Can chemical equilibrium only be achieved in a reversible process?
I have only seen equilibrium in processes that are reversible so I was wondering if it were possible in reactions that are not reversible.
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In any chemical reaction there is a generally a potential energy barrier between reactants and products. How easily this is crossed from reactants to products or vice versa depends primarily on the temperature. This is because to react, molecules have to gain energy that is more that the average to be able to cross the barrier. (This is called the activation energy).
The energy is accumulated randomly from solvent in solution and by collisions in gas phase, which is why some chemical reactions can be slow. Barriers are often high compared to thermal energy so it can take ages to get enough energy by chance to cross a barrier. The chance of having a certain energy E is determined by the Boltzmann distribution $exp(-E/k_bT)$ where $k_B$ is the Boltzmann constant, T temperature.
As Boltzmann distribution also depends on temperature reactions are generally observed to be faster at higher temperatures. If a reaction is called 'reversible' then one expects to see reactants and products in the mixture at the same time at amounts depending on the equilibrium constant. The product is reverting to reactant and reactant to product, assuming that all product is not continuously being removed, say by precipitation or otherwise.
In an 'irreversible' reaction the barrier from products to reactants is so high that in normal experience enough of the product never returns to reactant to be measurable. The effect can be very dramatic (orders of magnitude) with a relatively small change in activation energy because of the exponential dependance of the Boltzmann distribution.
All this means that there is no fundamental difference in 'reversible' and 'irreversible' reactions, just a matter of time-scale. However, it is obviously practically useful to distinguish these cases and so we can look at equilibrium constants to guide us.
Note (a) That thermodynamics does not inform us about time-scales but only the relative free energy of reactants and products. (b) The words ' reversible' when used as 'reversible process' has a special meaning in thermodynamics and needs to be used with care. (c) I have excluded the special case of 'barrierless' reactions.
In terms of a dynamic equilibrium where the rate of formation of products and reactants are the same, no, because the reaction will proceed to products completely and $K \gt\gt 1$. It is highly unlikely that the reaction will go back to reactants.
Irreversible reactions in chemistry are considered to achieve a static equilibrium because the reaction stops after a certain point where reactants are converted to products and the ratio of products:reactants stops changing.
A perfect example of this is the conversion of graphite to diamond.
For further info see this.