Moles of H\(_2\)SO\(_4\) taken:
\[ \text{Moles} = M \times V = 0.2 \times \frac{100}{1000} = 0.02 \, \text{moles} \]Moles of NaOH used to neutralize excess H\(_2\)SO\(_4\):
\[ \text{Moles} = 0.5 \times \frac{40}{1000} = 0.02 \, \text{moles} \]Since 2 moles of NaOH neutralize 1 mole of H\(_2\)SO\(_4\), moles of unreacted H\(_2\)SO\(_4\) are:
\[ \frac{0.02}{2} = 0.01 \, \text{moles} \]Moles of H\(_2\)SO\(_4\) reacted with NH\(_3\):
\[ 0.02 - 0.01 = 0.01 \, \text{moles} \]Moles of nitrogen in NH\(_3\):
\[ 2 \times 0.01 = 0.02 \, \text{moles} \] Step 2: Calculating the mass of nitrogen.Mass of nitrogen:
\[ 0.02 \times 14 = 0.28 \, \text{g} \]Given that nitrogen is 46% of the organic compound:
\[ x = \frac{0.28}{0.46} = 0.608 \, \text{g} \]Thus, the value of \( x \) is 0.608 g.