Ratio of masses

In the ion source, substances are converted into positive or negative ions having masses (m, mj,, m ) and a number (z) of electric charges. From a mass spectrometric viewpoint, the ratio of mass to charge (m,/z, m2/z,, m /z) is important. Generally, z = 1, in which case, m/z = mj,... 

FIG. 26-68 Ratio of mass flux for horizoutal pipe flow to that for orifice discharge for flashing liquids hy the homogeueoiis eqiiilihriiim model, (Leung and Gmlmes, AIChE J, 33 (3), pp. 524-527, 1987 reproduced by permission of AIChE. copy-right 1987. All rights reseroed.)... 

FIG. 26-69 Ratio of mass flux for inclined pipe flow to that for orifice discharge for flashing liquids by the homogeneous equilibrium model. Leung, J. of Loss Prev. Process Ind. 3 pp. 27-32, with kind peimission of Elsevier Science, Ltd, The Boulevard, Langford Lane, Kidlington, 0X5 IGB U.K., 1990.)... 

The distribution coefficient for n-heptane (solute i) distributed between ethylene glycol (solvent 1) and benzene (solvent 2) at 25°C is given as the ratio of mass fractions... 

Nitric-hydrofluoric acid test 1 10% HNO3 -1- 3% HF 4 h exptosure to 70° C solution Comparison of ratio of mass loss of laboratory annealed and as-received samples of same material Corrosion potential of 304 steel = -l-O-14 to -I-0-54 1. Chromium-depleted areas 2. Not for 0-phase 3. Used only for Mo-bearing steels... 

This was described in 1959 by Streicher , and consists of one period of exposure to a boiling solution of 50 mass% H2SO4 -I- 25 g 1 Fe2(S04)j for 120 h, assessment being based on mass loss (see Table 19.4). Streicher, however, usually reports a ratio of mass loss of sample to be assessed/weight loss of annealed sample (g dm ), and as for the HNO3-HF test considers that a ratio > 1-5-2-0 indicates susceptibility for Type 304 Streicher considers a rate >0-76 mm/y to indicate susceptibility, but Brown considers a higher figure to be acceptable (see Table 19.4)... 

Note that even though mass and volume are extensive properties, the ratio of mass to volume is intensive. Samples of copper weighing 1.00 g, 10.5 g, 264 g,... all have the same density, 8.94 g/mL at 25°C. 

The density of a substance is independent of the size of the sample because doubling the volume also doubles the mass so the ratio of mass to volume remains the same. Density is therefore an intensive property. We distinguish different substances by their intensive properties. Thus, we might recognize a sample as water by noting its color, density (1.00 g-cm-3), melting point (0°C), boiling point (100°C), and the fact that it is a liquid. 

We are now ready to calculate the mean residence time. According to Equation (1.41), f is the ratio of mass inventory to mass throughput. When the number of moles does not change, t is also the ratio of molar inventory to molar throughput. Denote the molar inventory (i.e., the total number of moles in the tube) as Nactimi- Then... 

Bartle et al. [286] described a simple model for diffusion-limited extractions from spherical particles (the so-called hot-ball model). The model was extended to cover polymer films and a nonuniform distribution of the extractant [287]. Also the effect of solubility on extraction was incorporated [288] and the effects of pressure and flow-rate on extraction have been rationalised [289]. In this idealised scheme the matrix is supposed to contain small quantities of extractable materials, such that the extraction is not solubility limited. The model is that of diffusion out of a homogeneous spherical particle into a medium in which the extracted species is infinitely dilute. The ratio of mass remaining (m ) in the particle of radius r at time t to the initial amount (mo) is given by ... 

The lumped material resistance properties of intestinal membranes as defined by permeability can be described macroscopically by the ratio of mass flux (J) through the membrane to the solute concentration difference across the membrane. Permeability (reciprocal resistance) has units of length per unit time. 

The law of multiple proportions states that when two different compounds are formed from the same elements, the ratio of masses of one element in the two compounds for a given mass of any other element is a small whole number. 

Once Dalton s hypotheses had been proposed, the next logical step was to determine the relative masses of the atoms of the elements. Since there was no way at that time to determine the mass of an individual atom, the relative masses were the best information available. That is, one could tell that an atom of one element had a mass twice as great as an atom of a different element (or times as much, or 17.3 times as much, etc.). How could even these relative masses be determined They could be determined by taking equal (large) numbers of atoms of two elements and by determining the ratio of masses of these collections of atoms. 

For example, a large number of carbon atoms has a total mass of 12.0g, and an equal number of oxygen atoms has a total mass of 16.0g. Since the number of atoms of each kind is equal, the ratio of masses of one carbon atom to one oxygen atom is 12.0 to 16.0. How can one be sure that there are an equal number of carbon and oxygen atoms One ensures equal numbers by using a compound of carbon and oxygen in which there are an equal number of atoms of the two elements (i.e., carbon monoxide). 

The ratio of 1.50 1 is equal to the ratio 3 2, and the law of multiple proportions is satisfied. Note that the ratio of masses of iron to oxygen is not necessarily a ratio of small integers the ratio of mass of oxygen in one compound to mass of oxygen in the other compound is what must be in the small integer ratio. 

Ans. The ratio of mass of oxygen to mass of copper is not necessarily integral. Take a constant mass of copper, for example, l.OOOg Cu. From the ratios given, there are... 

The ratio of masses of oxygen in the two compounds (for a given mass of Cu) is the ratio of small integers, as required by the law of multiple proportions. The ratio of mass of copper to mass of oxygen is not integral. 

The percentages are the same as those in part (a). That result might have been expected. Since the ratio of atoms of carbon to atoms of hydrogen is the same (1 2) in both compounds, the ratio of masses also ought to be the same, and their percent by mass ought to be the same. From another viewpoint, this result means that the two compounds cannot be distinguished from each other by their percent compositions alone. 

Ans. Choice (a). This is a useful definition of empirical formula. The molecular formula gives the ratio of moles of each element to moles of the compound, plus the information given by the empirical formula. The percent composition does not deal with moles, but is a ratio of masses. 

The second bracket contains the aspect ratio. The group in the first bracket is a measure of the approach to the limiting current modified by a total overpotential. The authors describe this group as a ratio of mass-transfer resistance to kinetic resistance. 

Dimensional Analysis (start by setting up the ratio of mass to volume, stochiometry) ... 

Dimensional Analysis (start by setting up the ratio of mass to volume, then convert to moles) MH3P04 soln = 0 °857l8 pf)P4°s 1 2 3 4 50ln X 97.99 = 0.0539 MH3P04... 

Plan Use the ratio of masses, rather than convert to moles. In this case, since 2 moles of A1203 produces 4 moles of Al, then the 2 x FW of A1203 (= 204 g) will produce 4 x AW (= 108 g) of aluminum and 204... 

The small burner at the heart of the balloon heats the air within the canvas hood of the balloon. The densities of all materials -solid, liquid or gas - alter with temperature. Almost universally, we find the density p increases with cooling. Density p is defined as the ratio of mass m to volume V, according to... 

As this represents a ratio of masses, if combined with a volume ratio, a ratio of concentrations, which is an equilibrium constant, can be obtained. The volume ratio is called the phase ratio and is the ratio of the volume of the mobile phase to the volume of the stationary phase. 

Since the absolute thickness of the effective hydrodynamic boundary layer is very small, below a particular size range minimum, no hydrodynamic effects are perceived experimentally with varying agitation. This, however, does not mean, that there are no such influences Further, the mechanisms of mass transfer and dissolution may change for very small particles depending on a number of factors, such as the fluid viscosity, the Sherwood number (the ratio of mass diffusivity to molecular diffusivity), and the power input per unit mass of fluid. 

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