Unit Equivalent and Conversions

APPENDIX C COMMON UNITS. EQUIVALENCES. AND CONVERSION FACTORS... 

About one hundred of the most frequently used units are defined in Table 3. Common equivalents and conversions are given in Table 4. 

We are asked to make a unit conversion. The SI base unit of length is the meter, and the SI base unit of time is the second. It is necessary to convert from miles to meters and from hours to seconds. The appropriate unit equivalences are... 

A record of all calculations performed in connection with the test, including units of measure, conversion factors, and equivalency factors. 

Consider the following gas-phase reaction that occurs at 350 K and a constant pressure of 200 kPa (Lynch, 1986) A- B + C, for which the rate law is (-/a) = 0.253cA/(l + 0.429cA)2, where (- rA) has units of mol m-3 s-1 cA has units of mol m-3. Pure A is fed to a reactor at a rate of 8 mol s-1. The desired fractional conversion, fA, is 0.99. A recycle PFR is proposed for the reaction. When the recycle ratio, R, is zero, the recycle reactor is equivalent to a PFR. As R approaches infinity, the system is equivalent to a CSTR. However, it is generally stated that the recycle reactor behavior is close to that of a CSTR once R reaches approximately 10 to 20. Furthermore, it is often stated that, for an equivalent fractional conversion, the volume... 

Figure 10-5. Conversion of deoxyuridylate (dUMP) to deoxythymidylate (dTMP) by thymidylate synthetase. The importance of folate coenzymes in this reaction is illustrated. NADPH + H provide the necessary reducing equivalents and serine is the source of one-carbon units present on N, N °-methylene tetrahydrofolate (THF).

In addition to learning the new units and symbols, one must convert the numerical values reported in the cgs or engineering unit systems to the equivalent SI units. The actual conversion is best handled through the use of conversion tables. When the tables are used, ancillary problems of significant figures, accuracy, and rounding become apparent. 

Dimensional analysis is the method to convert a number from one unit to another using a conversion factor. Conversion factors establish a relationship of equivalence in measurements between two different units. Examples of conversion factors are tabulated in Table 3.1 (metric prefixes) and Table 3.3 (common conversion factors). 

This is based on the concept of a membrane permeable to water, but not to solute molecules. For example, if a sucrose solution is placed on one side and pure water on the other, then a passive driving force will be created and water will diffuse across the membrane into the sucrose solution, since the effective water concentration in the sucrose solution wiU be lower. The tendency for water to diffuse into the sucrose solution could be counteracted by applying a hydrostatic pressure equivalent to the passive driving force. Thus, the osmotic pressure of a solution is the excess hydrostatic pressure required to prevent the net flow of water into a vessel containing the solution. The SI unit of osmotic pressure is the pascal. Pa (=kgm s ). Older sources may use atmospheres, or bars, and conversion factors are given in Box 9.1 (p. 72). Osmotic pressure and osmolality can be interconverted using the expression 1 osmol kg = 2.479 MPa at 25 °C. 

Ultimately we want to know how a crystal diffracts X rays and produces the diffraction pattern that it does, and conversely, how the diffraction pattern can be used to reconstruct the crystal. It will be found useful in this regard to consider the crystal as the combination, or product of two distinct components, or functions. The first of these is the contents of a unit cell, characterized mathematically by the coordinates of the atoms in an asymmetric unit along with their space group symmetry equivalent positions. The second is a point lattice that describes the periodic distribution of the unit cell contents, and is characterized by a, b, and c. A crystal may then be concisely defined as the first component, or function, repeated in identically the same way at every nonzero point of the second. This physical process of repetitive superposition is termed a convolution. It can be formulated mathematically as the product of the two components, or functions as... 

The factor-label method can be extended to the use of unit-factors (or conversion factors) in which numerator and denominator are equivalent but of different dimensions. 

The mass transfer coefficient km for gas-phase plus interfacial mass transport has units s 1. The rate / aq in (12.1 IS) is in equivalent gas-phase concentration units, but the conversion to aqueous-phase units is straightforward multiplying by H h. The mass transfer coefficient as a function of the accommodation coefficient cc and the droplet radius is shown in Figure 12.13. For values of a > 0.1 the mass transfer rate is not sensitive to the exact value of a. However, for a < 0.01, surface accommodation starts limiting the mass transfer rate to the drop, and km, decreases with decreasing a for all droplet sizes. 

Finally, the world literature on energy production and consumption is plagued by a proliferation of measurement units. Variously, data are presented in terms of the International System of Units (SI, e.g., metres, pascals, joules), traditional industry-based units e.g., barrels of oil, kilowatt hours of electricity, million tonnes of oil equivalent) and, especially in the USA, Imperial units e.g., miles, British thermal units of heat, quads of energy, cubic feet of natural gas, bars of pressure). For the expression of time, however, units of days and years are generally more appropriate than the SI unit (seconds) in this field. In order to assist readers in translating units into those with which they are familiar, a set of conversion factors has been included. 

The units 49 and 50 used in the synthesis of vitamin A are also used in many ways in carotenoid syntheses and are produced industrially in large scale. p-Ionone (17) can be converted into vinyl-p-ionol (51) by ethynylation to 52 and partial hydrogenation [42]. This conversion is also achieved in one step by 1,2-addition of vinylmagnesium chloride 55[43]. The two routes are, in principle, equivalent, and which one is used in practice is decided by conditions on site. In this example, the main considerations are the availability of acetylene (4) and vinyl chloride, operating experience, and permits for handling these materials. The Ci5-phosphonium salt 49 is formed directly from 51 by the action of triphenylphosphine and acid [44,45]. A step involving labile P-ionylidene-ethyl halide is thus avoided. Crystalline (lE,9E)-49 is obtained in excellent yield by reaction of 51 with triphenylphosphine and sulphuric acid in isopropanol/heptane [46]. 

Use the information in Table C.4 to write the equivalences and two conversion factors for each of the following pairs of units ... 

Roughly equivalent and perhaps more common units are milligrams per liter and milligrams per kilogram of solvent. Being a volumetric unit, conversion of mg/L should involve the density, but for dilute solutions, mg/L, mg/kg and ppm are about the same. Table 7.2 gives a comparison for Zn. 

These equations allow, for example, expressing the energy in temperature units or energy-equivalent mass units. During the conversion, however, the precision inherent in the values of the fundamental constants involved must be kept as much as possible and care should be taken of the correlation of uncertainties. For this reason, the safest procedure is to use the set of... 

Gardarelli, Francois. Encyclopedia of Scientific Units, Weirds and Measures Their SI Equivalences and Ori- ns. New fork Springer, 2003. A systematic review of the many incompatible systems of measurement that have been developed throughout history. It clearly relates those units to their modem SI equivalents and provides conversion tables for more than 19,000 units of measurement. 

Calculations may also involve measurements involving the density of gas, which should be expressed or converted to SI units of kg m". However, note that gdm" and kgm" are equivalent - no conversion is required. 

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