second-order reaction

Examples of second-order reaction in the following topics:

• 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.
  • We have determined that the reaction is second-order in A, and zero-order in B.
  • Therefore, the overall order for the reaction is second-order $(2+0=2)$, and the rate law will be:

• 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.
  • Consider, for example, a second-order reaction with a rate constant of 3 M-1 s-1 in which the initial concentration of A is 0.5 M:
  • The integrated rate law for a zero-order reaction is given by:

• 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:
  • For a reaction that is second-order overall, and first-order in two reactants, A and B, our rate law 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

• Kinetics

  • Chemists refer to the sum n + m as the kinetic order of a reaction.
  • In a simple bimolecular reaction n & m would both be 1, and the reaction would be termed second order, supporting a mechanism in which a molecule of reactant A and one of B are incorporated in the transition state of the rate-determining step.
  • A bimolecular reaction in which two molecules of reactant A (and no B) are present in the transition state would be expected to give a kinetic equation in which n=2 and m=0 (also second order).
  • All the reactions save 7 display second order kinetics, reaction 7 is first order.
  • On the other hand, the kinetic order of a reaction is an experimentally derived number.

• 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.

• Rate-Determining Steps

  • Chemists often write chemical equations for reactions as a single step that shows only the net result of a reaction.
  • However, most chemical reactions occur over a series of elementary reactions.
  • It is the "how" of the reaction, whereas the overall balanced equation shows only the "what" of the reaction.
  • Further, the experimental rate law is second-order, suggesting that the reaction rate is determined by a step in which two NO2 molecules react, and therefore the CO molecule must enter at another, faster step.
  • If the second or a later step is rate-determining, determining the rate law is slightly more complicated.

• 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.

• Hess's Law

  • This law states that if a reaction takes place in several steps, then the standard reaction enthalpy for the overall reaction is equal to the sum of the standard enthalpies of the intermediate reaction steps, assuming each step takes place at the same temperature.
  • In order to get these intermediate reactions to add to our net overall reaction, we need to reverse the second step.
  • Restating the first equation and flipping the second equation, we have:
  • This lesson uses two methods to find the heat of reaction for a given reaction.
  • The net reaction here is A being converted into D, and the change in enthalpy for that reaction is ΔH.

• 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.
  • In order to determine the overall order of the reaction, we need to determine the value of the exponent m.
  • We can then run the reaction a second time, but with a different initial concentration of N2O5.
  • We can now set up a ratio of the first rate to the second rate:

• Overall Reaction Rate Laws

  • Rate laws for reactions are affected by the position of the rate-determining step in the overall reaction mechanism.
  • Consider the following reaction:
  • At equilibrium, the rate of the forward reaction will equal the rate of the reverse reaction.
  • We can now substitute this expression into the rate law for the second, rate-determining step.
  • This overall rate law, which is second-order in NO and first-order in O2, has been confirmed experimentally.