Numbers ratios

In general, the larger lobe profile number ratios of a positive displacement motor, the higher the torque output and the lower the speed (assuming all other design limitations remain the same). 

The validity of this law depends on the fact that atoms combine in simple, whole-number ratios (postulate 3). Its relation to atomic theory is further illustrated in Figure A. 

A major task of chemical analysis is to determine the formulas of compounds. The formula found by the approach described here is the simplest formula, which gives the simplest whole-number ratio of the atoms present. For an ionic compound, the simplest formula is ordinarily the only one that can be written (e.g., CaCl2, Cr203). For a molecular compound, the molecular formula is a whole-number multiple of the simplest formula, where that number may be 1,2. 

The second of Faraday s observations was that the weights of different elements that were deposited by the same amount of electricity formed simple whole-number ratios when divided by the atomic weights of these elements. For example,... 

Atoms form chemical compounds by combining in whole-number ratios. 

A solid that contains cations and anions in balanced whole-number ratios is called an ionic compound. Sodium chloride, commonly known as table salt, is a simple example. Sodium chloride can form through the vigorous chemical reaction of elemental sodium and elemental chlorine. The appearance and composition of these substances are very different, as Figure 2-24 shows. Sodium is a soft, silver-colored metal that is an array of Na atoms packed closely together. Chlorine is a faintly yellow-green toxic gas made up of diatomic, neutral CI2 molecules. When these two elements react, they form colorless ciystals of NaCl that contain Na and Cl" ions in a 1 1 ratio. 

Masses and number ratios cannot be used to determine the limiting reactant" in bicycle manufacture either. Five chains are fewer in number than eight wheels and have less mass than eight wheels. Nevertheless, the wheels are used up before the... 

Potassium dichromate was used as a molecular marker to measure total system volume and plate count (1). The three column sets exhibited the equivalent of approximately 250-300 plates per foot. This was adequate, even with Set I, to give near baseline resolution of an equal weight blend of the 103 nm and 312 nm samples as shown in Figure 2. This Is approximately an 84 1 number ratio. 

Changing the size of metal particles leads to a change in the atom s mean coordination number, as in smaller particles the number ratio of surface atoms to bulk atoms increases. As a result, the metal s valence band becomes... 

Compounds are formed by joining the atoms of two or more elements. When forming a compound, the atoms of elements combine in whole-number ratios, such as 1 to 1,2 to 1,3 to 2, and so on. Water, with two atoms of hydrogen for every atom of oxygen, would he a compound with a ratio of 2 to 1. 

Figure 4.18 Family of curves of Nusselt number ratio versus quality for constant bulk wall vapor viscosity ratios. (From Varone and Rohsenow, 1990. Reprinted with permission of Massachusetts Institute of Technology, Cambridge, MA.)...

This is still not a whole number ratio, since 1.333 is much too far from an integer to round off. Since 1.333 is about l, multiply both numbers of moles by 3 ... 

O/C ratio. The observed and predicted variations with Z of the number ratio of SNIb/c and SNII shows an interesting agreement [11]. This is noticeable because of the possible connection WO stars - SNIb/c - GRBs (7 Ray Bursts). In this context, we consider WO stars as good candidate for GRB progenitors. 

Have you wondered about those funny curves drawn over the NMR peaks They re electronic integrations and they can tell you how many protons there are at each chemical shift. Measure the distances between the horizontal lines just before and just after each group. With a cheap plastic ruler I get 52 mm for the benzene ring protons, 21 mm for the —CH2— protons, and about 30 mm for the —CH3 protons. Now you divide all the values by the smallest one. Well, 21 mm is the smallest, and without a calculator I get 2.47 1 1.43. Not even close. And how do you get that 0.47 or 0.43 proton Try for the simplest whole number ratio. Multiply everything by 2, and you ll have 4.94 2 2.86. This is very close to 5 2 3, the actual number of protons in ethylbenzene. Use other whole numbers the results are not as good and you can t justify the splitting pattern—3 split BY 2 and 2 split BY 3—with other ratios. Don t use each piece of information in a vacuum. 

The Law of Conservation of Mass states that the total mass remains unchanged. This means that the total mass of the atoms of each element represented in the reactants must appear as products. In order to indicate this, we must balance the reaction. When balancing chemical equations, it is important to realize that you cannot change the formulas of the reactants and products the only things you may change are the coefficients in front of the reactants and products. The coefficients indicate how many of each chemical species react or form. A balanced equation has the same number of each type of atom present on both sides of the equation and the coefficients are present in the lowest whole number ratio. For example, iron metal reacts with oxygen gas to form rust, iron(III) oxide. We may represent this reaction by the following balanced equation ... 

Make sure that all atoms balance and the coefficients are in the lowest whole number ratio. 

In the problem above, we determined the percentage data from the chemical formula. We can determine the empirical formula if we know the percent compositions of the various elements. The empirical formula tells us what elements are present in the compound and the simplest whole-number ratio of elements. The data may be in terms of percentage, or mass or even moles. However, the procedure is still the same—convert each element to moles, divide each by the smallest, and then use an appropriate multiplier if necessary. We can then determine the empirical formula mass. If we know the actual molecular mass, dividing the molecular formula mass by the empirical formula mass, gives an integer (rounded if needed) that we can multiply each of the subscripts in the empirical formula. This gives the molecular (actual) formula, which tells what elements are in the compound and the actual number of each. 

The simplest whole-number ratio of the elements present in a compound is... 

In Chapter 2, we saw molecular and empirical formulas. Recall that the molecular formula indicates the kind and actual number of atoms present. The empirical formula simply shows the kind of atoms present and their lowest whole number ratio. In this chapter, structural formulas are important. The Lewis formula of a compound is an example of a structural formula. A structural formula shows the number and type of atoms present, as well as the bonding pattern. The bonding pattern shows which atoms bond to each other. It usually... 

An ionic compound is neutral (same number of positive and negative charges) and that the formula has the lowest whole number ratio of elements. 

Be careful when using the crisscross rule to reduce the subscripts to their lowest whole-number ratio. 

A balanced chemical equation provides many types of information. It shows which chemical species are the reactants and which species are the products. It may also indicate in which state of matter the reactants and products exist. Special conditions of temperature, catalysts, etc., may be placed over or under the reaction arrow. And, very importantly, the coefficients (the integers in front of the chemical species) indicate the number of each reactant that is used and the number of each product that is formed. These coefficients may stand for individual atoms/molecules or they may represent large numbers of them called moles (see the Stoichiometry chapter for a discussion of moles). The basic idea behind the balancing of equations is the Law of Conservation of Matter, which says that in ordinary chemical reactions matter is neither created nor destroyed. The number of each type of reactant atom has to equal the number of each type of product atom. This requires adjusting the reactant and product coefficients—balancing the equation. When finished, the coefficients should be in the lowest possible whole-number ratio. 

Answer all three of the following questions. Each question will have two parts—writing the balanced chemical equation and answering a question about the reaction. Coefficients in the balanced chemical equation must be in the lowest whole-number ratio. Do not include formulas for substances that remain unchanged during the reaction. Unless otherwise noted, assume all the reactions occur in aqueous solution. If a substance is extensively ionized and therefore is present as ions in solution, write its formula as ions. 

If magnesium, with two valence electrons to be lost, reacts with chlorine (which needs one additional electron), then magnesium will donate one valence electron to each of two chlorine atoms, forming the ionic compound MgCl2. Make sure the formula has the lowest whole number ratio of elements. 

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