Question
If a reaction has large value of KC, will it go to completion and why?

Answer
Let us consider a chemical reaction in general form: 
aA + bB → cC + dD,
where A and B are reactants, C and D are products and a, b, c and d are stoichiometric coefficients.

An equilibrium reaction proceeds until reaching equilibrium. And the value of KC characterizes this equilibrium.  Since the products are in the numerator of KC expression, the greater the KC the greater the concentration of products at the equilibrium, and vice versa: the small value of KC indicates great amount of reactants and small amount of products at the equilibrium.  So, if a reaction has large value of KC, amount of products considerably exceeds the amount of reactants, and this means the reaction reaches close to completion.

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