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In the question it doesnt say one mole of waterquestions says that there are one mole of water and ethyl ethanoate.
and when Kc has no units or when the volume of concentration cancel out, moles can be used in the equation.
[a]/[c][d] = (n(a)n(b)/V)/(n(c)n(d)/V) volume will cancel out giving number of moles only.