactant molecules.




However as you will find out in acid-base reactions, these kind of reactions still have important consequences. even when only small amounts of products exist in relationship to unreacted starting materials, like in the case of carbonic acid, H2CO3, (5), Keq = 4.4 x 10-7.





\LARGE{H_2CO_3\rightleftharpoons H_2O + CO_2}           (5)


The presence of carbonic acid and its equilibrium constant effects the levels of carbon dioxide in the atmosphere as well as regulation of the acidity of blood.




Irreversible Reactions




Reactions which have one or more of the products removed from the reaction mixture while the reaction progresses make irreversible reactions. Consider the combustion of a hydrocarbon as fuel (6):



\LARGE{2 C_6H_14 + 19 O_2\longrightarrow 14 H_2O + 12 CO_2}           (6)

Reversible reactions like this become irreversible because no equilibrium concentrations have the chance to occur. The products in the case of (6) have no concentration. They leave the reaction immediately when they form.