Conversions, unit concentrations

Molarity (M) A concentration unit defined to be the number of moles of solute per liter of solution, 95q, 259 concentration unit conversion, 261-262 potassium chromate, 263 Mole A collection of6.0122 X 1023 items. The mass in grams of one mole of a substance is numerically equal to its formula mass, 55. See also Amount Mole fraction (X) A concentration unit defined as the number of moles of a component divided by the total number of moles, 116-117,261 Mole-gram conversions, 55-56,68-68q... 

It is important to be able to convert among the different concentration units. Conversions between molality and mole fraction are performed by considering a solution containing 1 kg of solvent ... 

In these unit conversions on H, we have used the facts that 1 atm = 760 Torr and the ratio of densities PHg/ soin - /Psoin t onverts from Torr to millimeters of solution. These numerical examples show that experiments in which Apj, ATf, or ATj, are measured are perfectly feasible for solutes of molecular weight 100, but call for unattainable sensitivity for polymeric solutes of M = 10 . By contrast, osmometry produces so much larger an effect that this method is awkward (at least for 1% concentration) for a low molecular weight solute, but is entirely feasible with the polymer. 

A minor problem arises in regard to nitrogen oxides. It is common practice to add concentrations of nitrogen dioxide and nitric oxide in ppm (vol) and express the sum as "oxides of nitrogen." In metric units, conversion from ppm (vol) to /rg/m must be done separately for nitrogen dioxide and nitric oxide prior to addition. 

Conversions between concentration units are relatively straightforward provided you first decide on a fixed amount of solution. The amount chosen depends on the unit in which concentration is originally expressed. Some suggested starting quantities are listed below. 

No deaths or evidence of toxicity were attributable to diisopropyl methylphosphonate administered for 26 weeks in the drinking water of rats at concentrations of 0.6 ppb, 6.0 ppb, 10 ppm, and 1,000 ppm (6.6x 10"7, 6.6x 10"5, 0.011, and 1.1 mg/kg/day, respectively) (Army 1978). It should be noted that there is some confusion concerning the concentration units used in this study (EPA 1989). EPA (1989) states that conversions between ppm and mg/L were incorrectly calculated using the air conversion factor. 

These results are in apparent contradiction to others obtained by the same authors [53]. In this earlier paper" they reported that at -78°, with the same range of [A1C13] [/-C4H8] ratios, and at conversions of less than 10 per cent, the DP decreased from 5.4 x 103 at 4.8 x 10"3 wt.% A1C13 on isobutene, to about 2.5 x 103 at concentrations greater than about 1.3 x 10"2 wt.% of A1C13. The authors do not comment on this apparent discrepancy between their two series of results, which is rendered even more obscure by the different, but equally clumsy, concentration units which are used in the two papers. The matter... 

Raoult s law, osmotic pressure, and freezing point depression calculations use, without conversion, which of the following respective concentration units... 

Unfortunately, many of the standard equations encountered in electrochemistry require the concentration unit of mol cm (moles per cubic centimetre). The conversion between mol cm and the familiar mol dm is as follows ... 

Solubility concentratiorrs can be expressed many ways, including molarity (mol/L), molality (mol/kg), mole fraction, weight percent, mass per unit volume (e g., g/L), etc. The conversion formttlas for solutiotts having different concentration units are presented in Table 1. 

Table 1. Conversion Formulas for Various Concentration Units... 

For the batch reactor we saw in the previous chapter that by switching from Ca as the composition variable to fractional conversion X, we could easily write the differential equation to be solved for compositions versus time. We prefer to use concentration units whenever possible, but, if the density is a function of composition, concentrations become cumbersome variables, and we must switch to another designation of density such as the fractional conversion X. 

We always use Cj in moles per liter (or in moles per cubic decimeter or 1 kilomole/m for the SI purist) as the only unit of concentration. The subscript j always signifies species, while the subscript i always signifies reaction. We use j as the species designation and species A as the key reactant. For gases the natural concentration unit is partial pressure Pj, but we always convert this to concentration, Cj = Pj RT, before writing the mass-balance equations. Conversion X means the fiaction of this reactant that is consumed in the reactor, Ca = Cao( 1 — X), but we prefer to use C i rather than X and find the conversion after we have solved the equation in terms of G. We cannot use this unit of density of a species when the density of the fluid varies with conversion, but we prefer to do so whenever possible because the equations are simpler to write and solve. 

The conversion between concentration units and the expression of the units themselves can be confusing. We will now review the typical concentration units used in various environmental media. Concentration in water is usually given as mass per unit volume or moles per unit volume. The conversion between them is a straightforward application of molecular weights. For example, we have 2.0 g/m of CO2 dissolved in water. The molecular weight of carbon dioxide is 44 g/mole. Then the concentration in moles/m is... 

There are some abbreviations for concentration units that are often seen in the literature and will be used periodically in this text. These are listed in Table 1.3. Also listed is a common conversion to water or to air. 

Note that the value of the intercept, the value of r/RTc at infinite dilution, obeys the van t Hoff equation, Equation (25). At infinite dilution even nonideal solutions reduce to this limit. The value of the slope is called the second virial coefficient by analogy with Equation (27). Note that the second virial coefficient is the composite of two factors, B and (1/2) Vx/M. The factor B describes the first deviation from ideality in a solution it equals unity in an ideal solution. The second cluster of constants in B arises from the conversion of practical concentration units to mole fractions. Although it is the nonideality correction in which we are primarily interested, we discuss it in terms of B rather than B since the former is the quantity that is measured directly. We return to an interpretation of the second virial coefficient in Section 3.4. 

Table 4 shows the effect of monomer concentration, coinitiator concentration, and conversion on the composition of poly(4-methyl-1-pentene) using EtAlCl2 coinitiator at — 50° C. The 1,2-, 1,3-, and 1,4-repeat unit concentrations in the polymer have been determined from polymer spectra by use of a computer curve simulator-plotting program and are rounded to the nearest percent. No limits of error are indicated since none could be determined analytically. A reasonable error is thought to be +15% of the measured value. 

Energy Levels and Transition Probabilities of Some Atom of Photochemical Interest, 363 Conversion Factors for Absorption Cofficients, 373 Conversion Factors for Second Order Rate Constants, 37 1 Conversion Factors for Third Order Rate Constants, 374 Conversion from Pressure to Concentration Units, 375 Enthalpies of Formation of Atoms at 1 atm and 0°K in 11 . Idea Gas State, 375... 

Unit Conversion for Low Concentration Solubilities Mass-per-volume and mass-per-mass solubilities are related by... 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Note Although this problem is given to us and worked in mg/mL, any volumetric concentration units could have been used in this problem, so long as the same units are used throughout because the conversion factors cancel. 

Because virtually all stoichiometric calculations involve moles (abbreviated mol) of material, molarity is probably the most common concentration unit in chemistry. If we dissolved 1.0 mol of glucose in enough water to give a total volume of 1.0 L, we would obtain a 1.0 molar solution of glucose. Molarity is abbreviated with a capital M. Notice that, because molarity has units of moles per liter, molar concentrations are conversion factors between moles of material and liters of solution. 

We can also use percent concentrations as conversion factors. For example, how many liters of D5W is required to deliver 100 g of glucose Well, D5W is 5% w/v) glucose, so we can interpret 5% as 5 g of glucose/100 mL D5W solution. That s a conversion factor, and now the units can take us to the answer. 

Bonding density is a surface concentration of bonded ligands, and it is expressed in either number of moles per square meter (pmohm ) or in number of groups per square nanometer (groups/nm ). Unit conversion is shown in equation (3-7). 

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