Problem 1
Question
The unit of specific reaction rate constant for a firstorder (if the concentration is expressed in molarity) would be (a) \(\mathrm{s}^{-1}\) (b) mole \(\mathrm{s}^{-1}\) (c) mole \(\mathrm{L}^{-1} \mathrm{~s}^{-1}\) (d) mole \(\mathrm{L}^{-1}\)
Step-by-Step Solution
Verified Answer
The unit of the specific reaction rate constant for a first-order reaction is \( \text{s}^{-1} \) (option a).
1Step 1: Understanding the Reaction Order
A first-order reaction is one where the rate of reaction depends linearly on the concentration of one reactant. The equation representing a first-order reaction is typically expressed as \( \text{Rate} = k[A] \), where \( k \) is the rate constant and \([A]\) is the concentration of reactant A.
2Step 2: Analyzing the Units of the Rate
The unit of the rate of reaction is usually expressed as concentration per unit time. Since the concentration is expressed in molarity (moles/Liter), and time is in seconds, the unit of rate is \( \text{mole} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \).
3Step 3: Relating Rate to Rate Constant Units
For the first-order reaction, the formula \( \text{Rate} = k[A] \) implies that \( k = \frac{\text{Rate}}{[A]} \). The unit of concentration \([A]\) is \( \text{mole} \cdot \text{L}^{-1} \), so \( k \) has units \( \frac{\text{mole} \cdot \text{L}^{-1} \cdot \text{s}^{-1}}{\text{mole} \cdot \text{L}^{-1}} = \text{s}^{-1} \).
4Step 4: Conclusion and Answer
From the analysis, the unit of the specific reaction rate constant \( k \) for a first-order reaction, when concentration is expressed in molarity, is \( \text{s}^{-1} \). This matches option (a).
Key Concepts
Rate ConstantReaction RateMolarity
Rate Constant
The rate constant, often represented as \( k \), plays a crucial role in understanding chemical reactions. It helps quantify the speed of a reaction for given conditions. In the context of first-order reactions, the rate constant has a particularly straightforward role.
For a first-order reaction, the rate depends only on the concentration of one reactant. The equation that describes this is \( \text{Rate} = k[A] \). This simplicity makes it a good starting point for learners. In this scenario, \( k \), the rate constant, serves as a proportionality factor that links the reaction rate to the concentration of the reactant.
One important property of the rate constant is its unit. The units of \( k \) vary depending on the reaction order. For first-order reactions, the units of \( k \) are \( \text{s}^{-1} \). These units reflect that the reaction rate is expressed as concentration change over time.
For a first-order reaction, the rate depends only on the concentration of one reactant. The equation that describes this is \( \text{Rate} = k[A] \). This simplicity makes it a good starting point for learners. In this scenario, \( k \), the rate constant, serves as a proportionality factor that links the reaction rate to the concentration of the reactant.
One important property of the rate constant is its unit. The units of \( k \) vary depending on the reaction order. For first-order reactions, the units of \( k \) are \( \text{s}^{-1} \). These units reflect that the reaction rate is expressed as concentration change over time.
Reaction Rate
Understanding reaction rate is key to grasping chemical kinetics. Essentially, the reaction rate measures how fast reactants are converted into products in a given period. It’s typically represented through changes in molarity, which is the concentration of a substance in a solution.
For a first-order reaction, the rate equation is simpler, taking the form \( \text{Rate} = k[A] \). This equation indicates that the reaction rate is directly proportional to the concentration of the reactant. In real-world terms, if you were to double the concentration of the reactant, the reaction rate doubles as well.
The units for reaction rates are crucial for understanding: in first-order reactions, these units are \( \text{mole} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \). This includes moles per liter, reflecting concentration, and per second, reflecting time, thereby providing a full picture of how quickly a reaction proceeds.
For a first-order reaction, the rate equation is simpler, taking the form \( \text{Rate} = k[A] \). This equation indicates that the reaction rate is directly proportional to the concentration of the reactant. In real-world terms, if you were to double the concentration of the reactant, the reaction rate doubles as well.
The units for reaction rates are crucial for understanding: in first-order reactions, these units are \( \text{mole} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \). This includes moles per liter, reflecting concentration, and per second, reflecting time, thereby providing a full picture of how quickly a reaction proceeds.
Molarity
Molarity is a standard unit for expressing the concentration of a solute in a solution. It's calculated by dividing the number of moles of solute by the volume of solution in liters. The use of molarity is common in kinetics to measure reactant concentrations.
In the context of first-order reactions, molarity influences how we express both the rate of reaction and the rate constant. The concentration of reactant in molarity \([A] \) is part of the fundamental rate equation \( \text{Rate} = k[A] \).
Molarity inputs enable chemists to assess how concentration variations impact reaction rates, allowing for precise control over the chemical processes. When this concentration is in terms of molarity, it provides a clear picture of the substance's presence in the reaction environment and how it's influencing the reaction speed.
In the context of first-order reactions, molarity influences how we express both the rate of reaction and the rate constant. The concentration of reactant in molarity \([A] \) is part of the fundamental rate equation \( \text{Rate} = k[A] \).
Molarity inputs enable chemists to assess how concentration variations impact reaction rates, allowing for precise control over the chemical processes. When this concentration is in terms of molarity, it provides a clear picture of the substance's presence in the reaction environment and how it's influencing the reaction speed.
Other exercises in this chapter
Problem 4
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