When this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous. what is the chemical equation of this coupled process? show that the reaction is in equilibrium, include physical states, and represent graphite as c(s)?

The reaction of a graphite which is basically a carbon with oxygen which is a gas forms a carbon dioxide which is also a gas. 

The balance chemical reaction is shown below,
C + O2 --> CO2

This is already a balanced chemical equation because the number of elements in the left side of the equation is same that of the number on the right side.
C = 1 
O = 2

If we are to incorporate the physical states of the elements and compounds which are already given above, the equation would become,
C(s) + O2(g) --> CO2(g)