Source : Webster's Revised Unabridged Dictionary (1913)

Hopeful \Hope"ful\, a.
   1. Full of hope, or agreeable expectation; inclined to hope;
      expectant.

            Men of their own natural inclination hopeful and
            strongly conceited.                   --Hooker.

   2. Having qualities which excite hope; affording promise of
      good or of success; as, a hopeful youth; a hopeful
      prospect. ``Hopeful scholars.'' --Addison. --
      {Hope"ful*ly}, adv. -- {Hope"ful*ness}, n.

Source : WordNet®

hopefulness
     n 1: full of hope
     2: the feeling you have when you have hope [ant: {hopelessness}]