The Chemical Equation

Chemical reactions always involve change. Atoms, molecules, or ions rearrange to form different substances, sometimes in a spectacular manner. For example, the thermite reaction (shown in the chapter opening photo) is a reaction between aluminum metal and iron(III) oxide, which produces molten iron and aluminum oxide. The substances entering the reaction are called the reactants, and the substances formed are called the products. In our example, 

During reactions chemical bonds are broken and new bonds are formed. The reactants and products may be present as solids, liquids, gases, or in solution. 

In a chemical reaction atoms are neither created nor destroyed. All atoms present in the reactants must also be present in the products. 

A chemical equation is a shorthand expression for a chemical change or reaction. A chemical equation uses the chemical symbols and formulas of the reactants and products and other symbolic terms to represent a chemical reaction. The equations are written according to this general format  

Reactants are separated from products by an arrow (----- ) that indicates the di- 

As we saw in Section 3.6, we represent chemical reactions with chemical equations. For example, the reaction occurring in a natural-gas flame, such as the flame on a kitchen stove, is methane (CH4) reacting with oxygen (O2) to form carbon dioxide (CO2) and water (H2O). We represent this reaction with the equation  

The substances on the left side of the equation are the reactants, and the substances on the right side are the products. We often specify the state of each reactant or product in parentheses next to the formula. If we add states to our equation, it becomes  

TABLE 7.1 Abbreviations indicating the States of Reaotants and Products in Chemicai Equations 

In chemical equations, atoms cannot change from one type to another—hydrogen atoms cannot change into oxygen atoms, for example. Nor can atoms disappear (recall the law of conservation of mass from Section 3.7). 

The (g) indicates that these substances are gases in the reaction. Table 7.1 summarizes the common states of reactants and products and their symbols used in chemical reactions. 

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The chemical equation for combustion is then written asij/ J... 

The logarithm of the equilibrium constant, K,. for the chemical equation shown in Figure 3-8a for a substituted benzoic acid can be related to the logarithm of the... 

In order to obtain an improved yield of the desired product, an excess over the proportion required by the chemical equation of one (or more) of the reactants is often used. In a given preparation, the selection of the reagent to be employed in excess will depend upon a number of factors these include its relative cost and ease of removal after the reaction, and... 

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... 

The essential information implied by the chemical equation is the stoichiometry at the macroscopic level, ie, if a moles of M react, then b moles of B do also p moles of P are formed, etc. No inference should be made about behavior at the microscopic or atomic level, ie, there is no implication thatp molecules of P appear simultaneously. There may or may not be intermediates that appear and disappear in the course of the reaction. 

Results may be reported for any component. The functional form of the rate law and the exponents x,j, w,... are not affected by such an arbitrary choice. The rate constants, however, may change in numerical value. Similarly, the stoichiometric chemical equation may be written in alternative but equivalent forms. This also affects, at most, the numerical value of rate constants. Consequentiy, one must know the chemical equation assumed before using any rate constant. 

Theoretical Oxygen and Air for Combustion The amount of oxidant (oxygen or air) just sufficient to burn the carbon, hydrogen, and sulfur in a fuel to carbon dioxide, water vapor, and sulfur dioxide is the theoretical or stoichiometric oxygen or air requirement. The chemical equation for complete combustion of a fuel is... 

Although we have introduced net ionic equations to represent precipitation reactions, they have a much wider application. Indeed, we will use them for all kinds of reactions in water solution. In particular all of the chemical equations written throughout this chapter are net ionic equations. 

For an acid-base reaction, what is the reacting species, that is, the ion or molecule that appears in the chemical equation, in the following acids ... 

It is important to realize that the expressionfor K depends on the form of the chemical equation written to describe rite equilibrium system. To illustrate what this statement means, consider the N2O4-NO2 system ... 

Strategy First write the chemical equation for the equilibrium system. Then write the expression for K, leaving out pure liquids and solids. Remember that gases are represented by their partial pressures. 

SOLUTION From the chemical equation for the ionization of the weak acid, it should be clear that 1 mol of C9H704 is produced and 1 mol of HC9H7O4 is consumed for every mole of H+ produced. It follows that... 

Strategy First (1), write the chemical equation for the reaction that occurs when strong acid or base is added. Then (2), apply the principles of stoichiometry to find the numbers of moles of weak acid and weak base remaining after reaction. Finally (3), apply the relation [H+] = X mhb/mb to find [H+] and then the pH. 

The equilibrium constant expression for the dissolving of SrCr04 can be written following the rules in Chapters 12 and 13. In particular, the solid does not appear in the expression the concentration of each ion is raised to a power equal to its coefficient in the chemical equation. 

Strategy Start by writing the chemical equation for the solution process (solid on the left, ions in solution on the right). Then write the expression for fCsp) noting that—... 

Questions that test your knowledge of the specialized vocabulary that chemists use (e.g., write the names of formulas, write the chemical equation for a reaction that is described). 

Natural gas contains mainly the substance methane, with the formula CH4. The chemical equation for the burning of methane is... 

In this generalized equation, (75), we see that again the numerator is the product of the equilibrium concentrations of the substances formed, each raised to the power equal to the number of moles of that substance in the chemical equation. The denominator is again the product of the equilibrium concentrations of the reacting substances, each raised to a power equal to the number of moles of the substance in the chemical equation. The quotient of these two remains constant. The constant K is called the equilibrium constant. This generalization is one of the most useful in all of chemistry. From the equation for any chemical reaction one can immediately write an expression, in terms of the concentrations of reactants and products, that will be constant at any given temperature. If this constant is measured (by measuring all of the concentrations in a particular equilibrium solution), then it can be used in calculations for any other equilibrium solution at that same temperature. 

The term titrimetric analysis refers to quantitative chemical analysis carried out by determining the volume of a solution of accurately known concentration which is required to react quantitatively with a measured volume of a solution of the substance to be determined. The solution of accurately known strength is called the standard solution, see Section 10.3. The weight of the substance to be determined is calculated from the volume of the standard solution used and the chemical equation and relative molecular masses of the reacting compounds. 

Rule To find any proposed heat of reaction write down the chemical equations of the component reactions so that each symbol appears equally often on both sides of the sign of equality. If the heats of reaction (with proper signs) have been inserted, the unknown heat of reaction being denoted by x then the latter... 

If we compare (3) with the chemical equation of the reaction we arrive at the simple rule that the concentrations in the equilibrium state at a. given te i.perature and pressure must have... 

He also notes a situation where the rate constant for product buildup appears to be larger than that for reactant consumption. This signals intervention of an intermediate and is a special case of Eq. (4-25). The chemical equations are... 

Let us now examine sample sets of data. We shall consider two reactions, the formation of a biradical1 [Eq. (7-10)] and an electron transfer reaction between two ruthenium complexes [Eq. (7-11)], in which LN represent nitrogen-donor ligands specified in the original reference.2 The chemical equations are... 

We will first explore what salt effect is expected for k and k2, and then examine the general situation. It is convenient to proceed by defining the net activation process.15 This is the chemical equation for the hypothetical process in which the transition state is formed from the predominant forms of the reagents, and not from the reactive entities. For the two pathways implicit in Eq. (9-47), these are the net activation processes ... 

Write and balance the chemical equation for the combustion of hexane, GfcH14, to gaseous carbon dioxide gas and gaseous water. 

In a precipitation reaction, an insoluble solid product forms when we mix two electrolyte solutions. When an insoluble substance is formed in water, it immediately precipitates. In the chemical equation for a precipitation reaction, we use (aq) to indicate substances that are dissolved in water and (s) to indicate the solid that has precipitated ... 

Because the Na+ and N03 ions appear as both reactants and products, they play no direct role in the reaction. They are spectator ions, ions that are present while the reaction takes place but remain unchanged, like spectators at a sports event. Because spectator ions remain unchanged, we can simplify the chemical equation by canceling them on each side of the arrow in the ionic equation ... 

Canceling the spectator ions leaves the net ionic equation for the reaction, the chemical equation that displays the net change taking place in the reaction ... 

When concentrated aqueous solutions of barium nitrate, Ba(NO )2, and ammonium iodate, NH4I03, are mixed, insoluble barium iodate, Ba(I03)2, forms. The chemical equation for the precipitation reaction is... 

A complete ionic equation expresses a reaction in terms of the ions that are present in solution a net ionic equation is the chemical equation that remains after the cancellation of the spectator ions. 

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. 

Self-Test J.2A What acid and base solutions could you use to prepare rubidium nitrate Write the chemical equation for the neutralization. 

Self-Test J.2B Write the chemical equation for a neutralization reaction in which calcium phosphate is produced. 

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