Chapter 8: Problem 55
The decomposition of cyclopropane, was observed at \(500^{\circ} \mathrm{C}\) and its concentration was monitored as a function of time. The data set is given below. What is the order of the reaction with respect to cyclopropane? Time (hour) \(\quad\) [Cyclopropane], M 0 \(1.00 \times 10^{-2}\) 2 \(1.38 \times 10^{-3}\) 4 \(1.91 \times 10^{-4}\) 6 \(2.63 \times 10^{-5}\) a. First b. Second c. Third d. Zero
Short Answer
Step by step solution
Understand the Problem
Define the Rate Laws
Analyze Zero-Order Assumption
Analyze First-Order Assumption
Analyze Second-Order Assumption
Compare the Results
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
first-order reaction
In mathematical terms, the rate law for a first-order reaction can be expressed as:
- Rate = k[A]
- - Rate is the change in concentration over time.
- - k is the rate constant unique to the reaction.
- - [A] is the concentration of the reactant.
rate laws
- Rate = k[A]^m[B]^n
- - k is the rate constant.
- - [A] and [B] are the concentrations of the reactants.
- - m and n are the orders of reaction with respect to each reactant.
- - If m = 1 and n = 0, the reaction is first-order in A and zero-order in B, making it first-order overall.
- - If m = 2 and n = 1, the overall order is third-order.
concentration vs. time plot
For different reaction orders:
- - Zero-Order: The concentration vs. time plot is a straight line with a negative slope, indicating a constant rate of reaction independent of concentration.
- - First-Order: The natural logarithm of concentration plotted against time results in a straight line with a negative slope, reflective of an exponential decrease in concentration.
- - Second-Order: The reciprocal of the concentration plotted against time shows a straight line, indicating a quadratic relation.
cyclopropane decomposition
This decomposition is important for understanding reaction mechanisms in organic chemistry. In the context provided, cyclopropane decomposes in a manner that demonstrates a first-order kinetic behavior.
The process is typically studied by monitoring the concentration of cyclopropane over time. By analyzing this data and applying knowledge of rate laws, we can confirm that the decomposition of cyclopropane behaves as a first-order reaction. This means the rate of decomposition directly depends on the concentration of cyclopropane present, leading to an exponential decay pattern in concentration with time. This is valuable for both theoretical insights into reaction kinetics and practical applications where cyclopropane modification is involved, such as in fuel chemistry and materials science.