Questions: Determining the rate-law expression for the reaction below at the temperature at which the tabulated initial rate data were obtained: rate = A + 2B + 3C → Products Experiment Initial [A] Initial [B] Initial [C] Initial Rate 1 0.10 M 0.30 M 0.30 M 0.040 M/min 2 0.20 M 0.30 M 0.30 M 0.080 M/min 3 0.20 M 0.20 M 0.30 M 0.053 M/min 4 0.20 M 0.20 M 0.40 M 0.11 M/min

Determining the rate-law expression for the reaction below at the temperature at which the tabulated initial rate data were obtained: rate = A + 2B + 3C → Products Experiment Initial [A] Initial [B] Initial [C] Initial Rate 1 0.10 M 0.30 M 0.30 M 0.040 M/min 2 0.20 M 0.30 M 0.30 M 0.080 M/min 3 0.20 M 0.20 M 0.30 M 0.053 M/min 4 0.20 M 0.20 M 0.40 M 0.11 M/min
Transcript text: Determining the rate-law expression for the reaction below at the temperature at which the tabulated initial rate data were obtained: rate = A + 2B + 3C → Products Experiment | Initial [A] | Initial [B] | Initial [C] | Initial Rate 1 | 0.10 M | 0.30 M | 0.30 M | 0.040 M/min 2 | 0.20 M | 0.30 M | 0.30 M | 0.080 M/min 3 | 0.20 M | 0.20 M | 0.30 M | 0.053 M/min 4 | 0.20 M | 0.20 M | 0.40 M | 0.11 M/min
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Solution

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Solution Steps

Step 1: Determine the Order with Respect to A

To find the order of the reaction with respect to \( \text{[A]} \), compare experiments 1 and 2, where the concentration of \( \text{[B]} \) and \( \text{[C]} \) are constant.

  • Experiment 1: \([\text{A}] = 0.10 \, \text{M}\), Rate = 0.040 M/min
  • Experiment 2: \([\text{A}] = 0.20 \, \text{M}\), Rate = 0.080 M/min

The rate doubles when \([\text{A}]\) doubles, indicating a first-order reaction with respect to \( \text{[A]} \).

Step 2: Determine the Order with Respect to B

To find the order of the reaction with respect to \( \text{[B]} \), compare experiments 2 and 3, where the concentration of \( \text{[A]} \) and \( \text{[C]} \) are constant.

  • Experiment 2: \([\text{B}] = 0.30 \, \text{M}\), Rate = 0.080 M/min
  • Experiment 3: \([\text{B}] = 0.20 \, \text{M}\), Rate = 0.053 M/min

The rate decreases by a factor of \(\frac{0.053}{0.080} \approx 0.6625\) when \([\text{B}]\) decreases by a factor of \(\frac{0.20}{0.30} = \frac{2}{3}\). This suggests a first-order reaction with respect to \( \text{[B]} \).

Step 3: Determine the Order with Respect to C

To find the order of the reaction with respect to \( \text{[C]} \), compare experiments 3 and 4, where the concentration of \( \text{[A]} \) and \( \text{[B]} \) are constant.

  • Experiment 3: \([\text{C}] = 0.30 \, \text{M}\), Rate = 0.053 M/min
  • Experiment 4: \([\text{C}] = 0.40 \, \text{M}\), Rate = 0.11 M/min

The rate increases by a factor of \(\frac{0.11}{0.053} \approx 2.0755\) when \([\text{C}]\) increases by a factor of \(\frac{0.40}{0.30} = \frac{4}{3}\). This suggests a second-order reaction with respect to \( \text{[C]} \).

Final Answer

The rate-law expression for the reaction is:

\[ \boxed{\text{Rate} = k [\text{A}]^1 [\text{B}]^1 [\text{C}]^2} \]

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