12.28 | For the reaction Q → W + X, the following data were obtained at 30 °C: .

"For the reaction Q → W + X, the following data were obtained at 30 °C:
(a) What is the order of the reaction with respect to [Q], and what is the rate law?
(b) What is the rate constant?"
To analyze the order of the reaction Q → W + X and calculate the rate constant:

1. *Given Data:*
Data should include the concentration of Q ([Q]) at various time intervals and the corresponding reaction rates. Example data:

| [Q] (mol/L) | Rate (mol/L·s) |
|--------------|----------------|
| [Q]1 | Rate1 |
| [Q]2 | Rate2 |
| [Q]3 | Rate3 |
| ... | ... |

2. *Step (a): Determine the Order of the Reaction with Respect to [Q] and Rate Law:*

a. *Zero-Order Reaction:*
Rate Law: Rate = k
Integrated Rate Law: [Q] = [Q]0 - kt
Plot: [Q] vs. t
If the plot is linear, the reaction is zero-order, and the rate law is Rate = k.

b. *First-Order Reaction:*
Rate Law: Rate = k[Q]
Integrated Rate Law: ln[Q] = ln[Q]0 - kt
Plot: ln[Q] vs. t
If the plot is linear, the reaction is first-order, and the rate law is Rate = k[Q].

c. *Second-Order Reaction:*
Rate Law: Rate = k[Q]^2
Integrated Rate Law: 1/[Q] = 1/[Q]0 + kt
Plot: 1/[Q] vs. t
If the plot is linear, the reaction is second-order, and the rate law is Rate = k[Q]^2.

*Determine the Order:*
Plot the data for [Q] vs. t, ln[Q] vs. t, and 1/[Q] vs. t.
The graph that gives a straight line indicates the order of the reaction.
The rate law will follow from the appropriate order determined from the linear graph.

3. *Step (b): Determine the Rate Constant (k):*

After determining the order, calculate the rate constant using the integrated rate law.

a. *Zero-Order:* If the reaction is zero-order, use the equation [Q] = [Q]0 - kt to solve for k.

b. *First-Order:* If the reaction is first-order, use the equation ln[Q] = ln[Q]0 - kt to solve for k.

c. *Second-Order:* If the reaction is second-order, use the equation 1/[Q] = 1/[Q]0 + kt to solve for k.

4. *Example Calculation:*
Assume the reaction is first-order with respect to [Q].
If for one set of data: [Q]0 = 0.50 M, [Q] = 0.25 M after 10 seconds, and the rate = 0.02 M/s:
First-order rate law: Rate = k[Q]
k = Rate / [Q] = 0.02 / 0.25 = 0.08 s⁻¹

5. *Conclusion:*
The order of the reaction is determined from the graph that gives a straight line.
The rate constant k is calculated based on the determined order and the data.