Answer
$+90.2\ kJ/mol$
Work Step by Step
Manipulating the given reactions:
$\begin{smallmatrix}
1/2\ N_2(g)+3/2\ H_2(g)&\rightarrow&NH_3(g)&-45.9\ kJ/mol\\
NH_3(g)+5/4\ O_2(g)&\rightarrow&NO(g)+3/2\ H_2O(g)&-226.6\ kJ/mol\\
3/2\ H_2O(g)&\rightarrow& 3/2\ H_2(g)+3/4\ O_2(g)&+362.7\ kJ/mol\\
\hline\\
1/2\ N_2(g)+1/2\ O_2(g)&\rightarrow&NO(g)&+90.2\ kJ/mol
\end{smallmatrix}$
