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When k < 10^-3, we assume the change in reactant is negligible therefore the value of the reactants is the same. Ex) A + B --> C: std defn of k = [C]/([A][B]). After equilibrium k = [C+x]/([A-x][B-x]), with x denoting the change in concentration, however the change is negligible therefore the equation is k = [C+x]/([A][B]).
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