Explain the role of reducing agent in a reduction of metal oxides.

Explanation

During the reduction process the oxide of a metal decomposes and the reducing agent takes away the oxygen. The role of reducing agent is to provide `Delta_(r)G^(Theta)` negative and large enough to make the sum of `Delta_(r)G^(Theta)` of the two reactions, i.e, oxidation of the reducing agent and reduction of the metal oxide negative. 
If reduction is carried out by carbon the oxidation of the reducing agent (i.e., C) will be there
`C_((s)) + 1/2O_(2(g)) to CO_((g)) , Delta_(r)G_(C,CO)^(Theta) " " ....(ii)`
Also the complete oxidation of carbon to carbon dioxide may take place.
`1/2C_((s)) + 1/2 O_(2(g)) to 1/2CO_(2(g)) , 1/2 Delta_rG_(C,CO_2)^(Theta)" ".....(iii)`
On coupling the reactions (i) and (ii) we get
`M_(x)O_((s)) + C_((s)) to ""_(x)M_((s " or " l)) + CO_((g)) " " ....(iv)`
On coupling reactions (i) and (iii), we have
`M_(x)O_((s)) + 1/2 C_((s)) to xM_((s " or " l)) + 1/2 CO_(2(g)) " " ...(v)`
Similarly if carbon monoxide is reducing agent, it would oxidised as follows:
`CO_((g)) + 1/2O_(2(g)) + CO_(2(g)) - Delta_(r)G_(CO, CO_2)^(Theta) " "..... (vi)`
On coupling reaction (i) and (vi), we have
`M_(x)O_((s)) + CO_((g)) to xM_((s " or " l)) + CO_(2(g)) " " ...(vii)`
The reactions (iv) and (vii) actually describe the reduction of metal oxide` M_xO` that is need to be accomplished. The values of `Delta_r G^(@)` for these reactions in general, can be obtained from the corres-ponding `Delta_rG^@` values of oxides.
The temperature chosen for the reaction must be such that `Delta_rG^@` for two combined redox processes must be negative. This is indicated by the point of intersection of the two curves `Delta_rG^@` v/s T in Ellingham diagram, ie, curve for the formation of `M_xO` and that of the formation of oxide of the reducing substance. After that point, the `Delta_rG^@` becomes large negative for the combined process that makes reduction of `M_xO` possible.
The difference in the two `Delta_rG^@` values after that point determines whether reduction of the oxide of the element of the upper line is feasible by the element of which oxide formation is represented by the lower line. If the difference is large the reduction is easier.