ATOMS, MOLECULES, AND IONS

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CHAPTER 2

ATOMS, MOLECULES, AND IONS

Development of the Atomic Theory

• Law of conservation of mass: mass is neither created nor destroyed. The total mass before a

chemical reaction always equals the total mass after a chemical reaction.

Law of definite proportion: a given compound always contains exactly the same proportion of elements by mass. For example, water is always 1 g hydrogen for every 8 g oxygen.

Law of multiple proportions: When two elements form a series of compounds, the ratios of the mass of the second element that combine with 1 g of the first element always can be reduced to small whole numbers. For CO

• and CO discussed in section 2.2, the mass ratios

of oxygen that react with 1 g carbon in each compound are in a 2 : 1 ratio.

• From Avogadro’s hypothesis (law), volume ratios are equal to molecule ratios at constant

temperature and pressure. Therefore, we can write a balanced equation using the volume data, Cl

• + 5 F2 → 2 X. Two molecules of X contain 10 atoms of F and two atoms of Cl.

The formula of X is ClF

• for a balanced equation.

• a. The composition of a substance depends on the numbers of atoms of each element

making up the compound (depends on the formula of the compound) and not on the composition of the mixture from which it was formed.

• Avogadro’s hypothesis (law) implies that volume ratios are proportional to molecule

ratios at constant temperature and pressure. H

• + Cl2 → 2 HCl. From the balanced

equation, the volume of HCl produced will be twice the volume of H

• (or Cl2) reacted.

• Avogadro’s hypothesis (law) implies that volume ratios are equal to molecule ratios at

constant temperature and pressure. Here, 1 volume of N

• reacts with 3 volumes of H2 to

produce 2 volumes of the gaseous product or in terms of molecule ratios:

• N 2 + 3 H2 → 2 product

In order for the equation to be balanced, the product must be NH3.

• For CO and CO 2, it is easiest to concentrate on the mass of oxygen that combines with 1 g of

carbon. From the formulas (two oxygen atoms per carbon atom in CO

• versus one oxygen

atom per carbon atom in CO), CO

• will have twice the mass of oxygen that combines per

gram of carbon as compared to CO. For CO

• and C3O2, it is easiest to concentrate on the

(Chemical Principles, 8e Steven Zumdahl Donald DeCoste) (Solution Manual, For Complete File, Download Link at the of this File) 1 / 4

2 CHAPTER 2 ATOMS, MOLECULES, AND IONS

mass of carbon that combines with 1 g of oxygen. From the formulas (three carbon atoms per two oxygen atoms in C 3O2 versus one carbon atom per two oxygen atoms in CO2), C3O2 will have three times the mass of carbon that combines per gram of oxygen as compared to CO 2.As expected, the mass ratios are whole numbers as predicted by the law of multiple proportions.

23. Hydrazine: 1.44 ×

1 10 −

g H/g N; ammonia: 2.16 ×

1 10 −

g H/g N; hydrogen azide:

2.40 ×

2 10 −

g H/g N. Let's try all of the ratios:

0240.0

144.0

= 6.00;

0240.0

216.0

= 9.00;

0240.0

0240.0

= 1.00;

144.0 216.0

= 1.50 =

2 3

All the masses of hydrogen in these three compounds can be expressed as simple whole- number ratios. The g H/g N in hydrazine, ammonia, and hydrogen azide are in the ratios

6 : 9 : 1.

24. Compound 1: 21.8 g C and 58.2 g O ( 80.0 – 21.8 = mass O)

Compound 2: 34.3 g C and 45.7 g O ( 80.0 – 34.3 = mass O)

The mass of carbon that combines with 1.0 g of oxygen is:

Compound 1:

Og2.58 Cg8.21 = 0.375 g C/g O

Compound 2:

Og7.45 Cg3.34 = 0.751 g C/g O The ratio of the masses of carbon that combine with 1 g of oxygen is 1 2 375.0 751.0 = ; this supports the law of multiple proportions because this carbon ratio is a small whole number.

• To get the atomic mass of H to be 1.00, we divide the mass that reacts with 1.00 g of oxygen

by 0.126, that is, 0.126/0.126 = 1.00. To get Na, Mg, and O on the same scale, we do the same division.

Na:

126.0 875.2

= 22.8; Mg:

126.0 500.1

= 11.9; O:

126.0 00.1

= 7.94

H O Na Mg Relative value 1.00 7.94 22.8 11.9 Accepted value 1.0079 15.999 22.99 24.31

The atomic masses of O and Mg are incorrect. The atomic masses of H and Na are close.Something must be wrong about the assumed formulas of the compounds. It turns out that the correct formulas are H 2O, Na2O, and MgO. The smaller discrepancies result from the error in the assumed atomic mass of H.

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CHAPTER 2 ATOMS, MOLECULES, AND IONS 3

The Nature of the Atom

• Deflection of cathode rays by magnetic and electrical fields led to the conclusion that they

were negatively charged. The cathode ray was produced at the negative electrode and repelled by the negative pole of the applied electrical field. β particles are electrons. A cathode ray is a stream of electrons (β particles).

• From section 2.6, the nucleus has “a diameter of about 10

−13 cm” and the electrons “move about the nucleus at an average distance of about 10 −8 cm from it.” We will use these statements to help determine the densities. Density of hydrogen nucleus (contains one proton

only):

V nucleus =

3403143

cm105)cm105()14.3( 3 4 rπ 3 4

−−

××==

d = density = 315 340 24 g/cm103 cm105 g1067.1 × × × = − −

Density of H atom (contains one proton and one electron):

V atom = 32438 cm104)cm101()14.3( 3 4

−−

×× =

d = 3 324 2824 g/cm0.4 cm104 g109g1067.1= −

−−

× ×+×

• From Section 2.6 of the text, the average diameter of the nucleus is approximately 10

−13 cm, and the electrons move about the nucleus at an average distance of approximately cm10 8− .From this, the diameter of an atom is about 2 × cm10 8− .

cm101 cm102 13 8 − − × ×

= 2 × 10

5 ; grape1 in360,63 grape1 ft5280 grape1 mi1 == Because the grape needs to be 2 × 10 5 times smaller than a mile, the diameter of the grape would need to be 63,360/(2 × 10 5

• ≈ 0.3 in. This is a reasonable size for a small grape.
• First, divide all charges by the smallest quantity, 6.40 ×

10 −13 .

13 12

1040.6

1056.2

− − × ×

= 4.00;

640.0 68.7

= 12.00;

640.0 84.3

= 6.00

Because all charges are whole-number multiples of 6.40 × 10 −13 zirkombs, the charge on one electron could be 6.40 × 10 −13 zirkombs. However, 6.40 × 10 −13 zirkombs could be the charge of two electrons (or three electrons, etc.). All one can conclude is that the charge of an electron is 6.40 × 10 −13 zirkombs or an integer fraction of 6.40 × 10 −13 .

• The proton and neutron have similar mass, with the mass of the neutron slightly larger than

that of the proton. Each of these particles has a mass approximately 1800 times greater than that of an electron. The combination of the protons and the neutrons in the nucleus makes up the bulk of the mass of an atom, but the electrons make the greatest contribution to the chemical properties of the atom. 3 / 4

4 CHAPTER 2 ATOMS, MOLECULES, AND IONS

• If the plum pudding model were correct (a diffuse positive charge with electrons scattered

throughout), then α particles should have traveled through the thin foil with very minor deflections in their path. This was not the case because a few of the α particles were deflected at very large angles. Rutherford reasoned that the large deflections of these α particles could be caused only by a center of concentrated positive charge that contains most of the atom’s mass (the nuclear model of the atom).

Elements, Ions, and the Periodic Table

• a. A molecule has no overall charge (an equal number of electrons and protons are present).

Ions, on the other hand, have electrons added to form anions ( negatively charged ions) or electrons removed to form cations (positively charged ions).

• The sharing of electrons between atoms is a covalent bond. An ionic bond is the force of

attraction between two oppositely charged ions.

• A molecule is a collection of atoms held together by covalent bonds. A compound is

composed of two or more different elements having constant composition. Covalent and/or ionic bonds can hold the atoms together in a compound. Another difference is that molecules do not necessarily have to be compounds. H

• is two hydrogen atoms held

together by a covalent bond. H

• is a molecule, but it is not a compound; H2 is a diatomic

element.

• An anion is a negatively charged ion, for example, Cl

− , O 2− , and SO4 2− are all anions. A cation is a positively charged ion, for example, Na + , Fe 3+ , and NH4

• are all cations.

• The atomic number of an element is equal to the number of protons in the nucleus of an atom

of that element. The mass number is the sum of the number of protons plus neutrons in the nucleus. The atomic mass is the actual mass of a particular isotope (including electrons). As is discussed in Chapter 3, the average mass of an atom is taken from a measurement made on a large number of atoms. The average atomic mass value is listed in the periodic table.

• a. Metals: Mg, Ti, Au, Bi, Ge, Eu, and Am. Nonmetals: Si, B, At, Rn, and Br.

• Si, Ge, B, and At. The elements at the boundary between the metals and the nonmetals

are B, Si, Ge, As, Sb, Te, Po, and At. Aluminum has mostly properties of metals, so it is generally not classified as a metalloid.

• a. The noble gases are He, Ne, Ar, Kr, Xe, and Rn (helium, neon, argon, krypton, xenon,

and radon). Radon has only radioactive isotopes. In the periodic table, the whole number enclosed in parentheses is the mass number of the longest-lived isotope of the element.

• promethium (Pm) and technetium (Tc)

• Carbon is a nonmetal. Silicon and germanium are called metalloids as they exhibit both

metallic and nonmetallic properties. Tin and lead are metals. Thus metallic character increases as one goes down a family in the periodic table. The metallic character decreases from left to right across the periodic table.

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