$ $解:设$1 \mathrm {L}$水样中${\mathrm {NaNO}_{2}}$的质量为$x。$
${2\mathrm {NaNO}_{2} + 2\mathrm {KI} + 2\mathrm {H}_{2}\mathrm {SO}_{4}\xlongequal{}2\mathrm {NO}↑ + \mathrm {I}_{2} + 2\mathrm {H}_{2}\mathrm {O} + \mathrm {K}_{2}\mathrm {SO}_{4} + \mathrm {Na}_{2}\mathrm {SO}_{4}}$
138 254
x $5.08×10^{-3}\text{ mg}$
$$
\frac{138}{254}=\frac{x}{5.08×10^{-3}\text{ mg}},$$解得$ x = 2.76×10^{-3}\text{ mg}$
$$
$$答:$1 \mathrm {L}$水样中${\mathrm {NaNO}_{2}}$的质量为$2.76×10^{-3}\text{ mg}。$