Chemical equations calculations using

Calculate the reaction quotient, Q, for the cell reaction, given the measured values of the cell emf. Balance the chemical equations by using the smallest whole-number coefficients. 

FIGURE 34.1 Correlation of the chemical potential, calculated using (a) Equation 34.20 (b) Equation 34.29 with experimental values. Data are taken from Table 34.1. 

Stoichiometry is the calculation of the amount of one substance in a chemical equation by using another one. 

A balanced chemical equation was used in the calculation. The number of significant digits is correct. The units are also correct. 

A reaction between gaseous sulfur dioxide and oxygen gas to produce gaseous sulfur trioxide takes place at 600°C. At that temperature, the concentration of SO2 is found to be 1.50 mol/L, the concentration of O2 is 1.25 mol/L, and the concentration of SO3 is 3.50 mol/L. Using the balanced chemical equation, calculate the equilibrium constant for this system. 

Equation (19) gives the equilibrium constant from 298 - 2500 K for reaction (18). Chemical equilibrium calculations using this data and the solar elemental... 

In this chapter we define the mole, the fimdamental unit of measure of chemical arithmetic, learn to write and balance chemical equations, and use these tools to perform calculations of chemical quantities. 

In a subsequent study183 a linear correlation (equation 89) has been established by Dorie and Gouesnard between experimental chemical shifts <515Nexp and < 15N chemical shifts calculated using equation 90. 

For each of the following unbalanced chemical equations, calculate how many moles of each product would be produced by the complete conversion of 0.125 mol of the reactant indicated in boldface. State clearly the mole ratio used for fhe conversion. 

I Mole ratios derived from the balanced chemical equation are used in stoichiometric calculations. 

A chemical equation represents the reaction. That chemical equation is used to calculate how much of each element is needed and how much of each element will be produced. And that chemical equation needs to obey the Law of Conservation of Mass. 

However, when carboxylic acids are present in a mixture, fugacity coefficients must be calculated using the chemical theory. Chemical theory leads to a fugacity coefficient dependent on true equilibrium concentrations, as shown by Equation (3-13). ... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

The van der Waals p., p. isothenns, calculated using equation (A2.5.3), are shown in figure A2.5.8. It is innnediately obvious that these are much more nearly antisynnnettic around the critical point than are the conespondingp, F isothenns in figure A2.5.6 (of course, this is mainly due to the finite range of p from 0 to 3). The synnnetry is not exact, however, as a carefiil examination of the figure will show. This choice of variables also satisfies the equal-area condition for coexistent phases here the horizontal tie-line makes the chemical potentials equal and the equal-area constniction makes the pressures equal. 

The following equation is used to calculate tlie chemical reaction equilibrium constant K at a temperature T. 

Chemical intakes are calculated using equations that include variables for e.xposure concentration, contact rate, e.xposure frequency, e.xposure duration, body weight, and exposure averaging lime. The values of some of these variables depend on site conditions and the characteristics of The potentially c.xposcd population. 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

The emphasis is on writing and balancing chemical equations for these reactions. All of these reactions involve ions in solution. The corresponding equations are given a special name net ionic equations. They can be used to do stoichiometric calculations similar to those discussed in Chapter 3. 

Strategy Start by writing a balanced chemical equation for the reaction involved. Then use Equation 17.1 in combination with Table 17.1 to calculate the difference in entropy between products and reactants. For (b) note that you are asked to calculate AS° for one gram of methane. 

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. 

Stoichiometric calculations of the amount of product formed in a reaction are based on an ideal view of the world. They suppose, for instance, that all the reactants react exactly as described in the chemical equation. In practice, that might not be so. Some of the starting materials may be consumed in a competing reaction, a reaction taking place at the same time as the one in which we are interested and using some of the same reactants. Another possibility is that the reaction might not be complete at the time we make our measurements. A third possibility—of major importance in chemistry and covered in several chapters of this text—is that many reactions do not go to completion. They appear to stop once a certain proportion of the reactants has been consumed. 

STRATEGY Begin by writing the chemical equation for the complete oxidation of octane to carbon dioxide and water. Then calculate the theoretical yield (in grams) of CO, by using the procedure in Toolbox L.l. To avoid rounding errors, do all the numerical work at the end of the calculation. To obtain the percentage yield, divide the actual I mass produced by the theoretical mass of product and multiply by 100%. 

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 following plot shows how the partial pressures of reactant and products vary with time for the decomposition of compound A into compounds B and C. All three compounds are gases. Use this plot to do the following (a) Write a balanced chemical equation for the reaction, (h) Calculate the equilibrium constant for the reaction, (c) Calculate the value of Kc for the reaction at 25°C. 

STRATEGY Because NH4+ is a weak acid and Cl- is neutral, we expect pH < 7. We treat the solution as that of a weak acid, using an equilibrium table as in Toolbox 10.1 to calculate the composition and hence the pH. First, write the chemical equation for proton transfer to water and the expression for Ca. Obtain the value of Ka from Kh for the conjugate base by using K, = KxJKh (Eq. 11a). The initial concentration of the acidic cation is equal to the concentration of the cation that the salt would produce if the salt were fully dissociated and the cation retained all its acidic protons. The initial concentrations of its conjugate base and H30+ are assumed to be zero. 

Thus, the conjugated anion represents an intermediate for the halide transfer from a complex anion to a Lewis acid. The quantum chemical reaction energies for the halide transfer AE(r can be calculated using the values of the interaction energies from Table 18 in the equation AEtr = AE(I) — AE(II). The results are presented in Table 20 and allow the following generalization ... 

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... 

These four equations are perfectly adequate for equilibrium calculations although they are nonsense with respect to mechanism. Table 7.2 has the data needed to calculate the four equilibrium constants at the standard state of 298.15 K and 1 bar. Table 7.1 has the necessary data to correct for temperature. The composition at equilibrium can be found using the reaction coordinate method or the method of false transients. The four chemical equations are not unique since various members of the set can be combined algebraically without reducing the dimensionality, M=4. Various equivalent sets can be derived, but none can even approximate a plausible mechanism since one of the starting materials, oxygen, has been assumed to be absent at equilibrium. Thermodynamics provides the destination but not the route. 

Since the quantum chemical calculations used to parameterize equations 6 and 7 are relatively crude semiempirical methods, these equations should not be used to prove or disprove differences in mechanisms of decomposition within a family of initiators. The assumption made in the present study has been that the mechanism of decomposition of initiators does not change within a particular family of initiators (reactions 1-4). It is generally accepted that trow5-symmetric bisalkyl diazenes (1) decompose entirely by a concerted, synchronous mechanism and that trans-phenyl, alkyl diazenes (2) decompose by a stepwise mechanism, with an intermediate phenyldiazenyl radical (37). For R groups with equal or larger pi-... 

During an experiment, a chemist may measure physical quantities such as mass, volume, and temperature. Usually the chemist seeks information that is related to the measured quantities but must be found by doing calculations. In later chapters we develop and use equations that relate measured physical quantities to important chemical properties. Calculations are an essential part of all of chemistry therefore, they play important roles in much of general chemistry. The physical property of density illustrates how to apply an equation to calculations. 

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