Interpreting Equations and the Mole

Next we recognize that the three substances denoted as (aq) in that equation will exist as dissociated ions rather than intact molecules. This leads us to the total ionic equation  

Finally, we can cancel the sodium and chloride ions because they appear in equal numbers on both sides of the equation. This leads us to the net ionic equation  

When sodium sulfate, Na2S04, reacts with lead nitrate, Pb(N03)2, the products are solid lead sulfate and aqueous sodium nitrate. Write the molecrdar, ionic, and net ionic equations for this reaction. 

Note that for a precipitation reaction, the net ionic equation does not have a net charge on either the reactant or product side. 

The chemical equations that we have been learning to write are symbolic descriptions of chemical reactions. But to interpret these equations, we must think about them from another point of view, in terms of the actual substances and processes they represent. As often happens in chemistry, we can do this at either the microscopic or the macroscopic level. The microscopic interpretation visualizes reactions between individual molecules, and that interpretation is the one we 

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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 ... 

Torkar et al. [702,706—708] identified nucleation as an autocatalytic process at the (hk0) planes of hexagonal platelets of NaN3. The decelera-tory reaction fitted the first-order equation [eqn. (15)]. Values of E tended to be irreproducible for the pure salt E was about 180 kJ mole 1 but this was reduced to about half by doping. This influence of an additive and the observed similarities in magnitudes of E for decomposition and for diffusion were interpreted as indicating that growth of nuclei was controlled by a diffusion process. 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

Determination of miscibility by additive properties such as average molecular area can give only qualitative interpretations of II/A data. For example, if the film components are ideally miscible, the average molecular area of the binary film at a fixed surface pressure will be the sum of each of the molecular areas of the individual components 1 and 2 in their pure films, and will follow equation (11), where N is the mole fraction. Unfortunately,... 

The DPs obtained in polymerisations catalysed by SnCl4-CCl3C02H, with [SnCl4]/ [CC13C02H] 3-4, [SnClJ = (23-36) x 10 3 mole/l, at -20°, -50°, and -78° in w-hexane, chloroform, and methylene dichloride were studied by Imanishi, Higashimura, and Okamura [79]. They interpreted the results in terms of the Mayo equation in the form,... 

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

To interpret a titration, we need the stoichiometric relation from the chemical equation for the reaction. This relation is used to write the mole ratio in the usual way. The only new step is to use the molarities of the solutions to convert between the moles of reactants and the volumes of... 

This equation can be interpreted as giving the temperature of the equilibrium system as a function of the mole fraction of the liquid phase when A/r,[T, P, x] is known as a function of the temperature and mole fraction. For values of Xj very close to unity, A/r, may be taken as zero, and (H[(g) — / (/)) may be considered to be independent of the temperature and equal to the molar change of enthalpy on evaporation of the pure liquid at T. Then we obtain on integration... 

A chemical equation represents the relationship of the reactants and products through a numerical relationship expressed by the coefficients associated with the participants. The coefficients can be interpreted as telling us the number of molecules or moles of materials involved but they also represent the volumes of those participants that are gases, assuming a constant temperature and pressure (T and P). An example of these relationships is as follows ... 

A property that is useful for interpreting intermolecular association in liquids is that known as the solubility parameter, S. When a liquid vaporizes, energy in the form of heat must be supplied to separate the molecules (to overcome the cohesion energy that holds the molecules together in the liquid state) and to perform the work done in expansion of the gas against atmospheric pressure. If the expansion work for one mole of gas is represented as RT (where R is 8.314 J mol-1 K-1) and the heat of vaporization is given by AHvap, it follows that the cohesion energy of a mole of the liquid, Ec, can be expressed by the equation... 

Figure 1.7 The in-plane lab angular distribution of KBr from K + Br2 [2]. The Newton diagram is given for the most probable beam velocities (both beams are unselected and their temperature is given), and the circles indicate the length of u Br vectors corresponding to various values of E (kcal/mole). The simple interpretation of these results is to equate the lab peak at 0 = 17° with a c.m. peak at 0 = 0° (direct forward scattering) and hence estimate 1.2 kcal/mole.

When accurate data can be obtained over a range of both concentrations and temperatures, it is possible from the Michaelis-Menton model to obtain data on the first-order rate constant kz and the constant Km = kz + kz)/ki and their apparent activation energies Ez and Unfortunately, most of the values quoted in the literature for the activation energies of enzyme-catalyzed reactions are derived from the use of overly simple first-order equations to describe the reaction. Consequently these values are a composite of Kmj kzy and the other constants in the Michaelis-Menton equation and cannot be used for interpretive purposes. Where the constants have been separated it is found that the values of Ez are low and of order of magnitude of 5 to 15 Kcal/mole. It is of interest to note that enzyme preparations from different biological sources, which may show different specific activity for a given reaction, have very nearly the same temperature coefficient for their specific rate constants. ... 

This view is supported by the statistical-mechanical interpretation of the adsorption isotherm at such low coverages that the differential heat of adsorption of hydrogen is nearly constant at 26 kcal./mole. From the agreement between the surface fraction calculated by means of equation (18) with n = 2, and the experimentally found value 0ob., for the hydrogen adsorption on nickel, Kwan et al. concluded that the surface of reduced nickel is homogeneous, or that every surface element is equally available for the chemisorption of hydrogen. 

From the remarks in 34g it can be seen that equation (36.3) may be interpreted as implying that for a saturated solution of a gas the fugacity of the solute is pibpo onal to its mole fraction in the solution. If the gas behaves ideally, and the solution is dilute, it follows that the molar concentration of the... 

Interpret balanced chemical equations to calculate the moles of reactants and products involved in each of the reactions... 

The equation now tells us that 16.0 grams of CH4 reacts with 64.0 grams of O2 to form 44.0 grams of CO2 and 36.0 grams of H2O. The Law of Conservation of Matter is satisfied. Chemical equations describe reaction ratios, that is, the mole ratios of reactants A balanced equation may be and products as well as the relative masses of reactants and products. interpreted on a mass basis. 

We interpret both chemical equations in the usual way, and solve the problem in two steps. They tell us that one mole of C produces one mole of CO and that four moles of CO is required to produce one mole of Ni(CO)4. 

Chemical equations can be interpreted on either a particulate level (atoms, molecules, ions) or a mole level (moles of reactants and products). Write word statements to describe the combustion of butane on a particulate level and a mole level. 

For many cases, for example, for lightly substituted ethanes, propenes, and aldehydes, sufficiently low temperatures are not attainable to slow the interconversion rate such that the NMR spectrum is appreciably broadened. In this case it is necessary to study the spectrum while changing external variables (as temperature, pressure, solvent) and attempt to interpret the variation in parameters in terms of a model. This kind of study is beset with great difficulties. The method of analysis usually adopted is as follows Assume a trial set of values of AH, AS for the equilibria involved. Then, calculate Xp, the mole fractions of species i at temperature /. The overdetermined set of linear equations... 

According to these equations, the Tm of a random copolymer is essentially independent of the structure of the comonomer and only depends on its mole fraction. However, some pairs of repeat units are at least partially co-crystallizable, allowing some of the repeat units originating from the comonomer to be incorporated into the crystallites which then become less perfect than those of the homopolymer. If some of the comonomer-based repeat units are incorporated into crystallites rather than being excluded, Tm still decreases with increasing m since repeat units originating from the comonomer do not pack as well as the repeat units of the base polymer and instead behave like crystal defect sites. However, the behavior is interpreted physically and described quantitatively in a very different manner [166], as summarized in the next paragraph. 

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