Chemical equations stoichiometric coefficients

Rates determined by monitoring different species in a chemical reaction need not have the same value. The rate R in equation A5.2 and the rate R in equation A5.3 will have the same value only if the stoichiometric coefficients of A and C in reaction A5.1 are the same. In general, the relationship between the rates R and R is... 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

About 95% of Escherichia coli is C, H, O and N. The chemical formula for cell composition and the stoichiometric coefficients in (9.2.1) depend on media composition and the environment surrounding die cell.2,4 All die major elements in die above equation have to be balanced. Then die stoichiometric coefficients are identified by solving simultaneously the system of equations ... 

In each step, we may need to reverse the equation or multiply it by a factor. Recall from Eq. 16 that, if wc want to reverse a chemical equation, wc have to change the sign of the reaction enthalpy. If we multiply the stoichiometric coefficients by a factor, we must multiply the reaction enthalpy by the same factor. 

Now there are four H atoms, two Na atoms, and two O atoms on each side, and the equation conforms to the law of conservation of mass. The number multiplying an entire chemical formula in a chemical equation (for example, the 2 multiplying H20) is called the stoichiometric coefficient of the substance. A coefficient of 1 (as for H2) is not written explicitly. 

In other words, the stoichiometric coefficients multiplying the chemical formulas in any balanced chemical equation tell us the relative number of moles of each substance that reacts or is produced in the reaction. 

A balanced chemical equation symbolizes both the qualitative and the quantitative changes that take place in a chemical reaction. The stoichiometric coefficients tell us the relative numbers of moles of reactants and products taking part in the reaction. 

A chemical equation expresses a chemical reaction in terms of chemical formulas the stoichiometric coefficients are chosen to show that atoms are neither created nor destroyed in the reaction. 

Sometimes we need to know how much product to expect from a reaction, or how much reactant we need to make a desired amount of product. The quantitative aspect of chemical reactions is the part of chemistry called reaction stoichiometry. The key to reaction stoichiometry is the balanced chemical equation. Recall from Section H that a stoichiometric coefficient in a chemical equation tells us the relative amount (number of moles) of a substance that reacts or is produced. Thus, the stoichiometric coefficients in... 

Step 2 Use the mole ratio derived from the stoichiometric coefficients in the balanced chemical equation to convert from the amount of one substance (A) into the amount in moles of the other substance (B). For aA - / B or aA + hY> — cC, use... 

Because the stoichiometric coefficient of C6H6 in the chemical equation is 2, calculate AH for 2 mol CbHb from AH = q X (2 mol)/ . Because the reaction is exothermic, AH is negative. 

STRATEGY We write the chemical equation for the formation of HI(g) and calculate the standard Gibbs free energy of reaction from AG° = AH° — TAS°. It is best to write the equation with a stoichiometric coefficient of 1 for the compound of interest, because then AG° = AGf°. The standard enthalpy of formation is found in Appendix 2A. The standard reaction entropy is found as shown in Example 7.9, by using the data from Table 7.3 or Appendix 2A. 

The equilibrium composition of a reaction mixture is described by the equilibrium constant, which is equal to the activities of the products (raised to powers equal to their stoichiometric coefficients in the balanced chemical equation for the reaction) divided by the activities of the reactants (raised to powers equal to their stoichiometric coefficients). 

We can summarize these remarks as follows for chemical equations written with the smallest whole-number stoichiometric coefficients (Fig. 9.5) ... 

The powers to which the activities are raised in the expression for an equilibrium constant must match the stoichiometric coefficients in the chemical equation, which is normally written with the smallest whole numbers for coefficients. Therefore, if we change the stoichiometric coefficients in a chemical equation (for instance, by... 

The value of E is the same, regardless of how we write the equation, but the value of AG° depends on the stoichiometric coefficients in the chemical equation. When we multiply all the coefficients by 2 the value of AG° doubles. However, multiplying all the coefficients by 2 also doubles the value of n, and so E° = AG°/nF remains the same. That is, although the reaction Gibbs free energ) changes when the chemical equation is multiplied by a factor, E° does not change ... 

Division by the stoichiometric coefficients takes care of the stoichiometric relations between the reactants and products. There is no need to specify the species when reporting the unique average reaction rate, because the value of the rate is the same for each species. However, the unique average rate does depend on the coefficients used in the balanced equation, and so the chemical equation should be specified when reporting the unique rate. 

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. 

Gibbs free energy of reaction The difference in molar Gibbs free energies of the products and reactants, weighted by the stoichiometric coefficients in the chemical equation. 

Stem-Gerlach experiment The demonstration of the quantization of electron spin by passing a beam of atoms through a magnetic field, stick structure See line structure. stock solution A solution stored in concentrated form, stoichiometric coefficients The numbers multiplying chemical formulas in a chemical equation. 

Examples 1,1, and 2 in H2 + Br2 - 2 HBr. stoichiometric point The stage in a titration when exactly the right volume of solution needed to complete the reaction has been added, stoichiometric proportions Reactants in the same proportions as their coefficients in the chemical equation. Example equal amounts of H2 and Br2 in the formation of HBr. 

The drawings produced by students allow researchers to better conceptualize how some students interpreted a balanced chemical equations. This is especially useful in assessing their understanding of stoichiometric coefficients and the meaning of subscripts of chemical formulae. 

What is needed now is some means for calculating e. To do this, it is useful to consider some component, H, which is formed only by Reaction I, which does not appear in the feed, and which has a stoichiometric coefficient of v/// = 1 for Reaction I and stoichiometric coefficients of zero for all other reactions. It is always possible to write the chemical equation for Reaction I so that a real product has a stoichiometric coefficient of +1. For example, the decomposition of ozone, 2O3 3O2, can be rewritten as 2/3O3 —> O2. However, you may prefer to maintain integer coefficients. Also, it is necessary that H not occur in the feed, that there is a unique H for each reaction, and that H participates only in the reaction that forms it. Think of H as a kind of chemical neutrino formed by the particular reaction. Since H participates only in Reaction I and does not occur in the feed, Equation (2.40) gives... 

The summations in these equations include only those chemical species that directly participate in the reaction, and the weighting is by stoichiometric coefficient. Compare this with Equation (7.20) where the summation includes... 

The stoichiometric coefficients in a chemical equation are the smallest integers that give a balanced equation. 

The stoichiometric coefficients in a balanced chemical equation must be chosen so that the atoms of each element are conserved. Many chemical equations can be balanced by inspection. Balancing by inspection means changing stoichiometric coefficients until the number of atoms of each element is the same on each side of the arrow. Usually, we can tell what changes need to be made by looking closely at the reaction and matching the numbers of atoms of each element on both sides of the equation. Consider the following example. 

To summarize, the amounts of different reagents that participate in a chemical reaction are related through the stoichiometric coefficients in the balanced chemical equation. To convert from moles of one reagent to moles of any other reagent, multiply by the stoichiometric ratio that leads to proper cancellation of units ... 

Our analysis of the reaction of nitrogen dioxide molecules is not unique. The same type of path can be visualized for any chemical reaction, as Figure 6-20 shows. The reaction enthalpy for any chemical reaction can be found from the standard enthalpies of formation for all the reactants and products. Multiply each standard enthalpy of formation by the appropriate stoichiometric coefficient, add the values for the products, add the values for the reactants, and subtract the sum for reactants from the sum for products. Equation summarizes this procedure ... 

Entropy changes are important in every process, but chemists are particularly interested in the effects of entropy on chemical reactions. If a reaction occurs under standard conditions, its entropy change can be calculated from absolute entropies using the same reasoning used to calculate reaction enthalpies from standard enthalpies of formation. The products of the reaction have molar entropies, and so do the reactants. The total entropy of the products is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients in the balanced chemical equation. The total entropy of the reactants is a similar sum for the reactants. Equation... 

The rates for different species participating in a chemical reaction are related by the stoichiometric coefficients of the balanced chemical equation. Equation provides the exact relationship. 

Remember that the number of electrons transferred is not explicitly stated in a net redox equation. This means that any overall redox reaction must be broken down into its balanced half-reactions to determine n, the ratio between the number of electrons transferred and the stoichiometric coefficients for the chemical reagents. 

The coefficients of any balanced redox equation describe the stoichiometric ratios between chemical species, just as for other balanced chemical equations. Additionally, in redox reactions we can relate moles of chemical change to moles of electrons. Because electrons always cancel in a balanced redox equation, however, we need to look at half-reactions to determine the stoichiometric coefficients for the electrons. A balanced half-reaction provides the stoichiometric coefficients needed to compute the number of moles of electrons transferred for every mole of reagent. 

After this iteration the desired model precision was achieved. Using the estimates of stoichiometric coefficients in chemical reaction equations, the following system is obtained ... 

Most chemical reactions do not progress completely from reactants to products. Instead, the net reaction stops in the forward direction when equilibrium is established. Analysis of the contents of the reaction vessel would show a constant concentration of monomers and polymer once equilibrium is reached. This situation is actually a dynamic equilibrium, where the monomers are forming polymers at the same rate as the polymers depolymerize to monomer. Therefore, at equilibrium, the net concentrations of any one species remains constant. The amount of monomer converted into polymer will be defined by the equilibrium constant, K. This constant is the ratio of the concentration of the products to the reactants, with each concentration raised to the stoichiometric coefficients in the balanced equation. For Eq. 3.5 ... 

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