a$)$ Derive the Clausius$-$Clapeyron Equation using one of the four fundamental equations. Using

the relation and the $P-$T diagram of water; explain briefly how ice$-$skaters skate on ice easily.

b$)$ Derive the Van't Hoff equation. Briefly explain Temperature $-$ Kp $($Equilibrium constant$)$

relation, plotting respective graphs.

$Mn+\frac{1}{2}{O}_2=$MnO,$G_T^0=-388900+76\mathrm{.}32T(\frac{J}{m}ol)$

a$)$ Calculate the oxygen partial pressure $(P_{O_2})$ at $600$ and $1000K.$ Plot $log{P}_{O_2}-\frac{1}{T}$ change

of the reaction and label the phase fields.

b$)$ Calculate the direction of the reaction at $900K$ and $P_{O_2}={10}^{-30}$atm. Show this

conditions on the graph.

c$)$ Calculate the equilibrium temperature under $P_{O_2}={10}^{-30}$atm.

$C{O}_{2(g)}+C_{(s)}=2C{O}_{(g)}$

a$)$ Using the Bouduard reaction, calculate gas composition in a furnace under $1$atm total

pressure and $1100K.$

b$)$ Under the same furnace conditions, is it possible to reduce VO to $V$ by $CO?$

Using the Ellingham Diagram given below,

a$.$ Explain whether $C{u}_{2}O$ can be reduced at $1000C$ by Nickel $($Ni$)$ or not. Why?

b$.$ Explain the reason why oxidation reactions of carbon have negative and zero slope

$($forming $CO$ and $C{O}_2,$ respectively$),$ whereas all the others have positive slope.

d$.$ Which one $($Mg or $Al)$ has higher affinity to oxygen $($oxidation$)?$

e$.$ Determine the Entropy and Enthalpy change of the $Ti-Ti{O}_2$ reaction.

f$.$ At what temperature the reduction efficiency of $H_2$ and $CO$ will the same?

g$.$ For $Si-Si{O}_2$ reaction, determine the equilibrium $PC\frac{O}{P}C{O}_2$ and $\frac{P_{H_2}}{P_{H_{2}O}}$ ratio at $500C.$

h$.$ Which one can be reduced easier $($from its oxide$),$ copper, silver or calcium? W