Chapter 4: Stoichiometry
Expressing a Catalytic Rate Law in Terms of Conversion
\( A + B \xrightarrow{\text{Cat}} C \)
\(-r_A = \frac{k_A \left[ \frac{P_A P_B - P_C}{K_P} \right]}{1 + K_A P_A}\)
\(P_A = C_A RT\)
\(C_A = C_{A0} \frac{1 - X}{1 + \varepsilon X} y \frac{T_0}{T}\)
\(C_B = C_{B0} \frac{1 - X}{1 + \varepsilon X} y \frac{T_0}{T}\)
\(P_A = RTC_{A0} \frac{1 - X}{1 + \varepsilon X} y \frac{T_0}{T}\)
\(P_{A0} = RTC_{A0}\)
\(P_A = P_{A0} \frac{1 - X}{1 + \varepsilon X} y\)
\(\text{If } y = 1, \, P_{A0} = P_{B0}\)
\(-r_A = \frac{k_A P_{A0}^2 \left[ \frac{(1 - X)^2}{(1 + \varepsilon X)^2} - \frac{X}{K_p P_{A0} (1 + \varepsilon)} \right]}{1 + K_A P_{A0} \frac{1 - X}{1 + \varepsilon X}}\)
\(-r_A = \frac{k_A P_{A0}^2 \left[ \frac{(1 - X)^2}{(1 + \varepsilon X)^2} - \frac{X (1 + \varepsilon X)}{K_p P_{A0}} \right]}{(1 + \varepsilon X)^2 + K_A P_{A0} (1 - X)(1 + \varepsilon X)}\)
\(\varepsilon = y_{A0} \delta = \frac{1}{2}(1 - 1 - 1) = -1/2\)