Rate law

(noun)

An equation relating the rate of a chemical reaction to the concentrations or partial pressures of the reactants.

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

  • 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:

  • The Federal Funds Rate

    • The Federal Funds rate is the interest rate at which depository institutions actively trade balances held at the Federal Reserve.
    • The Federal Funds rate (or fed funds rate) is the interest rate at which depository institutions (primarily banks) actively trade balances held at the Federal Reserve.
    • If, by the end of the day, the bank's reserve ratio has dropped below the legally required minimum, it must add to its reserves in order to remain compliant with the law.
    • The Federal Funds rate is directly related to the interest rate paid by firms and individuals.
    • In fact, many mortgages and credit card interest rates are indexed to the Federal Funds rate - a homeowner might pay an adjustable interest rate that is set at the level of the Federal Funds rate plus four percent, for example.

  • Tax Rate

    • The tax rate is the amount of tax expressed as a percentage.
    • A statutory tax rate is the legally imposed rate.
    • An income tax could have multiple statutory rates for different income levels, whereas a sales tax may have a flat statutory rate.
    • In such cases, the average tax rate will be lower than the marginal tax rate.
    • In U.S. income tax law, the term is used in relation to determining whether a foreign income tax on specific types of income exceeds a certain percentage of U.S. tax that might apply on such income.