Working with ratios

The ratio of two species (or isotopes) with concentrations C 1 and C 2 in a mixture of n components is 

From equation (1.3.2), and using FeO/MgO for concentration ratios, we write 

Let a86 be the number of 86Sr atoms per gram of Sr. If/gn is the fraction of gneiss and 1 -/gn the fraction of basalt in the hybrid lava, we can write 

Given the extremely small variations of the Sr isotope compositions (most Sr is 88Sr), a86 is virtually identical for each component, hence it can be canceled out so that 

The hybrid magma contains proportions of gneiss and basalt in a ratio of 4 to 7.  

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This lesson covers the basics of working with ratio and proportions. The topics in this chapter are ... 

SAQ 7.4 and Worked Example 7.3 show how calculations of this type can be long-winded, boring and cumbersome. This explains why many analysts prefer to work with ratios of current. 

Oxidant air pollutants exist as parts of a complex mixture of gases, many of which may be phytotoxic. However, expect for ambient-air studies and simulated photochemical-oxidant studies, little research was done with pollutant combinations until the classic work of Menser and Heggestad in 1966. It is of interest that Thomas et suggested that sulfur dioxide might lessen the effect of oxidants in causing foliar injury to pinto bean. Middleton et working with ratios of sulfur... 

The meaning of the the term "hybrid receptor model" is not consistent in the literature. Following the definition proposed at the Quail Roost Receptor Modeling Workshop (15), we take it to be a combination of some meteorological aspects of traditional source-based models with some tracer aspects of receptor models. An important feature of such models is that one often works with ratios of species so that some of the most uncertain absolute parameters of classical models cancel out. As noted below, for example, one can calculate the concentration ratio of gas-phase SO2 to gas-phase B as a function of distance from a common source more accurately than the absolute concentration of either species. 

Try the following problems to practise working with ratios in balanced chemical equations. 

To evaluate, in more detail, the effect of the chemical structure of the reactants upon isothermal curing, the rate of conversion at vitrification (dx/dt)DF o.5 can be compared to the average rate before vitrification, (dx/dt), which equals XDF o.5ltDF o.5- It is necessary to work with ratios or relative rates r (Table 2.1) because the amine-epoxy system is much more reactive than the anhydride-epoxy system. For the latter system, the ratio r of (dx/df)Dir o.5 to (dx/df) is lower than 1 5 over the temperature range considered, which is much smaller than the lowest ratio of 1 2.4 for the epoxy-amine system. The ratio r also decreases with increasing cure temperature. 

By combining random flight statistics from Chap. 1 with the statistical definition of entropy from the last section, we shall be able to develop a molecular model for the stress-strain relationship in a cross-linked network. It turns out to be more convenient to work with the ratio of stretched to unstretched lengths L/Lq than with y itself. Note the relationship between these variables ... 

If the yeast does not get enough free amino nitrogen, the fermentation will be poor and the beer quaHty inferior. A neutral bacterial protease added at mashing-in can be used to raise the level of free amino nitrogen. This is useful when working with poorly modified malt or with high adjunct ratios. 

Stage compositions in the TG method are obtained by stage-to-stage calculations from both ends toward the feed stage. With reference to Fig. 13-1, the calculations work with the ratios v /d, Jd, v /h, and instead of v or f directly. 

For many calculations it is required to know the ratio of Cp/C, for a gaseous compound. The well-known expression Cp-C = R (where R is the universal gas constant) holds good only for gases under ideal conditions. When working with situations involving real gases, the relationship between Cp and C, is given as ... 

Fig. 4.11. Calculation of efficiency of simple CBT plants—single-.step cooled ICBTlica uncooled [CBT ]ii—a.s a function of specific work with pressure ratio (r) and maximum temperature as parameters and with r)p< = t), = 0.9. 7hi = 1073 K (after Ref. 5 ).

After 1900, genetic research—but not research on nucleic acids—blossomed. Nucleic acids were difficult to work with, hard to purify, and, even though they were present in all cells, did not seem to be very interesting. Early analyses, later shown to be inconect, were interpreted to mean that nucleic acids were polymers consisting of repeats of some sequence of adenine (A), thymine (T), guanine (G), and cytosine (C) in a 1 1 1 1 ratio. Nucleic acids didn t seem to offer a rich enough alphabet from which to build a genetic dictionary. Most workers in the field believed proteins to be better-candidates. 

Thomas Midgley, working with a group of researchers under Charles F. Kettering, discovered a fuel-additive, tetraethyl lead that enhanced the knock resistance of existing fuels. By the time this additive entered commercial use in 1923, the average compression ratio of new U.S. cars had advanced to 4.3. 

Such units may use chilled water or direct-expansion refrigerant, and will have the air filter at the top. It may not be possible to introduce outside air through it, so the room will have a pressurized fresh air supply, which will be filtered to remove fine dusts which may affect the computers. Computer room units work with a very high sensible heat ratio of 0.95 or more, so they have large coils to keep the ADP up near the dew point of the room air. Most will have an inbuilt steam humidifier to replace any moisture which is removed on the coil. 

A further complication arises with the application to temperate conditions of room air-conditioners which have heen designed primarily for tropical markets. These units typically work with a sensible/total heat ratio of 0.7. Plotting this process line on the psychrometric chart (see Figure 35.3) shows that the ADP will he about 9°C. 

Let s work with these data. Heartened by your results from your own laboratory data, let us compute the value of the ratio... 

Comparing equations 13.8 and 13.9, it is seen that the adiabatic saturation temperature i > equal to the wet-bulb temperature when s = h/hDpA. This is the case for most water vapour systems and accurately so when Jf = 0.047. The ratio (h/hopAs) = b is sometimes known as the psychrometric ratio and, as indicated, b is approximately unity for the air-water system. For most systems involving air and an organic liquid, b = 1.3 - 2.5 and the wet-bulb temperature is higher than the adiabatic saturation temperature. This was confirmed in 1932 by SHERWOOD and COMINGS 2 who worked with water, ethanol, n-propanol, n-butanol, benzene, toluene, carbon tetrachloride, and n-propyl acetate, and found that the wet-bulb temperature was always higher than the adiabatic saturation temperature except in the case of water. 

Polymer and coating chemists use computer models to predict the properties of formulated products from the characteristics of the raw materials and processing conditions (1, 2). Usually, the chemist supplies the identification and amounts of the materials. The software retrieves raw material property data needed for the modelling calculations from a raw material database. However, the chemist often works with groups of materials that are used as a unit. For instance, intermediates used in multiple products or premixes are themselves formulated products, not raw materials in the sense of being purchased or basic chemical species. Also, some ingredients are often used in constant ratio. In these cases, experimentation and calculation are simplified if the chemist can refer to these sets of materials as a unit, even though the unit may not be part of the raw material database. 

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