1.1 Reaction Rates and Rate Laws

Chemical reactions happen at different speeds. Reaction rates measure how fast reactants turn into products. Understanding rates helps us control and predict chemical processes in labs and industries.

Rate laws show how reaction speed depends on reactant amounts. We find rate laws by changing reactant concentrations and measuring initial rates. This helps us figure out reaction orders and rate constants.

Reaction rate and significance

Definition and units

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• Reaction rate is the change in concentration of a reactant or product per unit time
• Typically expressed in units of molarity per second (M/s) or molarity per minute (M/min)

Importance in chemical kinetics

• Reaction rates provide information about the speed and progress of a chemical reaction
• Crucial for understanding and controlling chemical processes
• The study of reaction rates and the factors that influence them is the main focus of chemical kinetics

Experimental determination

• Reaction rates can be determined experimentally by measuring the concentration of reactants or products at different time intervals during a reaction
• The rate of a reaction can vary over time, and the initial rate is often used to characterize the overall reaction rate

Determining rate law expressions

Rate law definition

• The rate law is an equation that relates the reaction rate to the concentrations of reactants and a rate constant
• Expresses the dependence of the rate on the reactant concentrations
• The general form of a rate law is: $Rate = k[A]^m[B]^n$, where $k$ is the rate constant, $[A]$ and $[B]$ are the concentrations of reactants, and $m$ and $n$ are the reaction orders with respect to each reactant

Experimental method

• To determine the rate law, the initial rates of the reaction are measured while varying the concentrations of one reactant at a time, keeping the concentrations of other reactants constant (method of initial rates)
• The reaction orders ($m$ and $n$) can be determined by analyzing the relationship between the initial rates and the corresponding reactant concentrations using a log-log plot or the method of initial rates
• The rate constant ($k$) can be calculated using the determined rate law expression and the experimental data

Differential vs Integrated rate laws

Differential rate laws

• Differential rate laws express the reaction rate as a function of reactant concentrations at a particular instant in time
• Derived directly from the reaction mechanism and the experimentally determined rate law expression

Integrated rate laws

• Integrated rate laws express the concentration of a reactant or product as a function of time
• Obtained by integrating the differential rate law and require knowledge of the initial concentrations of reactants
• Allow for the prediction of reactant or product concentrations at any given time during the reaction, provided that the initial concentrations and the rate constant are known

Distinguishing features

• The integrated rate law expressions differ depending on the reaction order (zero-order, first-order, or second-order)
• Can be used to determine the reaction order by analyzing the linearity of different plots (concentration vs. time, ln(concentration) vs. time, or 1/concentration vs. time)

Reaction order and rate law relationship

Definition of reaction order

• Reaction order is the power to which the concentration of a reactant is raised in the rate law expression
• Indicates the degree to which the reaction rate depends on the concentration of that reactant
• The overall reaction order is the sum of the individual reaction orders for each reactant in the rate law expression

Types of reaction orders

• A reaction can have different orders with respect to different reactants, and the order can be zero, fractional, or negative, depending on the reaction mechanism
• Zero-order reactions have rates that are independent of the reactant concentration (e.g., catalytic reactions)
• First-order reactions have rates that are directly proportional to the reactant concentration (e.g., radioactive decay)
• Second-order reactions have rates that are proportional to the square of the reactant concentration or the product of two reactant concentrations (e.g., bimolecular reactions)

Insights into reaction mechanism

• The reaction order can provide insights into the reaction mechanism
• The order with respect to a particular reactant indicates the number of molecules of that reactant involved in the rate-determining step of the reaction