Chemical Kinetics Flashcards - Rate Laws, Integrated Rate Laws, and Catalysis

Kinetics Study Notes

Rate: Basics and Definitions

  • Velocity (rate) is the change in a quantity per unit time:
    • Velocity (rate) = \text{rate} = \dfrac{\Delta \text{distance}}{\Delta \text{time}}
    • For chemical reactions, rate is the change in concentration over time:
      \text{rate} = -\dfrac{1}{a}\dfrac{\Delta[A]}{\Delta t} = -\dfrac{1}{b}\dfrac{\Delta[B]}{\Delta t} = \dfrac{1}{c}\dfrac{\Delta[C]}{\Delta t} = \dfrac{1}{d}\dfrac{\Delta[D]}{\Delta t}
  • Example (balancing): for the reaction aA + bB \rightarrow cC + dD
    • Rate definitions use the stoichiometric coefficients a, b, c, d as shown above.
  • The rate of a reaction is always taken positive for the purpose of rate expressions; signs come from the definition (consumption of reactants is negative in concentration changes).
  • Typical example of a reaction rate from lecture data:
    • For 2\,N2O5(g) \rightarrow 4\,NO2(g) + O2(g) the rate expressions relate to each species via the stoichiometric coefficients:
      -\dfrac{1}{2}\dfrac{d[N2O5]}{dt} = \dfrac{1}{4}\dfrac{d[NO2]}{dt} = \dfrac{d[O2]}{dt}

Rate Expressions

  • Rate expressions (also called rate laws) relate rate to concentrations:

    • For a general reaction aA + bB \rightarrow cC + dD
      \text{rate} = k[A]^m[B]^n\quad\text{where } m,n\text{ are the orders in A and B, and k is the rate constant.}

  • The rate law orders (m, n) are determined experimentally, not from stoichiometry; the overall order is m+n+\ldots (sum of all reactant orders).

  • Examples from course content:

    • NO(g) + O2(g) → NO2(g) with rate law \text{rate} = k[NO]^2[O_2] (second order in NO, first order in O2, third order overall).
    • F2(g) + 2ClO2(g) → 2FClO2(g) with rate law \text{rate} = k[ F2 ][ClO2] (first order in F2 and first in ClO2; overall second order).

  • For the reaction 2N2O5(g) \rightarrow 4NO2(g) + O2(g) the rate expressions in terms of concentration changes are:
    -\dfrac{1}{2}\dfrac{d[N2O5]}{dt} = \dfrac{1}{4}\dfrac{d[NO2]}{dt} = \dfrac{d[O2]}{dt}

  • Relation between rate expressions and rate laws:

    • Rate expressions are written in terms of concentration changes with time.
    • Rate laws express rate as a function of concentration with a rate constant: \text{rate} = k[A]^m[B]^n…

  • Practical derivations from data:

    • Example: For a reaction with measured average rate from two time intervals, you compute the instantaneous rate from slope of concentration vs time graphs and use definitions to relate to reactant/product changes.
    • Example: For 2N2O5(g) \rightarrow 4NO2(g) + O2(g) with data given in table form, you compute the rate of appearance of products or rate of disappearance of reactants and relate them through stoichiometric coefficients as shown above.

  • Average, Instantaneous, and Initial rates:

    • Average rate: change in concentration over a specified time interval.
    • Instantaneous rate: slope at a specific time (tangent to the curve at t).
    • Initial rate: tangent at time zero (t = 0).

  • Common exercise style: Given a balanced equation, determine the rate of reaction with respect to a particular species by using the appropriate coefficient. E.g., for 2A + B \rightarrow 3C, if you know the rate from C, you can relate to the rates of A and B via stoichiometry.

Rate Laws and Orders

  • The rate law for a reaction aA + bB → products has the form:
    \text{rate} = k[A]^m[B]^n\quad\text{where } m,n\text{ are the orders in A and B, respectively.}

  • Important notes:

    • Rate laws are determined experimentally.
    • Reaction order is defined with respect to reactants, not products.
    • The order of a reactant is not necessarily equal to its stoichiometric coefficient.
    • Orders can be 0, 1, 2, fractional, or even negative (less common).
    • Overall order = sum of the individual reactant orders (e.g., for m=2, n=1, overall order = 3).

  • Examples from notes:

    • For the reaction 2NO(g) + O2(g) \rightarrow 2NO2(g), rate law: \text{rate} = k[NO]^2[O_2]. Overall order = 3 (second order in NO, first in O2).
    • For CH3CHO (acetaldehyde) decomposition: \text{rate} = k[CH_3CHO]^{3/2}; order in CH3CHO is 3/2, overall order 3/2.
    • For H2O2 + I- + H+ reaction: \text{rate} = k[H2O2][I^-]; first order in H2O2, first order in I-, zero order in H+. Overall order = 2.

  • Common rate laws and units table (summary):

    • Zero order: Rate = k[A]^0; Units: M s^-1; Integrated: [A]t = [A]0 - kt; Graph: [A] vs t is linear.
    • First order: Rate = k[A]^1; Units: s^-1; Integrated: \ln[A]t = -kt + \ln[A]0; Graph: ln[A] vs t linear.
    • Second order: Rate = k[A]^2; Units: M^-1 s^-1; Integrated: \frac{1}{[A]t} = kt + \frac{1}{[A]0}; Graph: 1/[A] vs t linear.

  • Rate constant units depend on overall order; e.g., for second order in a single reactant, k has units M^-1 s^-1.

  • Typical problem workflow (method of initial rates):

    • Use data from experiments with varying initial concentrations to determine m and n by observing how the initial rate changes when one reactant concentration changes while others are held constant.
    • Once m and n are found, solve for k using any experiment’s initial rate and concentrations.
    • Example worked problems in notes show extracting m and n by comparing rate changes when [NO], [O2] are varied, then computing k from one data set.

  • Rate laws vs rate expressions:

    • Rate expression is the expression of a rate in terms of concentration changes over time for a particular stoichiometry (often the same as a rate law but sometimes presented in differential form with coefficients).
    • Rate law is the mathematical relation rate = f([A],[B],…) with exponents m,n determined experimentally.

Integrated Rate Laws and Graphical Methods

  • Integrated rate laws relate concentration to time for different reaction orders:

    • First order: \ln[A]t = -kt + \ln[A]0
    • Zero order: [A]t = [A]0 - kt
    • Second order: \frac{1}{[A]t} = kt + \frac{1}{[A]0}

  • How to determine order graphically:

    • If plotting \ln[A] vs t yields a straight line, the reaction is first order in A.
    • If plotting 1/[A] vs t yields a straight line, the reaction is second order in A.
    • If plotting [A] vs t yields a straight line with negative slope, the reaction is zero order in A.

  • Example from course: decomposition of N2O5 data is used to illustrate how to determine whether a plot of ln[A] vs t, 1/[A] vs t, or [A] vs t is linear to assign order.

  • Integrated rate law graphs provide a linear relationship (y = mx + b) allowing extraction of k (slope) and/or [A]0 (intercept).

  • Equation references:

    • For general A → products: [A]t = [A]0 - kt (zero order).
    • For first order: \ln[A]t = -kt + \ln[A]0; Slope = -k.
    • For second order: \frac{1}{[A]t} = kt + \frac{1}{[A]0}; Slope = k; intercept = 1/[A]_0.

  • Example problems and graphs shown in notes include:

    • Integration forms for representative reactions and use of slope-intercept form to determine k.
    • Graphical determination of reaction order for a multi-step example (N2O5 decomposition).

Half-Life and Its Dependence on Order

  • Definition: half-life t1/2 is the time required for [A] to fall