Answer
Please see the work below.
Work Step by Step
We know that
$10.0g\space N_2H_4\times\frac{1mol\space N_2H_4}{32.02g}\times \frac{1mol\space N_2O_4}{2mol\space N_2H_4}\times \frac{-1049KJ}{1mol\space N_2O_4}=-163.8J$
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