At A Certain Temperature, The Following Reaction Follows First-order Kinetics With A Rate Constant Of $0.00524 \, \text{s}^{-1}$:$2 \, \text{Cl}_2 \text{O}_5(g) \rightarrow 2 \, \text{Cl}_2(g) + 5 \, \text{O}_2(g$\]Suppose A Vessel
Introduction
Chemical kinetics is a crucial aspect of chemistry that deals with the study of rates of chemical reactions. It helps us understand how fast a reaction occurs and how the concentration of reactants and products changes over time. One of the fundamental concepts in chemical kinetics is the order of a reaction, which refers to the number of reactant molecules that must collide with each other to initiate a reaction. In this article, we will discuss first-order kinetics, a type of reaction where the rate of reaction depends on the concentration of only one reactant.
What is First-Order Kinetics?
First-order kinetics is a type of reaction where the rate of reaction is directly proportional to the concentration of only one reactant. Mathematically, this can be represented as:
r = k[A]
where r is the rate of reaction, k is the rate constant, and [A] is the concentration of the reactant.
In the given reaction, , the rate of reaction depends on the concentration of . Therefore, this reaction follows first-order kinetics.
Rate Constant
The rate constant, k, is a measure of the rate of reaction and is a characteristic of the reaction itself. It is a constant that depends on the temperature and the properties of the reactants. In the given reaction, the rate constant is .
Temperature Dependence
The rate constant, k, is temperature-dependent. As the temperature increases, the rate constant also increases. This is because higher temperatures provide more energy for the reactant molecules to collide and react.
Integrated Rate Law
The integrated rate law for a first-order reaction is given by:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, and k is the rate constant.
Half-Life
The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease by half. Mathematically, it can be represented as:
t1/2 = ln(2)/k
where t1/2 is the half-life and k is the rate constant.
Example Problem
Suppose we have a vessel containing at an initial concentration of . The rate constant for the reaction is . How long will it take for the concentration of to decrease by half?
Using the integrated rate law, we can calculate the half-life as follows:
ln([A]t/[A]0) = -kt
ln(0.05/0.1) = -0.00524t
-0.693 = -0.00524t
t = 132.5 s
Therefore, it will take approximately 132.5 seconds for the concentration of to decrease by half.
Conclusion
In conclusion, first-order kinetics is a type of reaction where the rate of reaction depends on the concentration of only one reactant. The rate constant, k, is a measure of the rate of reaction and is a characteristic of the reaction itself. The integrated rate law and half-life are important concepts in first-order kinetics that help us understand how the concentration of reactants and products changes over time. By understanding these concepts, we can better design and optimize chemical reactions for various applications.
References
- Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
- Levine, I. N. (2014). Physical chemistry. McGraw-Hill Education.
- Moore, J. W., & Pearson, R. G. (2012). Kinetics and mechanism: A dynamic approach. John Wiley & Sons.
First-Order Kinetics Q&A ==========================
Q: What is the difference between first-order and second-order kinetics?
A: First-order kinetics is a type of reaction where the rate of reaction depends on the concentration of only one reactant. Second-order kinetics, on the other hand, is a type of reaction where the rate of reaction depends on the concentration of two reactants.
Q: How do you determine if a reaction is first-order or second-order?
A: To determine if a reaction is first-order or second-order, you need to look at the rate law equation. If the rate law equation is in the form r = k[A], then the reaction is first-order. If the rate law equation is in the form r = k[A]^2, then the reaction is second-order.
Q: What is the half-life of a first-order reaction?
A: The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease by half. It can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.
Q: How does temperature affect the rate constant of a first-order reaction?
A: The rate constant of a first-order reaction increases with increasing temperature. This is because higher temperatures provide more energy for the reactant molecules to collide and react.
Q: Can you give an example of a first-order reaction?
A: Yes, the decomposition of hydrogen peroxide is a first-order reaction. The equation for this reaction is 2H2O2 β 2H2O + O2. The rate law equation for this reaction is r = k[H2O2], where r is the rate of reaction and k is the rate constant.
Q: How do you calculate the rate constant of a first-order reaction?
A: The rate constant of a first-order reaction can be calculated using the integrated rate law equation ln([A]t/[A]0) = -kt, where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, and k is the rate constant.
Q: What is the significance of the half-life of a first-order reaction?
A: The half-life of a first-order reaction is significant because it tells us how long it will take for the concentration of the reactant to decrease by half. This is useful in predicting the outcome of a reaction and in designing experiments to study the kinetics of a reaction.
Q: Can you give an example of how to use the half-life of a first-order reaction to predict the outcome of a reaction?
A: Yes, suppose we have a reaction where the half-life of the reactant is 10 minutes. If we start with an initial concentration of 1 M, we can use the half-life equation to predict the concentration of the reactant at different times. For example, after 20 minutes, the concentration of the reactant will be 0.25 M, and after 30 minutes, the concentration of the reactant will be 0.125 M.
Q: How do you determine the order of a reaction experimentally?
A: To determine the order of a reaction experimentally, you need to measure the rate of reaction at different concentrations of the reactant. If the rate of reaction is directly proportional to the concentration of the reactant, then the reaction is first-order. If the rate of reaction is proportional to the square of the concentration of the reactant, then the reaction is second-order.
Q: What are some common applications of first-order kinetics?
A: First-order kinetics has many applications in chemistry, including the study of reaction rates, the design of chemical reactors, and the prediction of the outcome of chemical reactions. It is also used in fields such as medicine, where it is used to study the kinetics of drug metabolism and the effects of drugs on the body.
Q: Can you give an example of how first-order kinetics is used in medicine?
A: Yes, first-order kinetics is used in medicine to study the kinetics of drug metabolism. For example, the metabolism of a drug can be studied using first-order kinetics to predict how long it will take for the drug to be eliminated from the body. This information can be used to design dosing regimens and to predict the effects of the drug on the body.