The word that gives the essay the most urgent connotation is crucial: <em>A strong essay is a </em><em>crucial </em><em>part of a successful college application. </em>
Explanation:
The word <em>crucial </em>implies an extremely important or necessary decision, result or fact. So as to convey an urgent connotation, the correct answer is <em>crucial</em> because it would refer the essay as a decisive, critical part of the college application,