$$FeO_4^{2-} \xrightarrow{+2.2 V} Fe^{3+} \xrightarrow{+0.70 V} Fe^{2+} \xrightarrow{-0.45 V} Fe^0$$
$$E^0_{FeO_4^{2-}/Fe^{2+}}$$ is $$x \times 10^{-3}$$ V. The value of x is _______.

Given reduction potentials:

$$FeO_4^{2-} + 3e^- \to Fe^{3+}$$, $$E° = +2.2$$ V

$$Fe^{3+} + e^- \to Fe^{2+}$$, $$E° = +0.70$$ V

We need $$E°$$ for: $$FeO_4^{2-} + 4e^- \to Fe^{2+}$$

Using the relationship $$\Delta G° = -nFE°$$:

$$\Delta G_1 = -3F(2.2) = -6.6F$$

$$\Delta G_2 = -1F(0.70) = -0.70F$$

For the combined reaction:

$$\Delta G_{total} = \Delta G_1 + \Delta G_2 = -6.6F - 0.70F = -7.30F$$

$$E°_{FeO_4^{2-}/Fe^{2+}} = \frac{7.30}{4} = 1.825 \text{ V} = 1825 \times 10^{-3} \text{ V}$$

The value of x is 1825.