(Solved): A dilute alcohol \( B(2 \% \) in water) is oxidized with pure oxygen (A) to t ...

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A dilute alcohol \( B(2 \% \) in water) is oxidized with pure oxygen (A) to the acid \( C \) (liquid) at 10 atmospheres in a trickle bed reactor packed with catalyst pellets at \( 40^{\circ} \mathrm{C} \). The reaction proceeds as follows: \[ A(\text { gas })+B \text { (liquid) } \rightarrow C \text { (liquid) }+\mathrm{H}_{2} \mathrm{O} \] with a rate, \[ -r_{\mathrm{A}}^{\prime}=k^{\prime} C_{\mathrm{A}} \] With \( \mathrm{k}^{\prime}=3 \times 10^{-5} \mathrm{~m}^{3} / \mathrm{kg} \mathrm{s} \) a) Give the overall rate equation for this reaction. [20 marks] b) Evaluate the pore diffusion resistance regime. [20 marks] c) Find the fractional conversion of \( B \) to \( C \). [20 marks] Additional information: the gas and liquid are fed to the top of a reactor in the following system, Gas stream: \( v_{g}=0.01 \mathrm{~m}^{3} \mathrm{~s}^{-1}, \quad \mathrm{H}_{\mathrm{A}}=84000 \mathrm{~Pa} \cdot \mathrm{m}^{3} / \mathrm{mol} \) Batch of liquid: \( v_{l}=1 \times 10^{-4} \mathrm{~m}^{3} \mathrm{~s}^{-1} \mathrm{C}_{\mathrm{B} 0}=300 \mathrm{~mol} / \mathrm{m} 3 \) Reactor: \( f_{s}=0.48,4 \mathrm{~m} \) length, \( 0.2 \mathrm{~m}^{2} \) cross section Catalyst: \( d_{p}=4 \mathrm{~mm}, \quad \rho_{s}=700 \mathrm{~kg} / \mathrm{m}^{3}, \quad D_{T A}^{e}=5 \times 10^{-10} \mathrm{~m}^{3} / \mathrm{m} \) cat.s Kinetics: \( k_{A g} a_{i}=3 \times 10^{-4} \frac{m o l}{m^{3} . P a . s}, k_{A l} a_{i}=0.02 \mathrm{~s}^{-1}, \mathrm{k}_{\mathrm{AC}}=3.86 \times 10^{-4} \mathrm{~m} / \mathrm{s} \)