first-order reaction

(noun)

A reaction that depends on the concentration of only one reactant (a unimolecular reaction). Other reactants can be present, but each will be zero-order.

Examples of first-order reaction in the following topics:

  • First-Order Reactions

    • A first-order reaction depends on the concentration of one reactant, and the rate law is: $r=-\frac{dA}{dt}=k[A]$ .
    • 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.
    • Thus, the rate law for an elementary reaction that is first order with respect to a reactant A is given by:
    • The decomposition of hydrogen peroxide to form oxygen and hydrogen is a first-order reaction.

  • 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:
    • Keep in mind that these conclusions are only valid for first-order reactions.
    • Consider, for example, a first-order reaction that has a rate constant of 5.00 s-1.
    • 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.

  • 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.
    • It can be second-order in either A or B, or first-order in both A and B.
    • The second scenario, in which the reaction is first-order in both A and B, would yield the following rate law:
    • In order to determine the reaction order for A, we can set up our first equation as follows:

  • 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.
    • This is the integrated rate law for a zero-order reaction.
    • The half-life of a reaction describes the time needed for half of the reactant(s) to be depleted, which is the same as the half-life involved in nuclear decay, a first-order reaction.
    • For a zero-order reaction, the half-life is given by:

  • 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 reaction between nitric oxide and ozone, $NO(g) + O_3(g)\rightarrow NO_2(g) + O_2(g)$ , is first order in both nitric oxide and ozone.
    • A variety of reaction orders are observed.

  • 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.

  • 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.
    • 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.
    • It not only shows first order kinetics (only the alkyl halide concentration influences the rate), but the chiral 3º-alkyl bromide reactant undergoes substitution by the modest nucleophile water with extensive racemization.

  • Overall Reaction Rate Laws

    • As discussed in the previous concept, if the first step in a reaction mechanism is the slow, rate-determining step, then the overall rate law for the reaction is easy to write, and simply follows the stoichiometry of the initial step.
    • Since the first step is the rate-determining step, the overall reaction rate for this reaction is given by this step: $\text{rate}=k[H_2][ICl]$.
    • If the rate-determining step is not the first step in the reaction mechanism, the derivation of the rate law becomes slightly more complex.
    • To get around this, we need to go back and consider the first step, which involves an equilibrium between NO and N2O2.
    • This overall rate law, which is second-order in NO and first-order in O2, has been confirmed experimentally.

  • Substitution and Elimination

    • In describing these, it is useful to designate the halogen-bearing carbon as alpha and the carbon atom(s) adjacent to it as beta, as noted in the first four equations shown below.
    • In order to understand why some combinations of alkyl halides and nucleophiles give a substitution reaction, whereas other combinations give elimination, and still others give no observable reaction, we must investigate systematically the way in which changes in reaction variables perturb the course of the reaction.
    • unless a structural rearrangement occurs first.
    • The first four halides shown on the left below do not give elimination reactions on treatment with base, because they have no β-hydrogens.
    • We would find a common substitution product, C2H5–CN, in all cases, but the speed or rate of the reaction would increase in the order: Cl < Br < I.

  • 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.
    • 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.
    • Since the first step is the slowest, and the entire reaction must wait for it, it is the rate-determining step.
    • If the first step in a mechanism is rate-determining, it is easy to find the rate law for the overall expression from the mechanism.