For aA+bB⇌cC+dD, K_a=[(a_C^c a_D^d)/(a_A^a a_B^b)]_eq, with activities defined relative to specified standard states. Dimensionless activities make K_a dimensionless. A hypothetical ideal-gas reference gives a_i=f_i/f_i°; for an ideal gaseous mixture, a_i=x_iP/P°=p_i/P°. With matching activity standard states, the standard reaction Gibbs energy satisfies K_a=exp[-Δ_rG°/(RT)].

Sources:

• https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_%28Ellgen%29/15%3A_Chemical_Potential_Fugacity_Activity_and_Equilibrium/15.02%3A_The_Chemical_Potential_and_Activity_of_a_Gas
• https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_%28Ellgen%29/15%3A_Chemical_Potential_Fugacity_Activity_and_Equilibrium/15.07%3A_Chemical_Potential_Activity_and_Equilibrium