Stoichiometric calculations dilution

We know the amounts of pure substances by converting their masses into number of moles. But for dissolved substances, we need the concentration— the number of moles per volume of solution—to find the volume that contains a given number of moles. In this section, we first discuss molarity, the most common way to express concentration (Chapter 13 covers others). Then, we see how to dilute a concentrated solution and how to use stoichiometric calculations for reactions in solution. 

L.ll A sample of barium hydroxide of mass 9.670 g was dissolved and diluted to the mark in a 250.0-mL volumetric flask. It was found that 11.56 mL of this solution was needed to reach the stoichiometric point in a titration of 25.0 ml. of a nitric acid solution, (a) Calculate the molarity of the HN03 solution. 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

However, in fuel-injection systems where the fuel is injected into a chamber containing air or an air stream, the fuel droplets or fuel jets bum as diffusion flames, even though the overall mixture ratio may be lean and the final temperature could correspond to this overall mixture ratio. The temperature of these diffusion flames is at the stoichiometric value during part of the burning time, even though the excess species will eventually dilute the products of the flame to reach the true equilibrium final temperature. Thus, in diffusion flames, more NO, forms than would be expected from a calculation of an equilibrium temperature based on the overall mixture ratio. The reduction reactions of NO are so slow that in most practical systems the amount of NO formed in diffusion flames is unaffected by the subsequent drop in temperature caused by dilution of the excess species. 

Figure 6.2 Transposed apparent conservation matrix (A ) for glycolysis at specified pH in dilute aqueous solution, calculated from the apparent stoichiometric number matrix in the previous figure. This conservation matrix shows the composition of the noncomponents (the last 10 rows) in terms of components (see Problem 6.3). [With permission from R. A. Alberty, J. Phys. Chem. B 104, 4807-4814 (2000). Copyright 2000 American Chemical Society.]...

The equilibrium composition for an enzyme-catalyzed reaction or a series of enzyme-catalyzed reactions can be calculated by using equcalcc or equcalccrx. The first of these programs requires a conservation matrix. The second requires a stoichiometric matrix. The second program is recommended, especially when water is involved as a reactant, because the convention that when dilute aqueous solutions are considered, the activity of water is taken to be unity, means that a second Legendre transform is necessary. 

For the titration of an acid HA in en (pATsH = 15.3) with overall dissociation constant of 10 with sodium aminoethoxide, calculate the pH at the following percentages of the stoichiometric amount of reagent added 0, 50, 90, 100, 110. Take the initial concentration of acid to be 0.01 M, neglect dilution, and assume that the salt has an overall dissociation constant of 10 and that pATj for sodium aminoethoxide is 5.84. 

Note that the charge imbalances calculated from Equation (5.1) are stoichiometric charge imbalances, which are based on the assumption that all measured elemental concentrations appear as charged ionic species, for example that all aluminum in the solution is Al3+ all the calcium is Ca2+ and so on. This stoichiometric charge-balance calculation tends to work well as a screen for checking the quality of dilute groundwater and surface water analyses, which are largely uncomplexed (see Hem, 1985). 

The reaction is moderate exothermic with AHr = -114 kJ/mol. A measure of exothermicity is the adiabatic temperature rise. Table 8.1 gives some values calculated for an inlet temperature of 400 K and 1 atm. The adiabatic temperature rise for the stoichiometric mixture is considerable (441.6 K), but the dilution with benzene in the ratio 5 1 makes drop it to 144.6. If diluted ethylene feedstock is considered, the... 

Having validated the mechanism on ammonia-oxygen flames, the yield of NO from nitrogen doped CH4-air flames was examined. Both NH3 and NO doping were investigated. Only post-flame NO concentrations were measured. These are compared with calculations of the full kinetics and with adiabatic equilibrium calculations. The calculated profiles indicate the complexity of the NO dynamics in these flames. The temperature and major species profiles in the undoped flames had been studied in earlier work( ). Three near stoichiometric methane-air flames having initial equivalence ratios(0) of 0.8, 1.0 and 1.2 are diluted with less than 5 volume percents of NH3 or NO. In this section NO concentration is expressed both as a mole fraction and as a fraction of the total nitrogen concentration ... 

Calculating Densities/Concentrations in Stoichiometric Compounds or Dilute Solutions... 

When calculating the mass density, molar concentration, or molar volume of a specific individual species that is present in combination with other species (e.g., in a compound or solution), further work is needed. If the material s composition can be expressed in terms of a single stoichiometric compound or formula unit, the approach is still fairly straightforward— it just requires application of the compound stoichiometry. Similarly, dilute solutions, where the solute species is present in very low concentrations relative to the host solvent, can be handled in a relatively straightforward manner by assuming that the host material s density is not affected by the presence of the solute species. 

For aqueous electrolytes the ionic association become important when b is higher than 5, a value typical of a 2 2 electrolyte at room temperature or a 1 1 electrolyte above 300 °C. Thus, the extrapolation of the apparent partial volume of these electrolytes at infinite dilution to obtain the standard partial molar volume is uncertain, because the free ions concentration depends on the stoichiometric electrolyte concentration. For a 2 2 electrolyte, as MgS04, at 25 °C the apparent partial molar volume approach the DHLL value at concentrations bellow 0.01 mol kg (Franks and Smith, 1967) and, at least the density could be measured with a precision of 1 ppm, V° for MgS04 can not be obtained by extrapolation. In this case one can calculate the standard partial molar volume from the known values of standard partial volume of 1 2 and 1 1 electrolytes by using the additivity rule (Lo Surdo et al, 1982) ... 

CO oxidation measurements were carried out in the SFR at varying CO/ O2 ratios. Ar-diluted gas mixtures were fed to the reactor with a flow rate of 15.5 SLPM (standard liter per minute at 293 K, 1 atm.). The calculated flow velocity and working pressure were 51 cm/s and 500 mbar, respectively. The reactor inlet temperature was 313 K. The reaction was studied at steady-state conditions (Table 2.2). At low temperatures, oxygen-rich conditions were selected to avoid external mass transport hmitations and examine the kinetic effects (Case 1). However, for moderate- and high-temperature regimes (Case 2 and Case 3), the reactions were examined under stoichiometric conditions. 

According to thermod)mamic calculations, for a stoichiometric mixture, a 30% dilution of methane with nitrogen leads to a reduction in the NO concentration by 20%, whereas a 60% dilution, to a decrease by more than 50%. These results are well consistent with those obtained in experiments with General Electric gas turbines operating on natural-gas diluted with nitrogen. The increase in the molar concentration of N2 to 48% resulted in an almost twofold decrease in the emission of NOx [299]. 

Fig. 5.25 Normalised estimates of first-order contributions to the overall variance of predicted butane mole fraction at 750 K calculated using first-order local sensitivities (grey) and the global HDMR method (black). Both are derived from a model describing the oxidation of n-butane in a jet stirred reactor (residence time of 6 s, atmospheric pressure, stoichiometric mixtures containing 4 % (mol) -butane diluted in helium). EXGAS notation is used. Adapted with permission from Cord et al. (2012). Copyright (2012) American Chemical Society...

Figure 2.22 illustrates the effect of a CO2 dUuent on the laminar flame velocity in a H2+air mixture. Figure 2.22a shows a comparison between the measured and calculated laminar flame velocity values in three lean mixtures containing 14%, 10% and 8% H2 before the dilution ((/> = 0.39, 0.26 and 0.21 respectively). The relative reduction of the velocity Su/Su , where denotes the flame velocity in the undiluted mixture, is presented in Fig. 2.22b. To reduce the velocity by half in the stoichiometric mixture (0 = 1) 20% of the CO2 diluent is required, whereas in the lean mixture...

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