Chapter 4: Stoichiometry

Old Exam Questions

The elementary gas phase reaction

takes place isothermally in a flow reactor with no pressure drop. The feed is equal molar in A and B. Write the rate of reaction, -r_A, solely as a function of the conversion, X [i.e. -r_A = f(X)].

Hint 1: What is the rate law?

(a) $-r_{A} = k_{A}C_{A}{C_{A}}^{\frac{1}{2}}$

(b) $-r_{A} = k_{A}C_{A}{C_{B}}$

(c) $-r_{A} = k_{A}{C_{A}}^2{C_{B}}$

Hint 2: What is e?

Hint 3: What is C_A as a function of X?

(a) $C_{A} = C_{A0}(1 - x)$

(b) $C_{A} = C_{A0}\frac{(1-x)}{(1+3x)}$

(c) $C_{A} = \frac{C_{A0}(1-x)}{1+\frac{3}{2}x}$

Hint 4: What is C_B as a function of X?

(a) $C_{B} = C_{A0}(\frac{1}{2} - \frac{1}{2}x)$

(b) $C_{B} = C_{A0}(1 - \frac{1}{2}x)$

(c) $C_{B} = C_{A0} \frac{1-\frac{1}{2}x}{1+\frac{3}{2}x}$

Solution

Hint 1:

Remember that the rate law for gases includes volume change.

Back to Problem

Hint 2

Back to Problem

Hint 3

What is C_A as a function of X?

Back to Problem

Hint 4

What is C_B as a function of X?

From the stoichiometry: b/a = 1/2

Equal Molar:

Back to Problem

Solution

We see species A is the limiting reactant as the feed is equal molar in A and B, but one mole of B consumes two moles of A.

Need to put everything in terms of per mole of limiting reactant A.

From the stoichiometry: b/a = 1/2

Equal Molar:

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Chapter 4: Stoichiometry

Old Exam Questions

(a) $-r_{A} = k_{A}C_{A}{C_{A}}^{\frac{1}{2}}$

(b) $-r_{A} = k_{A}C_{A}{C_{B}}$

(c) $-r_{A} = k_{A}{C_{A}}^2{C_{B}}$

(a) $C_{A} = C_{A0}(1 - x)$

(b) $C_{A} = C_{A0}\frac{(1-x)}{(1+3x)}$

(c) $C_{A} = \frac{C_{A0}(1-x)}{1+\frac{3}{2}x}$

(a) $C_{B} = C_{A0}(\frac{1}{2} - \frac{1}{2}x)$

(b) $C_{B} = C_{A0}(1 - \frac{1}{2}x)$

(c) $C_{B} = C_{A0} \frac{1-\frac{1}{2}x}{1+\frac{3}{2}x}$