IndietroStep-by-Step Guidance for Question 53: First-Order Reaction Analysis
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Q53. This reaction was monitored as a function of time: A → B + C. A plot of ln[A] versus time yields a straight line with slope −0.0045/s.
Background
Topic: Integrated Rate Laws for First-Order Reactions
This question tests your understanding of first-order kinetics, including how to determine the rate constant from a straight-line plot, write the rate law, calculate half-life, and use the integrated rate law to find concentrations at a given time.
Key Terms and Formulas
First-order reaction: Rate depends linearly on the concentration of A.
Integrated rate law for first-order:
Rate constant (): Slope of the line in a plot of vs. time.
Half-life for first-order:
Step-by-Step Guidance
Identify the slope of the vs. time plot. For a first-order reaction, the slope equals .
Write the rate law for a first-order reaction: .
Recall the formula for half-life: .
To find the concentration after a certain time, use the integrated rate law: .
Plug in the initial concentration ( M), the rate constant (), and the time ( s) into the integrated rate law to solve for .
Try solving on your own before revealing the answer!
Final Answer:
a. The value of the rate constant is (since slope = ).
b. The rate law is .
c. The half-life is .
d. Using :
The rate constant is determined from the slope, the rate law is standard for first-order, the half-life formula is applied, and the integrated rate law is used to find the concentration after 225 s.
