Question

The steady state gas phase reaction 3A + B $\rightarrow$ C + 2D takes place on a catalyst surface. What will be the value of the flux ratio $ N_A / N_D $?

• A. -2
• B. -0.5
• C. -1.5
• D. 2

Hint:

For a catalytic reaction, the flux ratio of species is determined by their stoichiometric coefficients: \( \frac{N_i}{\nu_i} = \text{constant} \).

Answer 1

The Correct Option is C

Step 1: Analyze the reaction stoichiometry.
The reaction is: \[ 3\text{A} + \text{B} \rightarrow \text{C} + 2\text{D}. \] In a steady-state gas phase reaction on a catalyst surface, the fluxes of species are related by their stoichiometric coefficients. The flux \( N_i \) represents the molar flux of species \( i \) (moles per unit area per unit time) toward or away from the catalyst surface. The stoichiometric coefficients are:
A: -3 (reactant, consumed),
B: -1 (reactant, consumed),
C: +1 (product, produced),
D: +2 (product, produced).
The negative sign indicates consumption, and the positive sign indicates production. Step 2: Apply the stoichiometric relationship for fluxes.
For a reaction \( \sum \nu_i S_i = 0 \), where \( \nu_i \) is the stoichiometric coefficient (negative for reactants, positive for products), the fluxes are related by: \[ \frac{N_i}{\nu_i} = \text{constant}. \] This means the molar fluxes are proportional to the stoichiometric coefficients. For species A and D:
\( \nu_A = -3 \),
\( \nu_D = +2 \).
Thus: \[ \frac{N_A}{\nu_A} = \frac{N_D}{\nu_D}, \] \[ \frac{N_A}{-3} = \frac{N_D}{2}. \] Solving for the flux ratio \( N_A / N_D \): \[ N_A = \frac{-3}{2} N_D, \] \[ \frac{N_A}{N_D} = -\frac{3}{2} = -1.5. \] Step 3: Interpret the sign of the flux ratio.
\( N_A \) is negative because A is a reactant being consumed (flux toward the surface).
\( N_D \) is positive because D is a product being produced (flux away from the surface).
The negative sign in the ratio \( N_A / N_D = -1.5 \) reflects the opposite directions of the fluxes.
Step 4: Evaluate the options.
(1) -2: Incorrect, as the ratio is -1.5, not -2. Incorrect.
(2) -0.5: Incorrect, as the ratio is -1.5, not -0.5. Incorrect.
(3) -1.5: Correct, as derived from the stoichiometric relationship.
Correct.
(4) 2: Incorrect, as the ratio is negative due to the opposite directions of the fluxes. Incorrect.
Step 5: Select the correct answer.
The flux ratio \( N_A / N_D \) for the reaction is -1.5, matching option (3).