zero-order reaction

Examples of zero-order reaction in the following topics:

• Zero-Order Reactions

  • Unlike the other orders of reaction, a zero-order reaction has a rate that is independent of the concentration of the reactant(s).
  • The rate law for a zero-order reaction is rate = k, where k is the rate constant.
  • In the case of a zero-order reaction, the rate constant k will have units of concentration/time, such as M/s.
  • This is the integrated rate law for a zero-order reaction.
  • For a zero-order reaction, the half-life is given by:

• Half-Life

  • If we know the integrated rate laws, we can determine the half-lives for first-, second-, and zero-order reactions.
  • Recall that for a first-order reaction, the integrated rate law is given by:
  • Thus the half-life of a second-order reaction, unlike the half-life for a first-order reaction, does depend upon the initial concentration of A.
  • The integrated rate law for a zero-order reaction is given by:
  • Therefore, for a zero-order reaction, half-life and initial concentration are directly proportional.

• The Integrated Rate Law

  • Recall that the rate law for a first-order reaction is given by:
  • This is the final form of the integrated rate law for a first-order reaction.
  • Recall that the rate law for a second-order reaction is given by:
  • Summary of integrated rate laws for zero-, first-, second-, and nth-order reactions
  • Graph integrated rate laws for zero-, first-, and second-order reactions in order to obtain information about the rate constant and concentrations of reactants

• Second-Order Reactions

  • A second-order reaction is second-order in only one reactant, or first-order in two reactants.
  • A reaction is said to be second-order when the overall order is two.
  • For a reaction with the general form $aA+bB\rightarrow C$, the reaction can be second order in two possible ways.
  • Next, we need to determine the reaction order for B.
  • We have determined that the reaction is second-order in A, and zero-order in B.

• Experimental Determination of Reaction Rates

  • In order to experimentally determine reaction rates, we need to measure the concentrations of reactants and/or products over the course of a chemical reaction.
  • If we know the order of the reaction, we can plot the data and apply our integrated rate laws.
  • For example, if the reaction is first-order, a plot of ln[A] versus t will yield a straight line with a slope of -k.
  • Recall that for zero-order reactions, a graph of [A] versus time will be a straight line with slope equal to -k.
  • For first-order reactions, a graph of ln[A] versus time yields a straight line with a slope of -k, while for a second-order reaction, a plot of 1/[A] versus t yields a straight line with a slope of k.

• First-Order Reactions

  • A first-order reaction depends on the concentration of only one reactant.
  • As such, a first-order reaction is sometimes referred to as a unimolecular reaction.
  • While other reactants can be present, each will be zero-order, since the concentrations of these reactants do not affect the rate.
  • Using the Method of Initial Rates to Determine Reaction Order Experimentally
  • In order to determine the overall order of the reaction, we need to determine the value of the exponent m.

• Balancing Redox Equations

  • Every balanced redox reaction is composed of two half-reactions: the oxidation half-reaction, and the reduction half-reaction.
  • We can split this reaction into two half-reactions.
  • Notice that this equation is balanced in both mass and charge: we have one atom of iron on each side of the equation (mass is balanced), and the net charge on each side of the equation is equal to zero (charge is balanced).
  • First, we need to split this reaction into its two half-reactions.
  • Lastly, in order to get our full balanced redox equation, we need to add our half-reactions so that all the electrons cancel out.

• The Rate Law

  • 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.
  • What is the reaction order?
  • The reaction is first-order in hydrogen, one-half-order in bromine, and $\frac{3}{2}$-order overall.
  • The overall order of the reaction is 1 + 1 = 2.
  • A variety of reaction orders are observed.

• Reaction Quotients

  • The reaction quotient is a measure of the relative amounts of reactants and products during a chemical reaction at a given point in time.
  • By comparing the value of Q to the equilibrium constant, Keq, for the reaction, we can determine whether the forward reaction or reverse reaction will be favored.
  • If Q < Keq, the reaction will move to the right (in the forward direction) in order to reach equilibrium.
  • If Q > Keq, the reaction will move to the left (in the reverse direction) in order to reach equilibrium.
  • The ball in the initial state is indicative a reaction in which Q < K; in order to reach equilibrium conditions, the reaction proceeds forward.

• Steady-State Approximation

  • Recall our mechanism for the reaction of nitric oxide and oxygen:
  • In order to do so, we must assume that the state of the reaction intermediate, N2O2, remains steady, or constant, throughout the course of the reaction.
  • Here, k1 and k-1 are the rate constants for the forward and reverse reactions, respectively.
  • Here we have our final rate law for the overall reaction.
  • Notice that after their initial production, the concentration of the reaction intermediates remains relatively constant (slope of green curve is approximately zero) throughout the course of the reaction.