After a BOF oxygen blow, steel has dissolved oxygen 0.03 wt.% at 1800 K. Assuming Henry-law behaviour and equilibrium of dissolved [C], [O] and CO at 1 atm, find carbon in wt.% to 2 decimals. Standard states are 1 wt.% Henrian for C and O and 1 atm for CO. Given $\Delta G^0=-19840-40.65T$ J for [C]+[O]→CO, and R = 8.314 J/(mol K).
At 1800 K, $\Delta G^0=-19840-40.65(1800)=-93010$ J. Equilibrium constant is $K=e^{-\Delta G^0/(RT)}\approx500$. With the stated standard states, $K=p_{CO}/([\%C][\%O])$. Therefore $[\%C]=1/[K(0.03)]\approx0.0666$ wt.%, or 0.07 wt.%. Use wt.% values directly in these specified Henry-law activities, not mass fractions.