Chemical equations overall equation

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. 

A mechanism is a series of simple reaction steps which, when added together, account for the overall reaction. The rate law for the individual steps of the mechanism may be written by inspection of the mechanistic steps. The coefficients of the reactants in the chemical equation describing the step become the exponents of these concentrations in the rate law for... 

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

Write the overall chemical equation and calculate K for the complete ionization of oxalic acid, H2C2O4. 

Write a balanced chemical equation for the overall cell reaction represented as... 

Step 1 Select one of the reactants in the overall reaction and write down a chemical equation in which it also appears as a reactant. 

Each of the following five procedures results in the formation of a precipitate. For each reaction, write the chemical equations describing the formation of the precipitate the overall equation, the complete ionic equation, and the net ionic equation. Identify the spectator ions. 

If a chemical equation can be expressed as the sum of two or more chemical equations, the equilibrium constant for the overall reaction is the product of the equilibrium constants for the component reactions. For example, consider the three gas-phase reactions... 

A catalyst speeds up both the forward and the reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard Gibbs free energy of reaction depends only on the identities of the reactants and products and is independent of the rate of the reaction or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

STRATEGY First, we write the chemical equation for the equilibrium between the solid solute and the complex in solution as the sum of the equations for the solubility and complex formation equilibria. The equilibrium constant for the overall equilibrium is therefore the product of the equilibrium constants for the two processes. Then, we set up an equilibrium table and solve for the equilibrium concentrations of ions in solution. 

Balancing the chemical equation for a redox reaction by inspection can be a real challenge, especially for one taking place in aqueous solution, when water may participate and we must include HzO and either H+ or OH. In such cases, it is easier to simplify the equation by separating it into its reduction and oxidation half-reactions, balance the half-reactions separately, and then add them together to obtain the balanced equation for the overall reaction. When adding the equations for half-reactions, we match the number of electrons released by oxidation with the number used in reduction, because electrons are neither created nor destroyed in chemical reactions. The procedure is outlined in Toolbox 12.1 and illustrated in Examples 12.1 and 12.2. 

The chemical equation for a reduction half-reaction is added to the equation for an oxidation half-reaction to form the balanced chemical equation for the overall redox reaction. 

The free O atom in the second mechanism is a reaction intermediate, a species that plays a role in a reaction but does not appear in the chemical equation for the overall reaction it is produced in one step but is used up in a later step. The two equations for the elementary reactions add together to give the equation for the overall reaction. 

A note on good practice The chemical equations for elementary reaction steps are written without the state symbols. They differ from the overall chemical equation, which summarizes bulk behavior, because they show how individual atoms and molecules take part in the reaction,. We do not use stoichiometric coefficients for elementary reactions. Instead, to emphasize that we are depicting individual molecules, we write the formula as many times as required. 

To construct an overall rate law from a mechanism, write the rate law for each of the elementary reactions that have been proposed then combine them into an overall rate law. First, it is important to realize that the chemical equation for an elementary reaction is different from the balanced chemical equation for the overall reaction. The overall chemical equation gives the overall stoichiometry of the reaction, but tells us nothing about how the reaction occurs and so we must find the rate law experimentally. In contrast, an elementary step shows explicitly which particles and how many of each we propose come together in that step of the reaction. Because the elementary reaction shows how the reaction occurs, the rate of that step depends on the concentrations of those particles. Therefore, we can write the rate law for an elementary reaction (but not for the overall reaction) from its chemical equation, with each exponent in the rate law being the same as the number of particles of a given type participating in the reaction, as summarized in Table 13.3. 

Third, students understanding of the triplet relationship for a particular type of reaction may be further consolidated by carrying out additional similar reactions using different reactants (e.g., using several metal oxides to react with different dilute acids will help illustrate the similarities in the chemical reactions although different salts are produced). Once students become aware of the similarities in the chemical reactions, they would be more likely to meaningfully deduce the ionic equations for the chemical reactions instead of the common practice of cancelhng out the spectator ions from the overall balanced chemical equation. 

Nitric acid (HNO3), which is produced in the gas phase at elevated temperature and pressure, is an important chemical in the fertilizer indushy because it can be converted into ammonium nitrate. The following overall chemical equation summarizes the industrial reaction ... 

Both proposed mechanisms for NO2 decomposition contain chemical species produced in the first step and consumed in the second step. This is the defining characteristic of an intermediate. An intermediate is a chemical species produced In an early step of a mechanism and consumed in a later step. Intermediates never appear in the overall chemical equation. Notice that neither the O atoms of Mechanism I nor the NO3 molecules of Mechanism II appear In the balanced chemical equation for NO2 decomposition. 

The sum of the individual steps in the mechanism must give the overall balanced chemical equation. Sometimes a step may occur more than once in the mechanism. 

After oxidation and reduction half-reactions are balanced, they can be combined to give the balanced chemical equation for the overall redox process. Although electrons are reactants in reduction half-reactions and products in oxidation half-reactions, they must cancel in the overall redox equation. To accomplish this, multiply each half-reaction by an appropriate integer that makes the number of electrons in the reduction half-reaction equal to the number of electrons in the oxidation half-reaction. The entire half-reaction must be multiplied by the integer to maintain charge balance. Example illustrates this procedure. 

When half-reactions are combined, there is often a duplication of some chemical species, particularly H2 0 and H3 O or OH. The overall equation is cleaned up by combining species that appear twice on the same side. Also, when a species appears on both sides of the balanced equation, equal numbers of the species are subtracted from each side. 

The proportionality constant k, called the rate constant, has a constant value for a given reaction at a given temperature. The terms in square brackets are concentration terms (compare Chap. 14), and x and y are exponents which are often integral. The exponent x is called the order with respect to A, and y is called the order with respect to B. The sum x +y is called the overall order of the reaction. The values for x and y can be 0, 1, 2, 3 or 0.5, 1.5, or 2.5, but never more than 3. These values must be determined by experiment, and do not necessarily equal the values of a and b in the chemical equation. 

For a given system, one particular set of chemical equations may in fact correspond to a set of chemical reactions or steps in a kinetics scheme that does represent overall reaction (as opposed to a kinetics mechanism that represents details... 

If you add together the three equations above, you will get the overall equation A + 2B E + F. C and D are reaction intermediates, chemical species that are produced and consumed during the reaction, but that do not appear in the overall reaction. 

The third chemical equation, involving nitric oxide, represents a termolecular reaction. Therefore, the overall order of the reaction is expected to exceed that of the second-order reaction generally assumed in the pre-mixed gas burning model. The high exothermicity accompanying the reduction of NO to N2 is responsible for the appearance of the luminous flame in the combustion of a double-base propellant, and hence the flame disappears when insufScient heat is produced in this way, i. e., during fizz burning. 

The Nernst equation corresponding to that overall chemical equation is ... 

Within the Horiuti s approach, the physical meaning of the molecularity is clear. Horiuti introduced the concept of stoichiometric numbers (Horiuti numbers, v) Horiuti numbers are the numbers such that, after multiplying the chemical equation for every reaction step by the appropriate Horiuti number v, and subsequent adding, all reaction intermediates are cancelled. The equation obtained is the overall reaction. In the general case, the Horiuti numbers form a matrix. Each set of Horiuti numbers (i.e. matrix column) leading to elimination of intermediates corresponds to the specific reaction route. ... 

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