Liquid steel is held in a graphite crucible long enough to establish equilibrium. What is carbon activity in the liquid, taking graphite as standard state?
Equilibrium with pure graphite equates the chemical potential of dissolved carbon to that of graphite. Since $\mu_C=\mu_C^\circ+RT\ln a_C$ and the standard is graphite, ln aC=0. Hence aC=1, C, even though carbon concentration is not 100%.
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