Ionic substances are not chemically bonded and do not exist as discrete molecules. However, they do associate in discrete ratios of ions. Thus, we can describe their formula weights, but not their molecular weights. In some types of analyses of it is important to know the percentage by mass of each type of element in a compound.
The law of definite proportions states that a chemical compound always contains the same proportion of elements by mass; that is, the percent composition—the percentage of each element present in a pure substance—is constant although there are exceptions to this law. A more complex example is sucrose table sugar , which is This means that First the molecular formula of sucrose C 12 H 22 O 11 is used to calculate the mass percentage of the component elements; the mass percentage can then be used to determine an empirical formula.
According to its molecular formula, each molecule of sucrose contains 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. A mole of sucrose molecules therefore contains 12 mol of carbon atoms, 22 mol of hydrogen atoms, and 11 mol of oxygen atoms. This information can be used to calculate the mass of each element in 1 mol of sucrose, which gives the molar mass of sucrose. These masses can then be used to calculate the percent composition of sucrose. To three decimal places, the calculations are the following:.
Thus 1 mol of sucrose has a mass of The mass percentage of each element in sucrose is the mass of the element present in 1 mol of sucrose divided by the molar mass of sucrose, multiplied by to give a percentage. The result is shown to two decimal places:. Thus It is also possible to calculate mass percentages using atomic masses and molecular masses, with atomic mass units.
Because the answer is a ratio, expressed as a percentage, the units of mass cancel whether they are grams using molar masses or atomic mass units using atomic and molecular masses. Aspartame is the artificial sweetener sold as NutraSweet and Equal. Asked for : mass percentage of all elements and mass of one element in sample. A We calculate the mass of each element in 1 mol of aspartame and the molar mass of aspartame, here to three decimal places:.
Thus more than half the mass of 1 mol of aspartame B To calculate the mass percentage of each element, we divide the mass of each element in the compound by the molar mass of aspartame and then multiply by to obtain percentages, here reported to two decimal places:. C The mass of carbon in 1. Calculate the mass percentage of each element in aluminum oxide Al 2 O 3.
Then calculate the mass of aluminum in a 3. Just as the empirical formula of a substance can be used to determine its percent composition, the percent composition of a sample can be used to determine its empirical formula, which can then be used to determine its molecular formula. Such a procedure was actually used to determine the empirical and molecular formulas of the first antibiotic to be discovered: penicillin.
Antibiotics are chemical compounds that selectively kill microorganisms, many of which cause diseases. Although antibiotics are often taken for granted today, penicillin was discovered only about 80 years ago. The subsequent development of a wide array of other antibiotics for treating many common diseases has contributed greatly to the substantial increase in life expectancy over the past 50 years.
The discovery of penicillin is a historical detective story in which the use of mass percentages to determine empirical formulas played a key role. In , Alexander Fleming, a young microbiologist at the University of London, was working with a common bacterium that causes boils and other infections such as blood poisoning. For laboratory study, bacteria are commonly grown on the surface of a nutrient-containing gel in small, flat culture dishes. Scientists did not know why the drug caused birth defects while also producing positive anti-nausea effects as well, until they discovered that the two enantiomers had different biological effects on the body.
The two enantiomers of thalidomide, R and S, are mirror images of each other; the enantiomers are different chiral structures of the same compound, differing at the stereocenter denoted by the asterisk. This case is different than the case of morphine versus heroin in the sense that these are the same compound rather than two similar but slightly different compounds; the enantiomers of thalidomide have the same chemical formula but are simply arranged differently.
Because of the different spatial orientations, each enantiomer reacts differently with the body. This results in highly different side effects, some positive and some negative. Although thalidomide was quickly recalled after this was discovered, it is still used today to treat things like leprosy and some cancers like multiple myeloma. However, it is very clear to doctors and patients that pregnant woman should not be prescribed this drug.
For clarity the two ambiguous bonds to oxygen are given different colors in these formulas. If only one formula for sulfur dioxide was correct and accurate, then the double bond to oxygen would be shorter and stronger than the single bond. This averaging of electron distribution over two or more hypothetical contributing structures canonical forms to produce a hybrid electronic structure is called resonance.
Likewise, the structure of nitric acid is best described as a resonance hybrid of two structures, the double headed arrow being the unique symbol for resonance. The above examples represent one extreme in the application of resonance. Here, two structurally and energetically equivalent electronic structures for a stable compound can be written, but no single structure provides an accurate or even an adequate representation of the true molecule.
In cases such as these, the electron delocalization described by resonance enhances the stability of the molecules, and compounds or ions composed of such molecules often show exceptional stability.
The electronic structures of most covalent compounds do not suffer the inadequacy noted above. Nevertheless, the principles of resonance are very useful in rationalizing the chemical behavior of many such compounds.
For example, the carbonyl group of formaldehyde the carbon-oxygen double bond reacts readily to give addition products. The course of these reactions can be explained by a small contribution of a dipolar resonance contributor, as shown in equation 3. Here, the first contributor on the left is clearly the best representation of this molecular unit, since there is no charge separation and both the carbon and oxygen atoms have achieved valence shell neon-like configurations by covalent electron sharing.
If the double bond is broken heterolytically, formal charge pairs result, as shown in the other two structures. The preferred charge distribution will have the positive charge on the less electronegative atom carbon and the negative charge on the more electronegative atom oxygen. Therefore the middle formula represents a more reasonable and stable structure than the one on the right. The application of resonance to this case requires a weighted averaging of these canonical structures.
The double bonded structure is regarded as the major contributor, the middle structure a minor contributor and the right hand structure a non-contributor. Since the middle, charge-separated contributor has an electron deficient carbon atom, this explains the tendency of electron donors nucleophiles to bond at this site.
The basic principles of the resonance method may now be summarized. These are the canonical forms to be considered, and all must have the same number of paired and unpaired electrons. The following factors are important in evaluating the contribution each of these canonical structures makes to the actual molecule.
The stability of a resonance hybrid is always greater than the stability of any canonical contributor. Consequently, if one canonical form has a much greater stability than all others, the hybrid will closely resemble it electronically and energetically. This is the case for the carbonyl group eq. On the other hand, if two or more canonical forms have identical low energy structures, the resonance hybrid will have exceptional stabilization and unique properties. This is the case for sulfur dioxide eq.
To illustrate these principles we shall consider carbon monoxide eq. In each case the most stable canonical form is on the left. For carbon monoxide, the additional bonding is more important than charge separation. Furthermore, the double bonded structure has an electron deficient carbon atom valence shell sextet. A similar destabilizing factor is present in the two azide canonical forms on the top row of the bracket three bonds vs.
The bottom row pair of structures have four bonds, but are destabilized by the high charge density on a single nitrogen atom. All the examples on this page demonstrate an important restriction that must be remembered when using resonance. No atoms change their positions within the common structural framework. Only electrons are moved.
A more detailed model of covalent bonding requires a consideration of valence shell atomic orbitals. The spatial distribution of electrons occupying each of these orbitals is shown in the diagram below. Very nice displays of orbitals may be found at the following sites: J.
Gutow, Univ. Wisconsin Oshkosh R. Spinney, Ohio State M. Winter, Sheffield University. This means that there are 6 empirical formula units in the molecular formula. When the subscripts of the empirical formula are then multiplied by the integer multiple of six 6 the result yields a molecular formula of glucose C 6 H 12 O 6.
In converse, a molecular formula may be reducible to a simple or empirical formula if all its subscripts are divisible by a common denominator.
For example, nicotine has a molecular formula of C 10 H 14 N 2 that can be divided to obtain the empirical formula of 5 H 7 N. Some experimental methods can be used to determine the molecular formula i. X-ray determination can, for example, allow the actual determination of the positions of atoms in some solids and thus allow direct evidence of the molecular formula. There are compounds that have the same molecular and empirical formula.
For example, methane has both an empirical formula and a molecular formula of CH 4. The simplest whole number ratio of hydrogens to carbon atoms is four hydrogen atoms to every carbon atom. Because CH 4 is also the molecular formula this specifies that in a molecule of methane, four hydrogen atoms are bonded to a single carbon atom.
The empirical formula for water, H 2 O, is also the correct molecular formula for water. The molecular formula for water specifies that two hydrogen atoms are bound to a single oxygen atom. Compounds may also share an empirical formula but dramatically differ in their molecular formulae. For example, acetylene and benzene both have an empirical formula of CH. Acetylene has a molecular formula of C 2 H 2 while benzene, has a molecular formula of C 6 H 6.
Some materials do not actually exist as isolated molecules so it is technically impossible to give a molecular formula for such substances.
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