$(30)$ a$)$ Determine the ratio of $P\frac{H_2}{P}{H}_{2}O$ gas mixture and the maximum pressure of water vapor in wet hydrogen at $1$atm pressure in which chromium can be heated without oxidation occurring at $1500K.$ First, write chemical reaction and then determine the equilibrium ratio of $P\frac{H_2}{P}{H}_{2}O$ from Ellingham diagram.

b$)$ Determine $G^0,H^0$ and $S^0$ for formation of $C{r}_2{O}_3$ with $P\frac{H_2}{P}{H}_{2}O$ gas mixture from Ellingham diagram at $1500K.$

Is the oxidation of $Cr$ by water vapor exothermic or endothermic?