Balanced equations quantitative information

The balanced equation represents a chemical reaction. It not only identifies the reactants and the products, but also gives quantitative information on the ratios of all substances involved in the reaction (Section 8.1). 

A chemical equation provides a variety of qualitative and quantitative information essential for the calculation of the quantity of reactants reacted and products formed in a chemical process. The balanced chemical equation must have the same number of atoms of each type in the reactants and products. Thus the balanced equation for butane is... 

A chemical equation for a reaction must be balanced before useful quantitative information can be obtained about the reaction. Balancing an equation ensures that the same number of atoms of each element appear on both sides of the equation. Many chemical equations can be balanced by trial and error, although some will involve more trial than others. 

In this chapter we continue the quantitative development of thermodynamics by deriving the energy balance, the second of the three balance equations that will be used in the thermodynamic description of physical, chemical, and (later) biochemical processes. The mass and energy balance equations (and the third balance equation, to be developed in the following chapter), together with experimental data and information about the process, will then be used to relate the change in a system s properties to a change in its thermodynamic state. In this context, physics, fluid mechanics, thermodynamics, and other physical sciences are all similar, in that the tools of each are the same a set of balance equations, a collection of experimental observ ations (equation-of-state data in thermodynamics, viscosity data in fluid mechanics, etc.), and the initial and boundary conditions for each problem. The real distinction between these different subject areas is the class of problems, and in some cases the portion of a particular problem, that each deals with. 

A balanced equation contains a wealth of quantitative information relating individual chemical entities, amounts of chemical entities, and masses of substances. It is essential for all calculations involving amounts of reactants and products if you know the number of moles of one substance, the balanced equation tells you the number of moles of all the others in the reaction. 

In a balanced equation, the number of moles of one substance is stoichiometrically equivalent to the number of moles of any other substance. The term stoichiometrically equivalent means that a definite amount of one substance is formed from, produces, or reacts with a definite amount of the other. These quantitative relationships are expressed as stoichiometrically equivalent molar ratios that we use as conversion factors to calculate these amounts. Table 3.3 presents the quantitative information contained in the equation for the combustion of propane, a hydrocarbon fuel used in cooking and water heating ... 

QUANTITATIVE INFORMATION FROM BALANCED EQUATIONS We use the quantitative information inherent in chemical formulas and equations together with the mole concept to predict the amounts of substances consumed or produced in chemical reactions. 

SECTION 3.6 Quantitative Information from Balanced Equations... 

QUANTITATIVE INFORMATION FROM BALANCED EQUATIONS AND LIMITING REACTANTS (SECTIONS 3.6 AND 3.7) The mole concept can be used to calculate the relative quantities of reactants and products in chemical reactions. The coefficients in a balanced equation give the relative numbers of moles of the reactants and products. To calculate the number of grams of a product from the number of grams of a reactant, first convert grams of reactant to moles of reactant. Then use the coefficients in the balanced equation to convert the nmnber of moles of reactant to moles of product Finally, convert moles of product to grams of product... 

The mole concept allows us to use the quantitative information available in a balanced equation on a practical macroscopic level. Consider the following balanced equation ... 

Chemical equations are very useful in doing quantitative chemical work. The arrow in a balanced chemical equation is like an equal sign. And the chemical equation as a whole is similar to an algebraic equation in that it expresses an equality. Let s examine some of the quantitative information revealed by a chemical equation. 

Chemical equations also can provide quantitative information, which means that it is possible to tell how much of a reactant or a product is involved. To do that, we assume that each symbol and formula present in the equation represents exactly one atom, one molecule, or one formula unit of the element or compound. It is possible to then indicate two or more atoms, molecules, or formula units by placing coefficients in front of each of the symbols or formulas, such that the number of total atoms of each element is the same on both sides. Such an equation is said to be balanced. Using our water formation example, the following represents a balanced equation ... 

There are two general types of aerosol source apportionment methods dispersion models and receptor models. Receptor models are divided into microscopic methods and chemical methods. Chemical mass balance, principal component factor analysis, target transformation factor analysis, etc. are all based on the same mathematical model and simply represent different approaches to solution of the fundamental receptor model equation. All require conservation of mass, as well as source composition information for qualitative analysis and a mass balance for a quantitative analysis. Each interpretive approach to the receptor model yields unique information useful in establishing the credibility of a study s final results. Source apportionment sutdies using the receptor model should include interpretation of the chemical data set by both multivariate methods. 

The 1,3-cyclohexadiene could not be prepared with higher purity than 98% and hence the analysis based on the final products is less meaningful. The yield of 3- and 4-hydroxycyclohexenes show that only 31% (0.18 pmolJ /0.58 pmolJ ) of the OH radicals add to the double bonds. There is no information about the missing 44% (100% — 25%—31%). Von Sonntag and coworkers suggested that the yield of hydroxy cyclohexenes is not indicative of the OH addition to the double bonds due to non-quantitative reaction of the ally lie radical 1 (equation 10) with RSH. Since, in the case of 1,4-cyclohexadiene, they found complete material balance, they concluded that the alky lie radical formed in reaction reacts quantitatively with the thiolic compound. Thus, radical 2 formed in reaction (11) will react quantitatively with RSH. The inefficiency of the reduction of the allylic radical by the thiol is probably due to the weak ally lie C—H bond which leads to a six orders of magnitude lower rate constant for the RSH-I- allylic radical reaction compared with the RSH-I- alkyl radical reaction. If all the material imbalance is due to incomplete reduction of the allylic radical, its formation is the main path of reaction of OH with 1,3-cyclohexadiene. 

There are two distinct classes of analytic approximation that comprise the second and third approaches that were just mentioned. The first is based on the use of so-called macroscopic balances. In this approach, we do not attempt to obtain detailed information about the velocity and pressure fields everywhere in the domain, but only to obtain results that are consistent with the Navier Stokes equations in an overall (or macroscopic) sense. For example, we might seek results for the volumetric flow rates in and out of a flow system that are consistent with an overall mass or momentum conservation balance but not attempt to determine the detailed form of the velocity profiles. The macroscopic balance approach is described in detail in many undergraduate textbooks.2 It is often extremely useful for derivation of quantitative relationships among the average inflows, outflows, and forces (or rates of working) within a flow system but is something of a black-box approach that provides no detailed information on the velocity, pressure, and stress distributions within the flow domain. 

This word equation shows that calcium oxide and water are reacting to form calcium hydroxide. The reactants are on the left the product is on the right. Though word equations can be useful, they can only provide the minimum amount of information about a reaction. Chemists prefer formula equations because they make it possible to keep track of the atoms of each element as reactants become products. A properly written and balanced formula equation can be used quantitatively, allowing the calculation of amounts of reactants and products. (This is the topic of Chapter 8.) The formula equation for the reaction of calcium oxide with water is ... 

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