Chapter 12: Reaction Rates and Order

Chapter 12 Study Notes

Key Concepts to Master

1. Calculating the Instantaneous Rate

• Definition: The instantaneous rate of a reaction is defined as the rate at which a reactant is consumed or a product is formed at a specific moment in time.

• Method: It can be calculated from the slope of a tangent line drawn to a concentration versus time plot.

  • Process:

  • Obtain a concentration vs. time graph for the reaction.

  • Choose the specific point in time for which the instantaneous rate is to be calculated.

  • Draw a tangent line at that point.

  • Calculate the slope of the tangent line, which corresponds to the instantaneous rate of the reaction.

2. Expressing Reaction Rate

• Definition: The reaction rate is often expressed in terms of changes in concentration over time, which reflects how quickly reactants are used up or products are formed during a chemical reaction.

• Mathematical Representation:

  • The general equation is:
    $ext{Rate} = - rac{ riangle [ ext{Reactant}]}{ riangle t} \ ext{or} \ ext{Rate} = rac{ riangle [ ext{Product}]}{ riangle t}$

  • Where:

  • $riangle [ ext{Reactant}]:$ Change in concentration of the reactant.

  • $riangle [ ext{Product}]:$ Change in concentration of the product.

  • $riangle t:$ Change in time interval over which the reaction occurs.

  • Units of Measurement:

  • Commonly expressed in terms of molarity per second (M/s).

3. Determining Reaction Order

• Definition: The reaction order is the power to which the concentration of a reactant is raised in the rate law, indicating how the rate of reaction depends on the concentration of that reactant.

• How to Determine Order:

  • Utilize a known rate law which is expressed in the form:
    $ext{Rate} = k[ ext{A}]^m[ ext{B}]^n$

  • Where:

  • $k$ is the rate constant,

  • $[ ext{A}]$ and $[ ext{B}]$ are the concentrations of the reactants,

  • $m$ and $n$ are the reaction orders of the respective reactants.

  • Example: If the rate law for a reaction is found to be:
    $ext{Rate} = k[ ext{A}]^2[ ext{B}]^1$

  • This indicates a second-order reaction with respect to A and a first-order reaction with respect to B.

4. Using Units of the Rate Constant to Confirm Reaction Order

• Importance of Units: The units of the rate constant $k$ vary depending on the overall reaction order.

• General Units of k:

  • Zero-order: $( ext{M} imes ext{s}^{-1})$

  • First-order: $( ext{s}^{-1})$

  • Second-order: $( ext{M}^{-1} imes ext{s}^{-1})$

  • Higher Orders: Corresponding units will extend accordingly based on the overall order.

• Confirmation Process:

  • Calculate the rate constant using experimental data.

  • Ensure the units of $k$ align with theoretical predictions based on the determined reaction order from the rate law.