The rate law for a reaction is known to involve only the reactant A, and is suspected to be either 1st or 2nd order. Describe how the order of the reaction can be determined by measuring how long it takes for [A] to reach 50% and 25% of its original value (i.e., using the method of half-lives.) b. How would you determine k for this reaction? To help explain, sketch 2 plots (one for 1st order, one for 2nd) with time on the x-axis and some form of [A] on the y-axis. a.

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**Rate Law for a Reaction Involving Reactant A**

The rate law for a reaction is known to involve only the reactant A and is suspected to be either 1st or 2nd order.

a. **Determine the Order of the Reaction**: You can determine the order of the reaction by measuring the time it takes for [A] to reach 50% and 25% of its original value, using the method of half-lives.

b. **Determine the Rate Constant (k)**: To determine k for this reaction, you can sketch two plots (one for 1st order, one for 2nd order) with time on the x-axis and some form of [A] on the y-axis.

**Explanation of the Plots**:
- **First Order Reaction**: Plot ln[A] versus time. The plot should yield a straight line if the reaction is first order, and the slope will be equal to -k.
  
- **Second Order Reaction**: Plot 1/[A] versus time. The plot should yield a straight line if the reaction is second order, and the slope will be equal to k.

These visual representations help in identifying the order of the reaction and calculating the rate constant.
Transcribed Image Text:**Rate Law for a Reaction Involving Reactant A** The rate law for a reaction is known to involve only the reactant A and is suspected to be either 1st or 2nd order. a. **Determine the Order of the Reaction**: You can determine the order of the reaction by measuring the time it takes for [A] to reach 50% and 25% of its original value, using the method of half-lives. b. **Determine the Rate Constant (k)**: To determine k for this reaction, you can sketch two plots (one for 1st order, one for 2nd order) with time on the x-axis and some form of [A] on the y-axis. **Explanation of the Plots**: - **First Order Reaction**: Plot ln[A] versus time. The plot should yield a straight line if the reaction is first order, and the slope will be equal to -k. - **Second Order Reaction**: Plot 1/[A] versus time. The plot should yield a straight line if the reaction is second order, and the slope will be equal to k. These visual representations help in identifying the order of the reaction and calculating the rate constant.
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