Chapter 14: External Diffusion Effects on Heteregeneous Reactions

Self Test: Finding WA

Diagram on the left shows reversible reaction: N₂O₄ ⇌ 2NO₂ with forward reaction N₂O₄ → 2NO₂ at the top and reverse reaction 2NO₂ → N₂O₄ at the bottom, with z-axis pointing upward. On the right, schematic representation shows B converting to 2A at the top surface, and 2A converting to B at the bottom surface. Vertical arrows show upward flux of B and downward flux of A.

\( K_{\text{eqv}} = \frac{y_{N_2O_4}/2}{y_{NO_2}^2} \quad , \quad y_{N_2O_4} = \frac{\sqrt{1 + 4K} - 1}{2K} \)

Write the constitutive equation for NO2 solely as a function of yA, DAB, and WA.

WA = ?

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Solution

\( A = NO_2 \quad B = N_2O_4 \)

\( 2A \longrightarrow B \)

\( W_A = -c D_{AB} \frac{dy_A}{dz} + y_A (N_A + N_B) \)

\( N_B = -\frac{1}{2} N_A \quad \left( W_A = -2 W_B \right) \)

\( W_A = \frac{-c D_{AB}}{1 - \frac{y_A}{2}} \frac{dy_A}{dz} \)

\( W_A = 2 c D_{AB} \frac{d}{dz} \ln \left( 1 - \frac{y_A}{2} \right) \)

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