Factors for Converting Volumes to

Stoichiometric problems involving gas volumes can be solved by the general mole-ratio method outlined in Chapter 9. The factors 1 mol/22.4 L and 22.4 L/1 mol are used for converting volume to moles and moles to volume, respectively. (See Figure 12.16.) These conversion factors are used under the assumption that the gases are at STP and that they behave as ideal gases. In actual practice, gases are measured at other than STP conditions, and the volumes are converted to STP for stoichiometric calculations. 

The permeation coefficient, K, has been modified slightly to include some other terms such as the density of the slip and a factor for converting the volume of water removed to the volume of clay particles deposited. The important point, however, is that Eq. (7.20) can now be integrated to give a relationship between the compact layer thickness and time ... 

For a gas under conditions other than STP, the ideal gas equation can be used to convert volume to moles, or the universal gas constant, R, can be used as a conversion factor. 

The advantage of molarity as a concentration unit is that the amount of solute is related to the volume of solution. Rather than having to weigh out a specified mass of substance, you can instead measure out a definite volume of solution of the substance, which is usually easier. As the following example illustrates, molarity can be used as a factor for converting from moles of solute to liters of solution, and vice versa. 

An alternative approach is to use equation (4.5). The known factors include the volume of solution to be prepared, (Vf = 250.0 mL) and the concentrations of the final (0.0100 M) and initial (0.250 M) solutions. We must solve for the initial volume, V. Note that although in deriving equation (4.5) volumes were expressed in liters, in applying the equation any volume unit can be used as long as we use the same unit for both Vj and Vf (milliliters in the present case). The term needed to convert volumes to liters would appear on both sides of the equation and cancel out. 

Figure 13-5 is the box model of the remote marine sulfur cycle that results from these assumptions. Many different data sets are displayed (and compared) as follows. Each box shows a measured concentration and an estimated residence time for a particular species. Fluxes adjoining a box are calculated from these two pieces of information using the simple formula, S-M/x. The flux of DMS out of the ocean surface and of nss-SOl back to the ocean surface are also quantities estimated from measurements. These are converted from surface to volume fluxes (i.e., from /ig S/(m h) to ng S/(m h)) by assuming the effective scale height of the atmosphere is 2.5 km (which corresponds to a reasonable thickness of the marine planetary boundary layer, within which most precipitation and sulfur cycling should take place). Finally, other data are used to estimate the factors for partitioning oxidized DMS between the MSA and SO2 boxes, for SO2 between dry deposition and oxidation to sulfate, and for nss-SO4 between wet and dry deposition. 

The relative bond enthalpies from the photoacoustic calorimetry studies can be placed on an absolute scale by assuming that the value for D//(Et3Si—H) is similar to D/f(Me3Si—H). In Table 2.2 we have converted the D/frei values to absolute T>H values (third column). On the basis of thermodynamic data, an approximate value of D//(Me3SiSiMc2—H) = 378 kJ/mol can be calculated that it is identical to that in Table 2.2 [1]. A recent advancement of photoacoustic calorimetry provides the solvent correction factor for a particular solvent and allows the revision of bond dissociation enthalpies and conversion to an absolute scale, by taking into consideration reaction volume effects and heat of solvation [8]. In the last colunm of Table 2.2 these values are reported and it is gratifying to see the similarities of the two sets of data. 

If you look at Figure 9-2, you can see that it isn t possible to convert directly between the mass of one substance and the mass of another substance. You must convert to moles and then use the mole-mole conversion factor before converting to the mass of a new substance. The same can be said for conversions from the particles or volume of one substance to that of another substance. The mole is always the intermediary you use for the conversion. 

Again, conversion factors are the way to approach these kinds of problems. Each problem features a certain volume of solution that contains a certain solute at a certain concentration. To begin each problem, convert your volume into liters — part (c) has already done this for you. Then rearrange the molarity formula to solve for moles ... 

Increase of pressure has also the effect of bringing the gaseous molecules closer and closer to one another (due to decrease in volume). This is an additional helpful factor in converting a gas into liquid. Thus, increase of pressure and decrease of temperature both tend to cause liquefaction of gases. For instance, sulphur dioxide can be liquefied at -8 C if the pressure is 1 atm. But it can be liquefied even at a higher temperature of 20 C if the pressure is increased to 3.24 atm. 

When data on airborne levels are available only in terms of mass/volume (e.g., mg/m ), it is not possible to accurately convert these to units of PCM fibers/mL, because the ratio between mass and fiber number depends on fiber type and size distribution and because of the measuring technique employed. For the purposes of making rough calculations when a more accurate conversion factor is not available, it has been assumed that a concentration of 1 mg/m in air is equal to 33 PCM fimL (EPA 1986a). 

Table 2-3 is provided to help with buoyancy calculations. Corrections for buoyancy with respect to stainless steel or brass mass (the density difference between the two is small enough to be neglected) and for the volume change of water and of glass containers have been incorporated into these data. Multiplication by the appropriate factor from Table 2-3 converts the mass of water at temperature T to (1) the corresponding volume at that temperature or (2) the volume at 20°C. 

In early days of Phase I, the predominant feedstock for ammonia synthesis was coke. Synthesis gas was either produced at atmospheric pressure in water-gas shift units or prepared by purification of coke oven gas. In these early plants, the process effluents from the ammonia converter were cooled without recovery of heat. Due to the lack of technology regarding the attainable size of the converter pressure shell, the physical dimensions of the converter were limiting factors for the achievable production capacity. Therefore, a particular emphasis was placed on maximization of the production capacity for a given volume [139]. During World War II, several plants were built in the United States, based on natural gas feedstock. Since then, natural... 

The BET surface area measurement is attributed to Brunauer et al. (1941). It is usually conducted with nitrogen at its normal boiling point (-195.8°C) and measured up to atmospheric pressure (p/Pvap = ) Essentially, the monolayer capacity (or loading) is estimated using the BET isotherm (see Table 14.3 and Section 14.3.2), and the numerical value is converted to a surface area using a factor that is believed to represent the coverage area per molecule for nitrogen. From the same data, it is possible to extract the cumulative pore volume. 

Now that we have placed units for the desired properties (mass and volume) in the correct positions, we convert the units we have been given to the specific units we want. For our problem, this means converting liters to milliliters. Because we want to cancel L and it is on the bottom of the first ratio, the skeleton of the next conversion factor has the Z on top. 

The molarity of phosphoric acid provides the conversion factor that converts from volume of H3PO4 solution to moles of H3PO4, and the molarity of sodium hydroxide provides the conversion factor that converts from moles of NaOH to volume of NaOH solution. The conversion from moles of H3PO4 to moles of NaOH is made with the molar ratio that comes from the coefficients in the balanced equation for the reaction. 

There are several ways to convert between moles of a gaseous substance and its volume. One approach is to use as a conversion factor the molar volume at STP. STP stands for standard temperature and pressure. Standard temperature is 0 °C, or 273.15 K, standard pressure is 1 atm, or 101.325 kPa, or 760 mmHg. The molar volume, or... 

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. 

The volume of water that must be added during interval 1 is 2.727 m, which is the product of the area of the tank and the liquid level. The water can be fed at. 25 m min" so the time required to add the water is 10.9 min. The mixing of the solid with the water is best done slowly to ensure homogeneity. Therefore, 30 min is to be allowed for interval 2. Given this, we can compute the mass flow of solid required from either of the following equations. We use both to verify the result. We note that the densities are in units of kg/L, whereas the volumes and levels are in units of meters. There are (as shown in what follows) 1000 L per m. Therefore, each of the densities must be multiplied by this factor to convert them to kg per m ... 

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