Concentrations of Reactants The Rate-Law Expression

The physical states of reacting substances are important in determining their reactivities. 

A puddle of liquid gasoline can burn smoothly, but gasoline vapors can burn explosively. Two immiscible liquids may react slowly at their interface, but if they are mixed to provide better contact, the reaction speeds up. White phosphorus and red phosphorus are different solid forms (allotropes) of elemental phosphorus. White phosphorus ignites when exposed to oxygen in the air. By contrast, red phosphorus can be kept in open containers for long periods of time without noticeable reaction. 5 

Samples of dry solid potassium sulfate, K2SO4, and dry sohd barium nitrate, Ba(N03)2, can be mixed with no appreciable reaction occurring for several years. But if aqueous solutions of the two are mixed, a reaction occurs rapidly, forming a white precipitate of barium sulfate. 

Two allotropes of phosphorus. White phosphorus (atrore) ignites and hums rapidly when exposed to oxygen in the air, 0 it is stored under water. Red phosphoras below) reacts wtth air much more slowly, so tt can he stored in contact wtth air. 

Powdered iron burns very rapidly when heated in a flame. Iron oxide is formed. 

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The coefficients of the balanced overall equation bear no necessary relationship to the exponents to which the concentrations are raised in the rate law expression. The exponents are determined experimentally and describe how the concentrations of each reactant affect the reaction rate. The exponents are related to the ratedetermining (slow) step in a sequence of mainly unimolecular and bimolecular reactions called the mechanism of the reaction. It is the mechanism which lays out exactly the order in which bonds are broken and made as the reactants are transformed into the products of the reaction. 

The negative sign arises because there is a loss of reactant. The value of n is often 1, but a value other than unity arises when one molecule of the reactant produces other than one molecule of the product. Rates are usually expressed in moles per liter per second, which we shall designate M s , although dm mol s is also a popular abbreviation. The rate law expresses the rate of a reaction in terms of the concentrations of the reactants and of any other species in solution, including the products, that may affect the rate. ... 

As the concentrations of reactants change at constant temperature, the rate of reaction changes. We write the rate-law expression (often called simply the rate law) for a reaction to describe how its rate depends on concentrations this rate law is experimentally deduced for each reaction from a study of how its rate varies with concentration. 

Order of a reactant The power to which the reactant s concentration is raised to the rate-law expression. 

Rate-law expression (also called rate law) An equation that relates the rate of a reaction to the concentrations of the reactants and the specific rate constant rate = [A] [B]J. The exponents of reactant concentrations do not necessarily match the coefficients in the overall balanced chemical equation. The rate-law expression must be determined from experimental data. 

The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to appropriate powers. The rate constant k for a given reaction changes only with temperature. 

The centerpiece of any kinetic study is the rate law (or rate equation) for the reaction in question. The rate law expresses the rate as a function of reactant concentrations, product concentrations, and temperature. Any hypothesis we make about how the reaction occurs on the molecular level must conform to the rate law because it is based on experimental fact. 

Thinking it Through The slow step is the reaction of NOj with Fj to form NO2F and F. The rate equation is therefore expected to contain both NO2 and F2, with the concentration of each raised to the first power. That is choice (C). Choice (D) contains a product (here, a fluorine atom) of the reaction rather than only reactants. Choice (B) is a commonly chosen wrong answer, since it is derived from the stoichiometry of the overall reaction. Choice (A) is the equilibrium constant expression rather than the rate-law expression. ... 

If we know the values of k, x, and y, as well as the concentrations of A and B, we can use the rate law to calculate the rate of the reactiom Like k, x and y must be determined experimentally. The sum of the powers to which all reactant concentrations appearing in the rate law are raised is called the overall reaction order. In the rate law expression shown, the overall reaction order is given hy x + y. For the reaction involving F2 and CIO2, the overall order is 1 + 1, or 2. We say that the reaction is first order in F2 and first order in CIO2, or second order overall. Note that reaction order is always determined by reactant concentrations and never by product concentrations. 

The rate law expresses the relationship of the rate of a reaction to the rate constant and the concentrations of the reactants raised to appropriate powers. The rate constant k for a given reaction changes only with temperature. Reaction order is the power to which the concentration of a given reactant is raised in the rate law. Overall reaction order is the sum of the powers to which reactant concentrations are raised in the rate law. The rate law and the reaction order cannot be determined from the stoichiometry of the overall equation for a reaction they must be determined by experiment. For a zero-order reaction, the reaction rate is equal to the rate constant. 

As the concentration of the reactant species A changes with time, its concentration fits the above equation (as long as the reaction follows second-order kinetics with respect to the species A). Note that for this equation, amounts must be expressed in concentration units if the rate law is expressed in concentration units-unlike equation 20.14 for first-order reactions, the amounts are not arranged in a ratio whose value remained invariant and independent of unit. We can rearrange equation 20.20 into a form that mimics a straight-line equation ... 

As reactants are used up, their concentrations decrease, the number of collisions decreases, and the reaction rate slows. A rate law is a mathematical expression that relates reaction rate to concentrations of reactants. The reaction order mathematically defines the extent to which reaction rate depends on the concentrations of reactants. Because most chemical reactions involve two or more reactants, the rate law often includes the concentrations of all reactants. 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

The goal of a kinetic study is to establish the quantitative relationship between the concentration of reactants and catalysts and the rate of the reaction. Typically, such a study involves rate measurements at enough different concentrations of each reactant so that the kinetic order with respect to each reactant can be assessed. A complete investigation allows the reaction to be described by a rate law, which is an algebraic expression containing one or more rate constants as well as the concentrations of all reactants that are involved in the rate-determining step and steps prior to the rate-determining step. Each concentration has an exponent, which is the order of the reaction with respect to that component. The overall kinetic order of the reaction is the sum of all the exponents in the... 

The simplest form of a physicochemical reaction takes place when one species simply changes to another. This can be written in a general way as A B. The rate of such a reaction is defined as the amount of reactant (the reacting species, A, in this case) or equivalently the product (B) that changes per unit time. The key feature here is the form of the rate law, i.e., the expression for the dependence of the reaction rate on the concentrations of the reactants. For a first-order reaction... 

The effect of concentration on the rate of a particular chemical reaction can be summarized in an algebraic expression known as a rate law. A rate law links the rate of a reaction with the concentrations of the reactants through a rate constant (jt ). In addition, as we show later in this chapter, the rate law may contain concentrations of chemical species that are not part of the balanced overall reaction. 

To see if the proposed mechanism predicts the correct rate law, we start with the rate-determining step. The second step in this mechanism is rate-determining, so the overall rate of the reaction is governed by the rate of this step Rate — 2[Br ][H2 ] This rate law describes the rate behavior predicted by the proposed mechanism accurately, but the law cannot be tested against experiments because it contains the concentration of Br atoms, which are intermediates in the reaction. As mentioned earlier, an intermediate has a short lifetime and is hard to detect, so it is difficult to make accurate measurements of its concentration. Furthermore, it is not possible to adjust the experimental conditions in a way that changes the concentration of an intermediate by a known amount. Therefore, if this proposed rate law is to be tested against experimental behavior, the concentration of the intermediate must be expressed in terms of the concentrations of reactants and products. 

Both relationships include a constant and both involve concentrations raised to exponential powers. However, a rate law and an equilibrium expression describe fundamentally different aspects of a chemical reaction. A rate law describes how the rate of a reaction changes with concentration. As we describe in this chapter, an equilibrium expression describes the concentrations of reactants and products when the net rate of the reaction is zero. 

The rate law of the oxidation by Fe(III) is dependent on the ratio of the concentrations of the reactants. When peroxide is in excess and when the acidity is sufficient to suppress hydrolysis of Fe(IlI) the rate expression... 

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