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Consider the zero-order reaction \(\mathrm{A} \longrightarrow\) product. (a) Write the rate law for the reaction. (b) What are the units for the rate constant? (c) Plot the rate of the reaction versus [A].

Short Answer

Expert verified
(a) Rate law: Rate = k; (b) Units for k: M/s; (c) Graph: Horizontal line at y = k.

Step by step solution

01

Identify the Rate Law for a Zero-Order Reaction

In a zero-order reaction, the rate of the reaction is independent of the concentration of the reactant, A. Therefore, the rate law for a zero-order reaction is expressed as:\[\text{Rate} = k\]where \(k\) is the rate constant.
02

Determine the Units for the Rate Constant

For a zero-order reaction, the rate is equal to the rate constant \(k\), which has the same units as the rate of reaction. The rate of reaction typically has units of concentration/time, which, for concentration in molarity (M) and time in seconds (s), gives the units:\[\text{Rate} = \text{M/s} \]Thus, the units for the rate constant \(k\) for a zero-order reaction are also \(\text{M/s}\).
03

Describe the Graph of Rate versus [A]

For a zero-order reaction, the rate of the reaction is a constant value as it does not depend on the concentration of [A]. Therefore, the graph of the rate of the reaction versus [A] will be a horizontal line parallel to the x-axis. The y-value of this line will be equal to the rate constant \(k\), and it will remain constant regardless of changes in [A].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Rate Law in Zero-Order Reactions
In a zero-order reaction, the rate of the reaction doesn't depend on the concentration of the reactant. This makes zero-order reactions quite unique. Rather than varying with different amounts of reactant, the rate stays constant throughout the reaction.
This means that in the equation representing the rate law, the concentration term, like \([A]\), won't appear. Instead, the rate law for a zero-order reaction is expressed simply as:
  • Rate = k
Here, \(k\) stands as the rate constant. It's the constant speed at which the reaction progresses, regardless of how much \(A\) is available.
This concept is central when studying or observing chemical reactions, as it shows how some reactions can proceed at a steady pace, driven by factors other than the concentration of the reactant.
Deciphering Rate Constant Units
The rate constant \(k\) in a zero-order reaction has specific units which can sometimes confuse students. Since in these reactions the rate is constant, the units for \(k\) must match those of the rate of the reaction itself.
Generally, the rate is measured in terms of concentration change over time. With a focus on molarity (M) for concentration and seconds (s) for time, we conclude that the units are:
  • \((\text{M/s})\)
Grasping these units emphasizes how the rate remains unaffected by changes in the reactant concentration. It reassures us that whether there's a lot or a little reactant, the reaction progresses at a uniform pace dictated by \(k\).
Understanding unit conversion is vital for analyzing different reactions, especially when dealing with experimental data.
Visualizing the Graph of Reaction Rate
A graph is one of the easiest ways to understand zero-order reactions visually. In such cases, a common plot is the reaction rate versus reactant concentration \([A]\).
For zero-order reactions, the rate steadily remains constant irrespective of how the concentration of \(A\) changes. This signifies that if you were to graph it:
  • The line would be flat and horizontal, paralleling the x-axis.
  • The position of this line on the y-axis represents the rate constant \(k\).
The constancy seen in this graph underscores the principle that the reaction rate is unaffected by concentration shifts. It's a powerful tool that can help visually confirm the core nature of a zero-order reaction, enriching your chemical kinetics comprehension.
The Essentials of Reaction Kinetics
Reaction kinetics help us explore the speed of chemical reactions and how they change under different circumstances. When we delve into kinetics, we deal with several types of reactions, like zero-order, where pace isn't reliant on reactant concentration.
The focus in kinetics is about:
  • Understanding how rates are influenced by external conditions like temperature or catalysts.
  • Connecting how molecular collisions play a pivotal role, triggering reactions.
Insights from kinetics enhance how we approach industrial chemical processes, so they're optimized for efficiency and effectiveness. This area of study is pivotal, as it bridges theoretical understanding with practical applications, impacting everything from pharmaceuticals to energy production.

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Most popular questions from this chapter

Use the Arrhenius equation to show why the rate constant of a reaction (a) decreases with increasing activation energy and (b) increases with increasing temperature.

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