Glossary

2.2 Rate laws and reaction orders

2 min read•july 22, 2024

Rate laws are the mathematical backbone of chemical kinetics. They show how reaction rates change with reactant concentrations, helping us predict and control reactions. Understanding rate laws is crucial for unraveling reaction mechanisms and optimizing industrial processes.

Reaction orders tell us how sensitive a reaction is to concentration changes. reactions don't care about concentration, while higher orders are increasingly affected. Determining reaction orders and rate constants from experimental data is a key skill in chemical kinetics.

Rate Laws and Reaction Orders

Concept of rate law

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  • Mathematical expression relating reaction rate to reactant concentrations
  • Determined experimentally by measuring reaction rates at different concentrations
  • Provides insight into reaction mechanism by revealing which reactants influence rate and to what extent
  • Significance in chemical kinetics
    • Predicts how reaction rate changes with reactant concentrations (doubling concentration of a reactant doubles rate)
    • Allows determination of and reaction order from experimental data
    • Helps in understanding underlying reaction mechanism by suggesting which elementary steps may be involved

Order of chemical reactions

  • Exponent to which is raised in rate law
  • Can be zero (rate independent of concentration), first (rate directly proportional to concentration), second (rate proportional to square of concentration), or fractional order
  • Determining reaction order
      • Vary concentration of one reactant while keeping others constant
      • Compare ratio of rate changes to ratio of concentration changes (doubling concentration of a first-order reactant doubles rate)
    • Graphical method
      • Plot log(rate) vs. log(concentration) for each reactant
      • Slope of line gives order with respect to that reactant (slope of 1 indicates first order)
  • Overall order is sum of orders with respect to each reactant
    • Example: Rate=k[A]2[B]\text{Rate} = k[\text{A}]^2[\text{B}] has overall order of 3 (second order in A, first order in B)

Rate constant determination

  • Proportionality constant kk in rate law
  • Determined experimentally by measuring reaction rate at known reactant concentrations
  • Depends on temperature (typically increases with temperature) but not on reactant concentrations
  • Units of rate constant depend on overall order of reaction
    • For rate law: Rate=k[A]m[B]n\text{Rate} = k[\text{A}]^m[\text{B}]^n
      • Units of kk = concentration1−(m+n)time\frac{\text{concentration}^{1-(m+n)}}{\text{time}}
      • Example: For a reaction (m+n=2m+n=2), units of kk are 1concentration⋅time\frac{1}{\text{concentration} \cdot \text{time}} (M−1^{-1}s−1^{-1})

Concentration effects on reaction rates

  • Increasing concentration of a reactant increases reaction rate
  • Extent of rate increase depends on order with respect to that reactant
    1. Zero-order reactions
      • Rate is independent of reactant concentration
      • Rate=k\text{Rate} = k
      • Example: Enzyme-catalyzed reactions at high substrate concentration
    2. First-order reactions
      • Rate is directly proportional to reactant concentration
      • Rate=k[A]\text{Rate} = k[\text{A}]
      • Doubling concentration doubles rate
      • Example: Radioactive decay, many enzyme-catalyzed reactions
    3. Second-order reactions
      • Rate is proportional to square of reactant concentration
      • Rate=k[A]2\text{Rate} = k[\text{A}]^2
      • Doubling concentration quadruples rate
      • Example: Dimerization reactions, some bimolecular elementary steps

Key Terms to Review (16)

Activation Energy: Activation energy is the minimum amount of energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to be transformed into products, linking the concepts of kinetics and thermodynamics in the context of chemical reactions.
Arrhenius: The Arrhenius concept, formulated by Svante Arrhenius in the late 19th century, describes how the rate of a chemical reaction depends on temperature and activation energy. This idea forms the basis for understanding reaction rates and is crucial in both zero-order kinetics and reaction orders, as it highlights the temperature dependency of these processes and how they can influence reaction rates.
Bodenstein: Bodenstein refers to George Bodenstein, a notable chemist known for his contributions to the understanding of reaction kinetics and mechanisms. His work has significantly impacted the study of rate laws and reaction orders by helping to elucidate how the speed of chemical reactions can be quantitatively described and understood through mathematical expressions.
Catalytic activity: Catalytic activity refers to the ability of a substance, typically a catalyst, to accelerate a chemical reaction without being consumed in the process. This activity is crucial in determining how effective a catalyst is in enhancing reaction rates, often influenced by factors like surface area, temperature, and the nature of reactants. A high catalytic activity means a catalyst can significantly lower the activation energy required for a reaction, leading to faster and more efficient reactions.
First-order: First-order refers to a type of reaction kinetics where the rate of reaction is directly proportional to the concentration of one reactant. In first-order reactions, as the concentration of that reactant decreases, the rate also decreases linearly, following a specific mathematical relationship. This concept is essential in understanding how different reactants influence the overall speed of chemical reactions and is often expressed in rate laws.
Half-life: Half-life is the time required for half of the reactant to be consumed in a chemical reaction, providing a measure of the rate at which a reaction occurs. This concept is crucial in understanding how quickly substances degrade or react, especially in applications such as pharmaceuticals and environmental science, where it helps predict the behavior of drugs and pollutants over time.
Homogeneous catalyst: A homogeneous catalyst is a catalyst that exists in the same phase as the reactants in a chemical reaction, typically in a solution. This type of catalyst facilitates a reaction by providing an alternative reaction pathway with a lower activation energy, thus increasing the reaction rate while being consumed in the process. The uniformity in phase allows for better interaction between the catalyst and reactants, impacting various aspects of chemical kinetics.
Integrated Rate Law: The integrated rate law is a mathematical equation that relates the concentration of a reactant to time for a chemical reaction. This law allows chemists to determine how the concentration of a reactant decreases over time and helps in understanding the relationship between reaction rate and concentration, which is crucial for identifying reaction orders and analyzing the kinetics of reactions.
Method of initial rates: The method of initial rates is a technique used to determine the rate law and reaction order by measuring the initial rate of reaction for different initial concentrations of reactants. This method allows for the calculation of how the rate changes with varying concentrations, helping to establish the relationship between concentration and rate, which is key to understanding differential rate laws and overall reaction kinetics.
Product Concentration: Product concentration refers to the amount of product formed in a chemical reaction at a given moment, usually expressed in terms of molarity (moles per liter). It plays a crucial role in determining the rate of reaction, as higher concentrations of products can influence the reaction dynamics and the forward and reverse reactions in equilibrium situations.
Rate Constant: The rate constant is a proportionality factor in the rate law that quantifies the speed of a chemical reaction at a given temperature. It connects the concentration of reactants to the reaction rate, showing how quickly the reaction proceeds. The value of the rate constant is influenced by factors such as temperature, activation energy, and the presence of catalysts, making it a key element in understanding reaction kinetics and dynamics.
Rate-determining step: The rate-determining step is the slowest step in a reaction mechanism that limits the overall rate of the reaction. This concept is crucial because it helps to identify which specific reaction step controls how fast a chemical reaction occurs, influencing the formulation of rate laws and determining the kinetics of reactions.
Reactant concentration: Reactant concentration refers to the amount of a substance present in a given volume of solution or reaction mixture, which significantly influences the rate at which chemical reactions occur. Higher reactant concentrations typically lead to more frequent collisions between molecules, thus increasing the rate of reaction. Understanding how concentration affects reaction rates is crucial for predicting the behavior of chemical systems and is foundational in analyzing rate laws and reaction orders.
Second-order: Second-order refers to a type of reaction where the rate is proportional to the square of the concentration of one reactant or the product of the concentrations of two different reactants. This concept is crucial in understanding how reaction rates are affected by concentration changes and plays a key role in determining the overall kinetics of a chemical reaction.
Temperature Dependence: Temperature dependence refers to how the rate of a chemical reaction changes with varying temperatures. Generally, an increase in temperature tends to accelerate reaction rates due to enhanced molecular motion and increased frequency of collisions between reactants, thus influencing various chemical processes.
Zero-order: Zero-order refers to a type of reaction rate where the rate of reaction is constant and does not depend on the concentration of the reactants. In this scenario, the rate remains unchanged as the concentration of the reactant decreases, indicating that the reaction proceeds at a steady pace until it is exhausted. This behavior is often observed in cases where a catalyst is involved or when a reaction occurs at a constant temperature, making it essential for understanding the dynamics of chemical reactions.
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