Limiting quantities mass calculations with

For problems in which the quantities of two (or more) reactants are given, we must determine if one of the reactants is present in a quantity less than, equal to, or greater than that required to react with all the other reactants. Determine which reactant is in limiting quantity and use that quantity to calculate the quantities of the substances that will be used up and produced. A table of reactant and product quantities is useful. If masses are... 

The quantity of antibody which can be attached to the wall of a well of a microtitre plate is limited by the surface of the well and the fraction of antibodies present in the immunoglobulin preparation. Assuming a maximum adsorption of 1.5 ng/mm and an average molecular weight of 150000 (IgG), the maximum attainable concentration of IgG attached to the wall is about 10 M using monoclonal antibodies, but for affmity-purified antibodies, hyperimmune antisera and postinfection sera, typically 3, 10, and 100 times less would be present, respectively. The fraction of antigen bound by the solid-phase antibody can be calculated with the law of mass action (eq. 3) ... 

Plan To identify the hmiting reactant, we can calculate the number of moles of each reactant and compare their ratio with the ratio of coefficients in the balanced equation. We then use the quantity of the limiting reactant to calculate the mass of water that forms. 

We use the given quantity of H2 (the limiting reactant) to calculate the quantity of water formed. We could begin this calculation with the given H2 mass, 150 g, but we can save a step by starting with the moles of H2,75 mol, we just calculated ... 

A sample containing 2.00 mol of graphite reacts completely with a limited quantity of oxygen at 25°C and 1.0 atm pressure, producing 481 kJ of heat and a mixture of CO and CO2. Calculate the masses of CO and CO2 produced. 

SO2 uptake was measured at total system pressures in the range of 20 to 50 Torr, consisting of 17.5 Torr H2O vapor with the balance either helium or argon. The observed mass accommodation coefficients, 74, are plotted in Figure 2 as a function of the inverse of the calculated diffusion coefficient of SO2 in each H20-He and l O-Ar mixture. The diffusion coefficients are calculated as a sum of the diffusion coefficients of SO in each component. The diffusion coefficients for SO in He and in Ar are estimated from the diffusion coefficient of SO2 in H 0 (Dg p = 0.124 (101) by multiplying this value by the quantity (mH-/mH Q)V2, anti (mAr/m 2o) 2> respectively. The curves in Figure 2 are plots ofEquation 7 with three assumed values for 7 0.08,0.11 and 0.14. The best fit to the experimental values of is provided by 7 = 0.11. Since gas uptake could be further limited by liquid phase phenomena as discussed in the following section, 7502 = 0.11 is a lower limit to the true mass accommodation coefficient for SO2 on water. 

The primary experimentally determined data in Tables 1.2 and 1.3 are the isotopic ratios and volume fractions in air and the total mass of air these are tabulated with their reported uncertainties. Quantities derived from these are shown without error limits in Tables 1.2 and 1.3 for reasons cited earlier, they are stated to more significant figures than are justified by the precision of the primary data from which they are calculated. 

The above calculation is quite tedious and gets complicated by the fact that the properties which ultimately control the magnitude of these fourteen unknown quantities further depend on the physical and chemical parameters of the system such as reaction rate constants, initial size distribution of the feed, bed temperature, elutriation constants, heat and mass transfer coefficients, particle growth factors for char and limestone particles, flow rates of solid and gaseous reactants. In a complete analysis of a fluidized bed combustor with sulfur absorption by limestone, the influence of all the above parameters must be evaluated to enable us to optimize the system. In the present report we have limited the scope of our calculations by considering only the initial size of the limestone particles and the reaction rate constant for the sulfation reaction. 

There is another method that some of our students find works well They calculate the mass of product expected based on each reactant. The limiting reactant is that reactant that gives the smallest quantity of product. For example, refer to the SiCL reaction with Mg on page 158. To confirm that SiCL is the limiting reactant, calculate the quantity of elemental silicon that can be formed starting with (a) 1.32 mol of SiCL and unlimited magnesium or (b) with 9.26 mol of Mg and unlimited SiCL. 

A scenario referred to as a sub-Chandrasekhar-mass supernova envisions a C-O WD capped with a helium layer accreted by a companion, and which explodes as the result of a hydrodynamical burning before having reached the Chandrasekhar limit. This type of explosions may exhibit properties which do not match easily the observed properties of typical SNIa events. It cannot be excluded, however, that they are responsible for some special types of events, depending in particular on the He accretion rate and on the CO-sub-Chandrasekhar WD (SCWD) initial mass (e.g. [85]). Unidimensional simulations of He cataclysmics characterized by suitably selected values of these quantities reach the conclusion that the accreted He-rich layer can detonate. Most commonly, this explosion is predicted to be accompanied with the C-detonation of the CO-SC WD. In some specific cases, however, this explosive burning might not develop, so that a remnant would be left following the He detonation. Multidimensional calculations cast doubt on the nature, and even occurrence, of the C-detonation in CO-SC WD (e.g. [86]). 

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