This is the 14311th most frequent German word.
hoffnungsvollen
"Hopeful."
Here, 'hoffnungsvollen' is an adjective describing 'Gesichter' (faces), implying they are filled with hope.
Er sah die hoffnungsvollen Gesichter seiner Schüler.
He saw the hopeful faces of his students.
In this sentence, 'hoffnungsvollen' modifies 'Moment' (moment), emphasizing the positive and hopeful nature of that specific instant.
In einem hoffnungsvollen Moment versprach sie, es zu versuchen.
In a hopeful moment, she promised to try.
Here, 'hoffnungsvollen' describes 'Kandidaten' (candidate), expressing the idea that this candidate embodies hope for the future.