Question 11 of 37intermediate🔧 ApplyNumerical3 marks

For the reaction: 2A+B→A2B2\text{A} + \text{B} \rightarrow \text{A}_2\text{B}, the rate =k[A][B]2= k[\text{A}][\text{B}]^2 with k=2.0×10−6 mol−2 L2 s−1k = 2.0 \times 10^{-6} \text{ mol}^{-2} \text{ L}^{2} \text{ s}^{-1}. Calculate the initial rate of the reaction when [A]=0.1 mol L−1[\text{A}] = 0.1 \text{ mol L}^{-1}, [B]=0.2 mol L−1[\text{B}] = 0.2 \text{ mol L}^{-1}. Calculate the rate of reaction after [A][\text{A}] is reduced to 0.06 mol L−10.06 \text{ mol L}^{-1}.

Correct Answer

Initial Rate Calculation:

Given: Rate = k[A][B]², k = 2.0×102.0 \times 10⁻⁶ mol⁻² L² s⁻¹, [A] = 0.1 mol L⁻¹, [B] = 0.2 mol L⁻¹

Step 1: Substitute values in rate law Initial rate = k[A][B]² = (2.0×102.0 \times 10⁻⁶) × (0.1) × (0.2)² = (2.0×102.0 \times 10⁻⁶) × (0.1) × (0.04) = 8.0×108.0 \times 10⁻⁹ mol L⁻¹ s⁻¹

Rate when [A] is reduced to 0.06 mol L⁻¹:

Step 2: Find change in concentration [A] reduced from 0.1 to 0.06 mol L⁻¹, so Δ[A] = 0.04 mol L⁻¹

Step 3: Calculate corresponding change in [B] From stoichiometry: 2A + B → A₂B When 0.04 mol L⁻¹ of A reacts, B reacted = 0.04/2 = 0.02 mol L⁻¹

Step 4: Find new [B] [B] = 0.2 - 0.02 = 0.18 mol L⁻¹

Step 5: Calculate new rate Rate = k[A][B]² = (2.0×102.0 \times 10⁻⁶) × (0.06) × (0.18)² = (2.0×102.0 \times 10⁻⁶) × (0.06) × (0.0324) = 3.89×103.89 \times 10⁻⁹ mol L⁻¹ s⁻¹

Exercise: EXERCISES | Q: 3.2 | (Page 25)
For More Understanding

Explanation

This question tests understanding of rate law application and stoichiometric relationships. The first part is a direct substitution into the rate equation. The second part requires understanding that when [A] decreases, [B] must also decrease according to the stoichiometry of the reaction (2A + B → A₂B). For every 2 moles of A consumed, 1 mole of B is consumed. This stoichiometric relationship is essential for determining the new concentration of B when calculating the new rate.

Solution Steps

  1. Step 1: Calculate initial rate using Rate = k[A][B]² with given concentrations

  2. Step 2: Determine the decrease in [A] (0.1 - 0.06 = 0.04 mol L⁻¹)

  3. Step 3: Use stoichiometry to find decrease in [B] (0.04/2 = 0.02 mol L⁻¹)

  4. Step 4: Calculate new [B] = 0.2 - 0.02 = 0.18 mol L⁻¹

  5. Step 5: Calculate new rate with [A] = 0.06 and [B] = 0.18 mol L⁻¹

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