= Solution
\b[The equilibrium molecular-acid concentration is $\boxed{[\mathrm{H_2N_2O_2}]=0.162\,\mathrm{mol\,L^{-1}}}$.] From the supplied <pH> convention,
$$
[\mathrm{H^+}]=c^\circ10^{-4}=10^{-4}\,\mathrm M.
$$
With only these monovalent <ions> appreciably present, <electroneutrality> requires $[\mathrm{HN_2O_2^-}]=[\mathrm{H^+}]$. Substitution in the <acid dissociation constant> gives
$$
[\mathrm{H_2N_2O_2}]
=\frac{(10^{-4}\,\mathrm M)^2}{(6.1690\times10^{-8})(1\,\mathrm M)}
=0.16210\,\mathrm M.
$$
This calculation assumes ideal <thermodynamic activities> for the acid and its conjugate base as well as for $\mathrm H^+$, negligible water <autoionization>, negligible second dissociation, and no additional electrolyte. The acid's analytical concentration would include its dissociated fraction and be approximately $0.16220\,\mathrm M$, rather than exactly the molecular-acid concentration requested.
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