Stoichiometric relationship

A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of determining the amount of oxalic acid, H2C2O4, in rhubarb. One method for this analysis uses the following reaction in which we oxidize oxalic acid to CO2. 

The balanced chemical reaction provides the stoichiometric relationship between the moles of Fe used and the moles of oxalic acid in the sample being analyzed— specifically, one mole of oxalic acid reacts with two moles of Fe. As shown in Example 2.6, the balanced chemical reaction can be used to determine the amount of oxalic acid in a sample, provided that information about the number of moles of Fe is known. 

Stoichiometric relationships and calculations are important in many quantitative analyses. The stoichiometry between the reactants and products of a chemical reaction is given by the coefficients of a balanced chemical reaction. When it is inconvenient to balance reactions, conservation principles can be used to establish the stoichiometric relationships. 

Using conservation principles, write stoichiometric relationships for the following... 

In an indirect analysis the precipitate does not contain the analyte, but is the product of a reaction involving the analyte. Despite the additional complexity, a stoichiometric relationship between the analyte and the precipitate can be written by applying the conservation principles discussed in Section 2C. 

Since ah the sulfur in H2SO4 comes from sulfanilamide, we use a conservation of mass on sulfur to establish the following stoichiometric relationship. 

Locate the equivalence point for each of the titration curves in problem 1. What is the stoichiometric relationship between the moles of acid and moles of base at each of these equivalence points ... 

X 10 , 7.8 X 10 , and 6.8 X 10 k The titration curve shown here is for H4Y with NaOH. What is the stoichiometric relationship between H4Y and NaOH at the equivalence point marked with the arrow ... 

Solvation—Desolvation Equilibrium. From the observation of migration of plasticizer from plasticized polymers it is clear that plasticizer molecules, or at least some of them, are not bound permanently to the polymer as iu an internally plasticized resia, but rather an exchange—equiHbrium mechanism is present. This implies that there is no stoichiometric relationship between polymer and plasticizer levels, although some quasi-stoichiometric relationships appear to exist (3,4). This idea is extended later ia the discussion of specific iateractions. 

The stoichiometric relationship between chlorine dioxide added and color removed during bleaching is nonlinear, but it is independent of temperature, pH, and pulp concentration under conditions normally used. Models used to explain the kinetics and stoichiometry show a strong dependence on chromophore concentration that probably results from differences in the reaction rates of the various chromophores present in the pulps (80). 

The first demonstration of catalytic conversion of synthesis gas to hydrocarbons was accompHshed ia 1902 usiag a nickel catalyst (42). The fundamental research and process development on the catalytic reduction of carbon monoxide was carried out by Fischer, Tropsch, and Pichler (43). Whereas the chemistry of the Fischer-Tropsch synthesis is complex, generalized stoichiometric relationships are often used to represent the fundamental aspects ... 

All six carbons of glucose are liberated as CO2, and a total of four molecules of ATP are formed thus far in substrate-level phosphorylations. The 12 reduced coenzymes produced up to this point can eventually produce a maximum of 34 molecules of ATP in the electron transport and oxidative phosphorylation pathways. A stoichiometric relationship for these subsequent processes is 1... 

A common feature of both these methods is that the quantity of treatment chemical can be calculated from stoichiometric relationships in the reactions involved. This is not so with conventional inhibitor treatments. With these the concentration of inhibitive chemicals can only be determined on the basis of experimental laboratory studies, service trials and overall practical experience. 

Although these results establish with reasonable certainty the reaction sequences leading from the sugar to the dye, no stoichiometric relationships have been shown to exist between the amounts of sugar employed and the quantities of dyes formed. Both tests are, therefore, still empirical,... 

Perhaps the first stoichiometric relationship to be discovered was the law of combining volumes, proposed by Gay-Lussac in 1808 The volume ratio of any two gases in a reaction at constant temperature and pressure is the same as the reacting nude ratio. 

Where yield coefficients are constant for a particular cell cultivation system, knowledge of how one variable changes can be used to determine changes in the other. Such stoichiometric relationships can be useful in monitoring fermentations. For example, some product concentrations, such as CO2 leaving an aerobic bioreactor, are often the most convenient to measure in practice and give information on substrate consumption rates, biomass formation rates and product formation rates. 

The stoichiometric relationship for 100% sodium sulfite with oxygen (02) is 7.88 1.0 in practice, 10 1 is commonly used... 

The stoichiometric relationship for hydrazine with oxygen is 1 1, but it is always added at between two and four times theoretical to ensure that the reaction proceeds to completion. Even so, it may be some time after startup (often one to two weeks) before hydrazine appears in the BW as a reserve. This probably is due to the hydrazine reducing all existing ferric oxide in the system first. During this time, the color of the oxide debris and surface oxides change from reddish brown to black (passivation). 

From the stoichiometric relationship 2[P2]a> + [Pi] = [A]0, it follows that the final ratio of products is given by... 

Again, a negative root was rejected. The simultaneous solution also produces the stoichiometric relationship... 

The general stoichiometric relationships for a single reaction in a batch reactor are... 

Analytical Solution A stoichiometric relationship can be used to eliminate A>b-Combine the two ODEs to obtain... 

Again, the seven-step approach to equilibrium problems will lead to the correct result. This is a more complicated example than Example, so a concentration table as part of Step 5 helps keep track of the stoichiometric relationships. 

This is an electrochemical stoichiometry problem, in which an amount of a chemical substance is consumed as electrical current flows. We use the seven-step strategy in summary form. The question asks how long the battery can continue to supply current. Current flows as long as there is lead(IV) oxide present to accept electrons, and the batteiy dies when all the lead(IV) oxide is consumed. We need to have a balanced half-reaction to provide the stoichiometric relationship between moles of electrons and moles of Pb02. 

Galvanic cells use redox reactions to generate electrical current. Electrical current can also drive redox reactions, and the same stoichiometric relationships apply to such processes, as we describe in Section 19-1. 

If the initiation and termination steps are excluded because the chain is long, the sum of the propagation reactions gives the stoichiometric relationship (A). 

Detailed Investigation of this B L conversion suggests that about 2Bi + 2L occur for each L - CO adsorbed. The stoichiometric relationship Induced by L - CO adsorption causing 2 i 2L Is shown In Figure 7, where Isotoplcally labeled CO has been employed In separate experiments as or as L. After a small correction Is made for the experimentally determined difference In extinction coefficient for 3co(ads) compared to 12co(ads), It may be seen that the stoichiometry 2B + L -> 3L Is closely verified. 

Figure 7. The stoichiometric relationship induced by L-CO adsorption causing 2B- —2L.

In the presence of TMP derivatives, on the other hand, a controlling influence on the course of the reaction appears only two products are formed, and these in amounts bearing a stoichiometric relationship to the amount of DBK decomposed (reaction (5)). This surprising effect of HALS derivatives has not previously been reported. Therefore the question arises is this... 

From a thermodynamic point of view, the heteropolymer globule in hand represents a subsystem which is composed of a macromolecule involving lu l2 units Mi, M2 and molecules of monomers Mi, M2 whose numbers are Mi,M2. Among these variables and volume fractions a in the framework of the simplest Flory-Huggins lattice model there are obvious stoichiometric relationships... 

Diphenylcarbazone and diphenylcarbazide have been widely used for the spectrophotometric determination of chromium [ 190]. Crm reacts with diphenylcarbazone whereas CrVI reacts (probably via a redox reaction combined with complexation) with diphenylcarbazide [ 191 ]. Although speciation would seem a likely prospect with such reactions, commercial diphenylcarbazone is a complex mixture of several components, including diphenylcarbazide, diphenylcarbazone, phenylsemicarbazide, and diphenylcarbadiazone, with no stoichiometric relationship between the diphenylcarbazone and diphenylcarbazide [192]. As a consequence, use of diphenylcarbazone to chelate Crm selectively also results in the sequestration of some CrVI. Total chromium can be determined with diphenylcarbazone following reduction of all chromium to Crm. 

The result is rather tedious to obtain, but the method can be the same as that in Example 3-5 use of the stoichiometric relationship and the introduction of , followed by integration by partial fractions and reversion to cA and cB to give... 

The representation of the biological conservation of substrate to cell mass by an overall chemical reaction. The stoichiometric relationships are then used to calculate various rates such as cell mass concentration [83]. 

Background This experiment uses the concept of continuous variation to determine mass and mole relationships. Continuous variation keeps the total volume of two reactants constant, but varies the ratios in which they combine. The optimum ratio would be the one in which the maximum amount of both reactants of known concentration are consumed and the maximum amount of product(s) is produced. Since the reaction is exothermic, and heat is therefore a product, the ratio of the two reactants that produces the greatest amount of heat is a function of the actual stoichiometric relationship. Other products that could be used to determine actual molar relationships might include color intensity, mass of precipitate formed, amount of gas evolved, and so on. 

Relationship between MnC>2 colloid surface area concentration and ccc of Ca2+ a stoichiometric relationship exists between ccc and the surface area concentration in case of Na+, however, this interaction is weaker, so that primarily compaction of the diffuse part of the double layer causes destabilization. 

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