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I believe what is meant by dynamic equilibrium is that when a reaction is in equilibrium, there still are reactions occurring. It is not a static system. When a reaction is at equilibrium, concentrations of reactant and product are the same because the reactants are forming products at the same rate that products are forming reactants. Chemical reactions are occurring constantly during equilibrium which makes it dynamic even though there is no overall net change in concentration of either product or reactant.
Dynamic equilibrium basically emphasizes the idea that when the reactants and products are in equilibrium, that doesn't mean that everything just stays still. Reactions are still occurring, just at the same rate as they're being formed/consumed.
During a dynamic equilibrium, a reaction is still occurring. However, the rates of the forward and reverse reactions are occurring at the same rate resulting in a net 0 rate. A reaction is never static as collisions continue to occur between atoms/molecules to form products/reactants.
We know when something is in dynamic equilibrium when the forward and reverse reactions are still occurring, despite the composition of the products and reactants being the same. One possible way to test this is to remove an amount of products and if the reaction produces more products to reestablish equilibrium, then we would know that the reactions are still occurring, thus making it dynamic equilibrium.
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