A first-order reaction is characterized by a number of distinguishing features, which relate to how the reaction rate depends on the concentration of the reactants and how the reaction progresses over time. Here are some of the special features of first-order reactions:
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Rate Law: The rate of a first-order reaction is directly proportional to the concentration of a single reactant. It can be expressed as: \[ \text{Rate} = k[A] \] where \( k \) is the rate constant and \([A]\) is the concentration of the reactant.
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Integrated Rate Law: For a first-order reaction, the relationship between concentration and time can be described by the integrated rate law: \[ \ln[A] = -kt + \ln[A_0] \] where \([A_0]\) is the initial concentration of the reactant, \( t \) is the time, and \( k \) is the first-order rate constant.
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Half-Life: The half-life of a first-order reaction is a constant and does not depend on the initial concentration of the reactant. It is given by: \[ t_{1/2} = \frac{0.693}{k} \] This means that the time required for half of the reactant to be consumed remains the same, regardless of its concentration.
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Exponential Decay: The concentration of the reactant decreases exponentially over time, which is characteristic of first-order kinetics. As the reaction proceeds, the amount of reactant decreases more slowly over time.
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Graphical Representation: A plot of \(\ln[A]\) versus time will yield a straight line with a slope of \(-k\). This is a key test for determining if a reaction is first-order.
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Units of Rate Constant: The units of the rate constant \( k \) for a first-order reaction are typically expressed as \( \text{s}^{-1} \), indicating it relates to changes in concentration over time.
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Reaction Mechanism: First-order reactions often involve a single molecular event (such as the dissociation of a single molecule) and are frequently observed in unimolecular reactions.
Understanding these features is crucial for analyzing reaction kinetics and for predicting the behavior of first-order reactions in chemical processes.
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