Prefixes and Equalities

Perform the following calculations and round off the calculator display or add zeros to give each answer with the correct number of decimal places  

Hundredths place Thousandths place Ones place 

LEARNING GOAL Adjust calculated answers to give the correct number of significant figures. 

19 Why do we usually need to round off calculations that use measured numbers  

In the metric and SI systems of units, a prefix attached to any unit increases or decreases its size by some factor of 10. Table 2.6 lists some of the SI and metric prefixes, their symbols, and their numerical values. 

The prefix centi is like cents in a dollar. One cent wonld be a centidollar, or 0.01 of a dollar. That also means that one dollar is the same as 100 cents. The prefix deci is like the value of a dime to a dollar. One dime would be a decidollar, or 0.1 of a dollar. That also means that one dollar has the same value as 10 dimes. 

The relationship of a prefix to a unit can be expressed by replacing the prefix with its numerical value. For example, when the prefix kilo in kilometer is replaced with its value of 1000, we find that a kilometer is equal to 1000 m. Other examples follow  

Prefix Symboi Numerical Value Scientific Notation Equality  

A 1 terabyte hard disk drive stores 10 bytes of information. 

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Translating a formula into a name is equally simple. All you need to do is convert the subscripts into prefixes and attach them to the names of the elements that make up the compound. For example, for the compound N20, you simply attach the prefix di- to nitrogen to indicate the two nitrogen atoms and tetra- to oxygen to indicate the four oxygen atoms, giving you dinitrogen tetroxide. 

The answer is that Pasteur started with a 50 50 mixture of the two chiral tartaric acid enantiomers. Such a mixture is called a racemic (ray-see-mi c) mixture, or racemate, and is denoted either by the symbol ( ) or the prefix cl,I to indicate an equal mixture of dextrorotatory and levorotatory forms. Racemic mixtures show no optical rotation because the (+) rotation from one enantiomer exactly cancels the (-) rotation from the other. Through luck, Pasteur was able to separate, or resolve, racemic tartaric acid into its (-f) and (-) enantiomers. Unfortunately, the fractional crystallization technique he used doesn t work for most racemic mixtures, so other methods are needed. 

It is possible, of course, to use some sort of blank symbol to separate code words, but this would really imply that a tertiary alphabet was available. One easy way to guarantee that the code words can be separated from each other is to use a prefix code. We define a prefix code as a code in which no code word is the same as the initial part, or prefix, of another code word. More precisely, for any i and j, if % < np then vt must not be equal to the first nt digits of v. The following theorem now gives necessary and sufficient conditions on the set of lengths %, , n that can be used in a prefix code. 

An equal molar mixture of the dextrorotatory and levorotatory enantiomers of a chiral compound is called a racemic mixture or a racemate. Racemates do not show overall optical rotation because the equal and opposite rotations of the two enantiomers cancel each other out. A racemic mixture is designated by adding the prefix (+) or rac- before the name of the molecule. 

As shown above, the SI unit for volume is the cubic meter (m3), but most chemists use the liter (L, which is equal to 1 cubic decimeter (dm3)) or milliliter (mL). Appendix A lists the SI base units and prefixes, as well as some English-SI equivalents. 

In all compounds, the total charge must be zero. There are NO exceptions. Thus, to determine the formula in those cases where no prefixes are given, it is necessary to have some idea what the individual charges are. The species with the positive charge is listed and named first this is followed by the species with the negative charge. Subscripts may be needed to make sure the sum of the charges (valances) will equal zero. Examples ... 

Like other units, the unit of molarity can be modified by standard prefixes, as in millimolar (mM, which equals 10 mol/L) and micromolar (pM, which equals 10 mol/L). 

IUPAC Rule 64 (41) states "The expression lowest numbers signifies those that include the lowest individual number or numbers . Thus, 1,3 is lower than 2,4 1,1,3 lower than 1,3,3 1,5,5 lower than 2,2,6 1,2,3,5 lower than 1,3,4,5. At one time Chemical Abstracts interpreted "lowest numbers to mean those which yielded the lowest sum — for example, 2,2,6 (which adds up to 10) was considered lower numbering than 1,5,5 (which adds up to 11). Now, however, this practice has been abandoned, and the lowest individual numbers are the determining factor (10, 44). If two sets of lowest numbers for double bonds and substituents are equally possible according to IUPAC Rule 64, then the chosen order of prefixes — that is, alphabetical or complexity — becomes the determining factor. Examples of this numbering rule from formulas and names shown in Chart 6 are The substituents in No. 30 are at 1,5,5 and not at... 

Ionic Compounds To name an ionic compound, you just name the cation and then the anion. There is a crucial difference between naming ionic compounds and molecular compounds. In molecular compounds you must include prefix multipliers (di, tri, etc.) to indicate the number of each kind of atom in the molecule. In ionic compounds you must not include prefix multipliers, because the number of each ion in the formula unit is controlled by the charges on the ions. If the cation is a representative element, it is not necessary to indicate the charge, because (with few exceptions) these metals form cations with an ionic charge equal to the group number. 

Isotope Isotopic specification is indicated by prefixing the atomic symbol with a number equal to the integral isotopic mass—for example, [2H] for deuterium and [13C] for carbon-13. 

The worksheet can be made easier to look at by adding lines that separate the column labels and numbers. To create a line under the labels one moves the cell pointer to cell C7, type then =. In LOTUS the backslash ( ) serves as a repeating label prefix. Whatever is typed after the backslash is repeated until it fills the cell. After pressing RETURN cell C7 now contains a row of equal signs ( = ). To continue the double line across the worksheet from cell C7 to cell 07 one can use the / Copy Command. 

A DECIMAL IS a number that is written using one or more of ten symbols. The ten decimal symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These ten symbols can be used to write any number in the decimal system, such as 17 or 323,119. The prefix dec- means ten, which is why the decimal system is also called a base-ten system. Each digit in a decimal number is equal to that digit multiplied by a power of ten. 

McBain s term Sorption applies to all cases when a gas or solute is taken up by a solid. Adsorption means strictly the formation of a layer on an impermeable surface a sorption to penetration, or solution, into the interior. With the zeolites, there are pores of quite regular shape and size, only a few A. across. With charcoal there are irregular pores of similar size, as well as larger ones. Foreign substances, finding their way into these very fine pores may be said to be adsorbed on the walls of the pores, but as they permeate the whole structure of the solid more or less uniformly, they may equally be said to be absorbed by the solid. McBain avoids this difficulty simply by omission of the prefix. 

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