Answer
$$[Hg_2^{2+}]_{eq} = 0.0099 \space M$$
Work Step by Step
1. Write the K expression:
$$K = \frac{[Fe^{2+}]^2[Hg^{2+}]^2}{[Fe^{3+}]^2[Hg_2^{2+}]}$$
2. Solve for $[Hg_2^{2+}]$
$$[Hg_2^{2+}] =\frac{[Fe^{2+}]^2[Hg^{2+}]^2}{[Fe^{3+}]^2K}$$
3. Substitute the values and calculate:
$$[Hg_2^{2+}] = \frac{(0.0018)^2(0.0025)^2}{(0.015)^2(9.14 \times 10^{-6})} M = 0.0099 \space M$$