Molarity and Equation Stoichiometry

Martin s next bold suggestion was to do a large scale test in the ocean itself. Due to the difficulty of controlling conditions in the real world, ocean tests on the scale he suggested had never been done. 

Because the decrease in CO2 in the water was less than expected and because the increase in phytoplankton growth requires a constant addition 

The general steps we have been following in setting up equation stoichiometry calculations can be summarized as follows. 

Measurable property 1 moles 1 moles 2 Measurable property 2 

For pure liquids and solids, as we have seen, the most convenient measurable property is mass. It is very easy to measure the mass of a pure solid or liquid, and we can convert between that and the number of particles it represents using the molar mass as a conversion factor. 

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In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

Here x is the conversion of SiH4. combines the effect of the molar expansion in the deposition process as well as the change in the volumetric flow and the dispersion coefficient, D, with temperature. At low pressures and small Re in LPCVD reactors the dispersion occurs mainly by molecular diffusion, therefore, we have used (D/D0) = (T/T0)l 65. e is the expansion coefficient and the stoichiometry implies that e = (xi)q, the entrance mole fraction of SiH4. The expansion coefficient, e is introduced as originally described by Levenspiel (33) The two reaction terms refer to the deposition on the reactor wall and wafer carrier and that on the wafers, respectively. The remaining quantities in these equations and the following ones are defined at the end of the paper. The boundary conditions are equivalent to the well known Danckwerts1 boundary conditions for fixed bed reactor models. 

Molar mass conversions and molarity conversions can be combined to solve equation stoichiometry problems, as we see in Example 10.7. 

Because the ideal gas equation applies to all ideal gases, the molar volume at STP applies to all gases that exhibit the characteristics of the ideal gas model. In equation stoichiometry, the molar volume at STP is used in much the way we use molar mass. Molar mass converts between moles and the measurable property of mass molar volume at STP converts between moles and the measurable property of volume of gas. Note that while every substance has a different molar mass, all ideal gases have the same molar volume at STP. Example 13.5 provides a demonstration. 

Between this chapter and Chapter 10, we have now seen three different ways to convert between a measurable property and moles in equation stoichiometry problems. The different paths are summarized in Figure 13.10 in the sample study sheet on the next two pages. For pure liquids and solids, we can convert between mass and moles, using the molar mass as a conversion factor. For gases, we can convert between volume of gas and moles using the methods described above. For solutions, molarity provides a conversion factor that enables us to convert between moles of solute and volume of solution. Equation stoichiometry problems can contain any combination of two of these conversions, such as we see in Example 13.8. 

Convert between volume of gas and moles of gas in an equation stoichiometry problem using either the molar volume at STP, the ideal gas equation, or i as a conversion factor. 

Recall that the coefficients in a balanced equation give the relative number of moles of reactants and products, aexs (Section 3.6) To use this information, we must convert the masses of substances involved in a reaction into moles. When dealing with pure substances, as we did in Chapter 3, we use molar mass to convert between grams and moles of the substances. This conversion is not valid when working with a solution because both solute and solvent contribute to its mass. However, if we know the solute concentration, we can use molarity and volume to determine the number of moles (moles solute = M X F). T Figure 4.17 summarizes this approach to using stoichiometry for the reaction between a pure substance and a solution. 

A common laboratory technique, called titration, requires understanding solution stoichiometry. A solution-phase reaction is carried out under controlled conditions so that the amount of one reactant can be determined with high precision. A carefully measured quantity of one reactant is placed in a beaker or flask. A dye called an indicator can be added to the solution. The second reactant is added in a controlled fashion, typically by using a burette (Figure 4.6). When the reaction is complete, the indicator changes color. When the indicator first changes color, we have a stoichiometric mixture of reactants. We know the number of moles of the first reactant (or the molarity and volume) and the volume of the second reactant used. So as long as we know the balanced equation for the reaction, we can find the unknown concentration of the second reactant. 

A titration problem is an applied stoichiometry problem, so we will need a balanced chemical equation. We know the molarity and volume for the NaOH solution, so we can find the number of moles reacting. The mole ratio from the balanced equation lets us calculate moles of H2SO4 firom moles of NaOH. Because we know the volume of the original H2SO4 solution, we can find its molarity. 

The numerator of Equation 11.1 and Equation 11.2 includes the molar stoichiometry (Vsioic) of the metal atoms in the surface metal oxide (MO ) and its molecular weight (MJ. These equations differ in calculation of the denominator Equation 11.1 uses the surface area of the calcined, pure support oxide (no surface oxide), and Equation 11.2 uses the surface area of the calcined composite catalyst. Unless the support oxide shows negligible sintering and the support oxide content is low, ps rfi and psuj(2 are numerically different. 

The following conditions should be noted for Equation (13) (a) molecular formulae are used to aid the subsequent material and energy balances (b) any target protein (e.g. IFN-y) is combined with the biomass which is expressed by a C-molar formula as customarily utilised for microbial biomass (see the Chapter by Duboc et al. in this Volume and also Reference [20]) and (c) the stoichiometric coefficient of the cell mass is set at unity and so the enthalpy change of the growth reaction now is based on unit number of C-molar biomass [105], It has been shown from experimentation (see Figure 27) that there is a one-to-one monotonic relationship between the metabolic flux (see Equation (7)) and the stoichiometry of the growth equation (Equation (13)). This can be expressed by ... 

Such problems as this one involve many steps or conversions. Try to break the problem into simpler ones involving fewer steps or conversions. It may also help to remember that solving a stoichiometry problem involves three steps (1) converting to moles, (2) converting between moles, and (3) converting from moles. Use molarities and molar masses to carry out volume-mole conversions and gram-mole conversions, respectively, and stoichiometric factors to carry out mole-mole conversions. The stoichiometric factors are constructed from a balanced chemical equation. 

As can be seen from equation 8.14, we may improve a method s sensitivity in two ways. The most obvious way is to increase the ratio of the precipitate s molar mass to that of the analyte. In other words, it is desirable to form a precipitate with as large a formula weight as possible. A less obvious way to improve the calibration sensitivity is indicated by the term of 1/2 in equation 8.14, which accounts for the stoichiometry between the analyte and precipitate. Sensitivity also may be improved by forming precipitates containing fewer units of the analyte. 

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 ... 

Since the molar concentration of monomer is substantially greater than the molar concentration of polymer, Equations 14, 18 and 19 predict a balanced stoichiometry during the cure. The summation terms represent the invariant number of reactive sites on a continuously decreasing number of polymeric species. 

Stoichiometry Calculate reactant and product masses using the balanced equation and molar... 

In general, concentrations of the products are divided by the concentrations of the reactants. In the case of gas-phase reactions, partial pressures cire used instead of molar concentrations. Multiple product or reactant concentrations are multiplied. Each concentration is raised to an exponent equal to its stoichiometric coefficient in the balanced reaction equation. (See Chapters 8 and 9 for details on balanced equations and stoichiometry.)... 

Introduction and Orientation, Matter and Energy, Elements and Atoms, Compounds, The Nomenclature of Compounds, Moles and Molar Masses, Determination of Chemical Formulas, Mixtures and Solutions, Chemical Equations, Aqueous Solutions and Precipitation, Acids and Bases, Redox Reactions, Reaction Stoichiometry, Limiting Reactants... 

In applying a rate equation to a situation where the volume of a given reaction mixture (i.e. the density) remains constant throughout the reaction, the treatment is very much simplified if the equation is expressed in terms of a variable X, which is defined as the number of moles of a particular reactant transformed per unit volume of reaction mixture (e.g. Cao Ca) at any instant of time t. The quantity X is very similar to a molar concentration and has the same units. By simple stoichiometry, the moles of the other reactants transformed and products generated can also be expressed in terms of x, and the rate of the reaction can be expressed as the rate of increase in X with time. Thus, by definition,... 

We need to calculate the amount of methyl tert-bu tyl ether that could theoretically be produced from 26.3 g of isobutylene and compare that theoretical amount to the actual amount (32.8 g). As always, stoichiometry problems begin by calculating the molar masses of reactants and products. Coefficients of the balanced equation then tell mole ratios, and molar masses act as conversion factors between moles and masses. 

From the system of equations (3.27), it follows that there may be a few variants of occurrence and further growth of the ApBq,ArBs mdA Bn layers, depending on the values of the chemical constants k0, the stoichiometry of the compounds and the ratio of their molar volumes. 

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