Chapter 3: Rate Laws
Deriving -rA:
| The forward rate is: |
\( r'_{A_{\text{for}}} = \frac{-k_A P_A P_B}{1 + K_A P_A} \) |
| And the reverse rate law is: |
\( r'_{A_{\text{rev}}} = \frac{k_{-A} P_C}{1 + K_A P_A} \) |
| The net rate for species A is the sum of the forward and reverse rate laws: |
\( r_A = r_{A_{\text{net}}} = r_{A_{\text{for}}} + r_{A_{\text{rev}}} \) |
| Substituting for rfor and rrev: |
\( r_A = \frac{-k_A P_A P_B}{1 + K_A P_A} + \frac{k_{-A} P_C}{1 + K_A P_A} \) |
\( -r_A = \frac{k_A P_A P_B}{1 + K_A P_A} - \frac{k_{-A} P_C}{1 + K_A P_A} = \frac{k_A P_A P_B - k_{-A} P_C}{1 + K_A P_A} \) |
\( K_P = \frac{P_{C_e}}{P_{A_e} P_{B_e}} = \frac{k_A}{k_{-A}} \) |
\( -r'_{A} = \frac{k_A}{1 + K_A P_A} \left( P_A P_B - \frac{P_C}{K_P} \right) \) |