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A very large K value means the reaction at equilibrium will heavily lean towards the products. The equilibrium constant is basically concentration of products over concentration of reactants, so for K to be a large value, the numerator (product) should be big while denominator (reactant) should be small.
K stands for the equilibrium constant and represents the fixed ratio between products and reactants under specific conditions. If K is large, there is a higher percentage of products in the equilibrium solution in comparison to reactants. This emphasizes that the forward reaction is therefore stronger (more likely to occur) than the reverse reaction.
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