= Solution
With ideal <thermodynamic activities> $a_i=[i]/c^\circ$, the dimensionless <acid dissociation constant> is
$$
\boxed{K_a=\frac{a_{\mathrm{H^+}}a_{\mathrm{HN_2O_2^-}}}{a_{\mathrm{H_2N_2O_2}}}
=\frac{[\mathrm{H^+}][\mathrm{HN_2O_2^-}]}{[\mathrm{H_2N_2O_2}]c^\circ},\qquad c^\circ=1\,\mathrm{mol\,L^{-1}}.}
$$
The factor $c^\circ$ makes the <equilibrium constant> compatible with $\Delta_rG^\circ=-RT\ln K_a$. If the concentration quotient without $c^\circ$ is used instead, it has concentration units and its numerical value is identical only when the standard concentration is expressed as $1\,\mathrm M$.
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