Dilution equation

Another method is a series of exhaust dilution equations based on Wilson and Lamb " and a series of earlier papers summarized in ASHRAE. This method is based on wind tunnel tests on simplified buildings and is intended to provide conservative (low dilution) results. Wilson and Lamb compared the model to actual field data collected at a university campus and found that the model did indeed predict dilutions similar to measured worst-case dilutions suitable for a screening model. However, many cases resulted in conservative Linderpredictions of dilutions. ... 

Dilution equations Mathematical equations that allow the determination of the decay rate of a pollutant in a space due to mechanical or natural ventilation. 

If a solution is prepared by diluting another solution whose concentration is precisely known (another possibility mentioned in Section 4.2), the following dilution equation maybe used to calculate molarity ... 

If a solution is to be prepared by diluting another solution, whether high precision and accuracy are important or not, the dilution equation, Equation (4.2), is again used ... 

Rearranging the dilution equation to calculate VB, we have the following ... 

The dilution equation (see solution to Example 6.3) may also be used to solve this problem. In that case, all variables are known except CB. 

The concentrations of the diluted solutions (measurement 2) are calculated by using the dilution equation. 

The concentrations of the other solutions (measurement 3) are calculated from the balanced chemical equation and the dilution equation. 

Using the molar mass, calculate the moles of all weighed samples. The moles of substances are converted to molarities by dividing by the volume (in liters) of the solution. Molarities may also be determined from pipet or buret readings using the dilution equation. (If a buret is used, one of the volumes is calculated from the difference between the initial and final readings.) The dilution equation may be needed to calculate the concentration of each reactant immediately after all the solutions are mixed. 

The concentrations of the solutions may be calculated by using the dilution equation. Concentrations may then be converted to moles by multiplying the concentration by the liters of solution. This procedure applies to buffer components or any reactant species. 

A direct result of the ability to measure isotope ratios with ICP-MS is the technique known as isotope dilution analysis. This is done by spiking the sample to be analysed with a known concentration of an enriched isotopic standard, and the isotope ratio is measured by mass spectrometry. The observed isotope ratio (RJ of the two chosen isotopes can then be used in the isotope dilution equation (Eqn. 5.7) to calculate the concentration of the element in the sample ... 

How do you know how much of the stock solution to use and how much of the pure solvent to use It depends on the concentration of the stock and on the concentration and volume of the final solution you want. You can answer these kinds of pressing questions by using the dilution equation, which relates concentration (C) and volume (V) between initial and final states ... 

You can use the dilution equation with any units of concentration, provided you use the Scime units throughout the calculation. Because molarity is such a common way to express concentration, the dilution equation is sometimes expressed in the following way, where Mj and refer to the initial and final molarity, respectively ... 

Add 67 mL 1.5 M NaOH stock solution to 433 mL water. Use the dilution equation, AfjKj =M2V2- The initial molarity, Mj, comes from the stock solution and is therefore 1.5 M. The final molarity is the one you want in your final solution, which is 0.200 M. The final volume is the one you want for your final solution, 500 mL, which is equivalent to 0.500 L. Using these known values, you can calculate the initial volume, Vf... 

The following formula works because the number of moles of a solute doesn t change when you dilute the solution. You can use the dilution equation to calculate an initial concentration or volume (Mj, Kj) or a final concentration or volume (M, as long as you know the other three values. Volumes don t have to be in particular units, as long as they re the same. See Chapter 12 for more information on dilutions. 

Complete retention of the enzyme in the reactor is essential for successful use of the EMR. In a CSTR Eq. (5.53) is valid as the wash-out equation (dilution equation), with R as degree of retention (0 < R < 1) this is completely analogous to the... 

The concentrations must first be changed from a mass basis to a volumetric basis, so that the dilution equation will apply. Concentrations include mass, but are not a direct statement of the mass. 

A general approach to 4,6-dicarbastannocanes 394-396 is based on the reaction of difunctional Grignard reagents with SnCLj, SnBr4 or PhSnCl3 in THF/toluene under sufficient dilution (equations 70a and 70b)530,821 826 827. 

Recall that NK and N are the numbers of atoms in the mixture due to sample and tracer, respectively. To convert them to weight requires use of the familiar Avo-gadro relationship and involves multiplying both sides of the equation by 1.0 twice, thereby introducing the atomic weights of sample and tracer (i.e., multiply each side by A JAS and A/At). Note that Avogadro s number appears on both sides of the equation and cancels out. As and Ar on the other hand, are not equal and do not cancel. The resulting equation is one form of the isotope dilution equation. 

For systems that are ideal or very dilute, Equation (3.99) then reverts back to Equation (3.96). Table 3.9 shows the distribution of succinic acid between water (Cj) and ether (C2). The ratio (partition coefficient) is relatively constant (==7.53, between 7.41 and 7.67). 

Solution of weak acid If HA but not A" is added to water, Ca- = 0, and since hydrogen ions are formed, [H" ] [OH ] for solutions that are not highly dilute. Equation (3-17) then becomes... 

Let us now consider a solution which is not perfect, but which is ideal when sufficiently dilute. Equation (21.3) will now only be valid if the mole fraction of solvent is sufficiently close to unity and the other mole fractions are small. By considering the behaviour as a ->1 we can, as before, write... 

The table on p 227 contains the values computed by Lewis and Linhart by means of equation (2) for a series of electrolytes over a considerable range of dilution Equation (1), and consequently equation (2), cannot be applied to solutions of greater concentration than o iN... 

As used here [rj] c denotes the increment in relative viscosity which results when a resin molecule is added to the solution at concentration c. Consequently, its value for a given resin can strongly depend on the concentration, and on the nature of the diluent. At infinite dilution Equation 1 gives Meff = M, and the intrinsic viscosity has its conventional meaning, i.e., the limiting value of (rj8 — r)o)/voc at infinite dilution. Here rj8 is the viscosity of a solution of concentration c (grams/dl) and 770 is the solvent viscosity. 

Many chemical reagents are supplied in solutions of much higher concentration than their use requires. The concentrated solutions need to be diluted with solvent to prepare solutions of lower concentration. Adding solvent increases the volume of the solution without changing the number of moles of solute, and the concentration of the solution decreases. For molar solutions, the volume of the solution in liters times the molarity of the solution equals the number of moles of solute. Because the number of moles of solute remains constant with dilution, a relationship in terms of volumes and molarities can be derived that is very useful for dilution problems. This is called the dilution equation. 

VConc and Mconc are the volume and molarity of the concentrated solution (the one of greater molarity) VdU and Mdi, are the volume and molarity of the diluted solution. If any three of the four terms are known, the fourth can be calculated. When using the dilution equation, volumes can be in liters or milliliters. If two volumes are used in the equation, the usual case, they both must be in the same unit. 

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