Start Learning Free

Before You Begin

Question #44710

Difficulty: 8/10 | 🟢 Free

The Question

A gaseous reactant \ce{A} is continuously bubbled through an aqueous solution containing 0.20 M0.20 \text{ M} of reactant \ce{B} at 298 K298 \text{ K}. The partial pressure of \ce{A(g)} above the solution is maintained constant at 0.60 bar0.60 \text{ bar}. The Henry's law constant for \ce{A} in water at 298 K298 \text{ K} is given as KH=12.0 bar L mol−1K_H = 12.0 \text{ bar L mol}^{-1}.

The overall reaction is: \ce2A(aq)+3B(aq)−>A2B3(aq)\ce{2A(aq) + 3B(aq) -> A2B3(aq)}

The proposed mechanism for this reaction is: Step 1: \ce{2A(aq) <=> A2(aq)} \quad (Fast equilibrium, Kc=4.0 L mol−1K_c = 4.0 \text{ L mol}^{-1}) Step 2: \ce{A2(aq) + B(aq) -> A2B(aq)} \quad (Slow, k1=2.5×10−2 L mol−1 s−1k_1 = 2.5 \times 10^{-2} \text{ L mol}^{-1} \text{ s}^{-1}) Step 3: \ce{A2B(aq) + 2B(aq) -> A2B3(aq)} \quad (Fast)

Assuming ideal behavior, what is the initial rate of disappearance of \ce{B}?

Options

  • A.

    1.5×10−4 mol L−1 s−11.5 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}

  • B.

    5.0×10−5 mol L−1 s−15.0 \times 10^{-5} \text{ mol L}^{-1} \text{ s}^{-1}

  • C.

    4.6×10−1 mol L−1 s−14.6 \times 10^{-1} \text{ mol L}^{-1} \text{ s}^{-1}

  • D.

    3.1×100 mol L−1 s−13.1 \times 10^{0} \text{ mol L}^{-1} \text{ s}^{-1}

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Henry’s Law Constant (Kh) Trends|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

The question tests two major traps.

First, the 'Unit Conversion Trap' in Henry's Law: students often blindly use P=KHxP = K_H x and multiply the resulting mole fraction by the molarity of water (55.5 M55.5 \text{ M}) to find concentration, ignoring that KHK_H is explicitly given in bar L mol−1\text{bar L mol}^{-1}, which directly relates pressure to molarity (P=KHCP = K_H C).

Second, the 'Stoichiometric Coefficient Division' trap: students frequently equate the rate of the rate-determining step directly to the rate of disappearance of a reactant, failing to account for the additional moles of the reactant consumed in subsequent fast steps.

Here, the stoichiometry of the mechanism dictates that the rate of disappearance of B is three times the rate of the slow step.

Quick Facts About This Question

Question Information

SubjectChemistry
ChapterSolutions - Class 12
ConceptHenry’s Law Constant (Kh) Trends
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree