15. A reaction was found to be third order in A. Increasing the concentration of A by a factor of 3 will cause the reaction rate to increase by a factor of
15. A reaction was found to be third order in A. Increasing the concentration of A by a factor of 3 will cause the reaction rate to increase by a factor of
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Question
![**Question 15: Reaction Order and Rate Increase**
15. A reaction was found to be third order in A. Increasing the concentration of A by a factor of 3 will cause the reaction rate to increase by a factor of ______.
**Explanation:**
In chemical kinetics, the order of a reaction with respect to a particular reactant can determine how changes in the concentration of that reactant affect the reaction rate. For a reaction that is third order with respect to reactant A, the rate of the reaction is proportional to the concentration of A raised to the power of 3.
Given the relationship:
\[ \text{Rate} = k [A]^3 \]
where \(\text{Rate}\) is the reaction rate, \(k\) is the rate constant, and \([A]\) is the concentration of reactant A.
If the concentration of A is increased by a factor of 3, the new concentration of A would be \(3[A]\). Substituting this into the rate equation:
\[ \text{New Rate} = k (3[A])^3 = k \cdot 27[A]^3 \]
This simplifies to:
\[ \text{New Rate} = 27 \times (\text{Original Rate}) \]
Therefore, the reaction rate will increase by a factor of 27 when the concentration of A is increased by a factor of 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11d31645-d778-49a4-a6b7-e1d91f006470%2Faf7387a9-c4e1-4b83-b794-880c22e54918%2Fmnkumks_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 15: Reaction Order and Rate Increase**
15. A reaction was found to be third order in A. Increasing the concentration of A by a factor of 3 will cause the reaction rate to increase by a factor of ______.
**Explanation:**
In chemical kinetics, the order of a reaction with respect to a particular reactant can determine how changes in the concentration of that reactant affect the reaction rate. For a reaction that is third order with respect to reactant A, the rate of the reaction is proportional to the concentration of A raised to the power of 3.
Given the relationship:
\[ \text{Rate} = k [A]^3 \]
where \(\text{Rate}\) is the reaction rate, \(k\) is the rate constant, and \([A]\) is the concentration of reactant A.
If the concentration of A is increased by a factor of 3, the new concentration of A would be \(3[A]\). Substituting this into the rate equation:
\[ \text{New Rate} = k (3[A])^3 = k \cdot 27[A]^3 \]
This simplifies to:
\[ \text{New Rate} = 27 \times (\text{Original Rate}) \]
Therefore, the reaction rate will increase by a factor of 27 when the concentration of A is increased by a factor of 3.
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