Rate law

Examples of Rate law in the following topics:

• Overall Reaction Rate Laws

  • Step two is the slow, rate-determining step, so it might seem reasonable to assume that the rate law for this step should be the overall rate law for the reaction.
  • The overall rate law cannot contain any such intermediates, because the rate law is determined by experiment only, and such intermediates are not observable.
  • We can now substitute this expression into the rate law for the second, rate-determining step.
  • Remember, the overall rate law must be determined by experiment.
  • Therefore, the rate law must contain no reaction intermediates.

• The Integrated Rate Law

  • Recall that the rate law for a first-order reaction is given by:
  • Recall that the rate law for a second-order reaction is given by:
  • The final version of this integrated rate law is given by:
  • In this case, we can say that [A]=[B], and the rate law simplifies to:
  • This is the standard form for second-order rate law, and the integrated rate law will be the same as above.

• Rate Laws for Elementary Steps

  • The rate law for an elementary step is derived from the molecularity of that step.
  • The rate law of the rate-determining step must agree with the experimentally determined rate law.
  • However, we cannot simply add the rate laws of each elementary step in order to get the overall reaction rate.
  • The molecularity of an elementary step in a reaction mechanism determines the form of its rate law.
  • Write rate laws for elementary reactions, explaining how the order of the reaction relates to the reaction rate

• The Rate Law

  • The rate law for a chemical reaction relates the reaction rate with the concentrations or partial pressures of the reactants.
  • The rate law for a chemical reaction is an equation that relates the reaction rate with the concentrations or partial pressures of the reactants.
  • For example, the rate law $Rate=k[NO]^2[O_2]$ describes a reaction which is second-order in nitric oxide, first-order in oxygen, and third-order overall.
  • A certain rate law is given as $Rate=k[H_2][Br_2]^\frac{1}{2}$.
  • The rate law equation for this reaction is: $Rate = k[NO]^{1}[O_{3}]^{1}$.

• Rate-Determining Steps

  • If this reaction occurred in a single step, its rate law would be:
  • The fact that the experimentally-determined rate law does not match the rate law derived from the overall reaction equation suggests that the reaction occurs over multiple steps.
  • If the second or a later step is rate-determining, determining the rate law is slightly more complicated.
  • We will explore how to write that rate law later.
  • Describe the relationship between the rate determining step and the rate law for chemical reactions

• Steady-State Approximation

  • The steady state approximation can be used to determine the overall rate law when the rate-determining step is unknown.
  • In this case, the overall rate law will be:
  • We need to write this rate law in terms of reactants only.
  • Now, both of these rates can be written as rate laws derived from our elementary steps.
  • Here we have our final rate law for the overall reaction.

• Zero-Order Reactions

  • A zero-order reaction has a constant rate that is independent of the concentration of the reactant(s); the rate law is simply $rate=k$ .
  • The rate law for a zero-order reaction is rate = k, where k is the rate constant.
  • By rearranging this equation and using a bit of calculus (see the next concept: The Integrated Rate Law), we get the equation:
  • This is the integrated rate law for a zero-order reaction.
  • Use graphs of zero-order rate equations to obtain the rate constant and the initial concentration data

• Second-Order Reactions

  • If the reaction were second-order in either reactant, it would lead to the following rate laws:
  • The second scenario, in which the reaction is first-order in both A and B, would yield the following rate law:
  • Note that on the right side of the equation, both the rate constant k and the term $(0.200)^y$ cancel.
  • Therefore, the overall order for the reaction is second-order $(2+0=2)$, and the rate law will be:
  • Manipulate experimentally determined second-order rate law equations to obtain rate constants

• First-Order Reactions

  • A first-order reaction depends on the concentration of one reactant, and the rate law is: $r=-\frac{dA}{dt}=k[A]$ .
  • Thus, the rate law for an elementary reaction that is first order with respect to a reactant A is given by:
  • Since there is only one reactant, the rate law for this reaction has the general form:
  • We then measure the new rate at which the N2O5 decomposes.
  • We can now set up a ratio of the first rate to the second rate:

• Chemical Kinetics and Chemical Equilibrium

  • Each reaction also has a reaction rate.
  • The unit of this rate is usually M/second.
  • Instead, the reaction rate can be accurately modeled by a rate equation.
  • The reaction rate can be determined using a rate law, which depends on the concentrations of the reactants, among other things.
  • You can read more about reaction rates and rate laws in the Kinetics unit.