Chapter 3: Rate Laws
Solving for KP:
Remember, the expression we're trying to derive is that: \( K_P = \frac{P_{C_e}}{P_{A_e} P_{B_e}} \)
At equilibrium, \( r_{\text{net}} \cong 0 \), so: \( -r_A \cong 0 = \frac{k_A}{1 + K_A P_{A_e}} \left( P_{A_e} P_{B_e} - \frac{P_{C_e}}{K_P} \right) \)
Solving for KP: \( 0 = P_{A_e} P_{B_e} - \frac{P_{C_e}}{K_P} \)
\( P_{A_e} P_{B_e} = \frac{P_{C_e}}{K_P} \)
\( K_P = \frac{P_{C_e}}{P_{A_e} P_{B_e}} \)
The conditions are satisfied.