The surface of copper gets tarnished by the formation of copper oxide. $$N_2$$ gas was passed to prevent the oxide formation during heating of copper at $$1250$$ K. However, the $$N_2$$ gas contains 1 mole per cent of water vapour as an impurity. The water vapour oxidises copper as per the reaction given below:
$$2Cu(s) + H_2O(g) \rightarrow Cu_2O(s) + H_2(g)$$
$$ P_{H_2}$$ is the minimum partial pressure of $$H_2$$ (1 bar) needed to prevent the oxidation at 1250 K. The value of In$$(P_{H_2})$$ is .......
[Given: Total pressure = 1 bar, $$R$$ (universal gas constant) = $$8 J K^{-1} mol^{-1}, ln (10) = 2.3, CuO(s)$$ and $$Cu_2O(s)$$ are mutually immiscible.
At 1250 K: $$2Cu(s) + \dfrac{1}{2}O_2(g) \rightarrow Cu_2O(s), \Delta G^0 = -78,000 \ J mol^{-1}$$
$$H_2(g) + \dfrac{1}{2}O_2(g) \rightarrow H_2O(g); \Delta G^0 = 1,78,000 \ J mol^{-1}$$