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Prep Chem

04/25/09

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Atomic Theory


�Before You Begin:

To master this material you need to understand the difference between a law and a theory, specifically, you need to accept the idea that we will use more than one theory, depending on the task at hand. To be able to answer the concept check questions, you will need a periodic table or list of the elements and their atomic numbers.


 

Dalton’s Atomic Theory

There were a few important theories that tried to explain what was happening on a fundamental level during chemical changes. Some chemistry professors will want their students to know which ancient Greek first postulated the existence of the atom, for example. Although everybody agrees, in principle, that a foundation in the history of chemistry is nice, the guys who actually expect you to know this stuff coming in to General Chemistry are in the minority. However, everyone will expect you to know Dalton and his theory. That is because half of the first semester lab experiments are based on Dalton’s model of the atom.

Postulates of Dalton’s theory

·        Matter is made up of tiny, indivisible particles called atoms.

·        The atoms of any given element are identical to one another and different from the atoms of any other element.

·        Atoms are neither created nor destroyed during ordinary chemical reactions, nor are they converted to another type of atom.

·        During chemical changes atoms are regrouped to form chemical compounds which always contain the same type and relative proportion of atoms.

 

Law of conservation of matter (or mass)

During any ordinary chemical reaction, mass is neither lost nor gained. This was known in Dalton’s time. It is explained by the idea that atoms are finite and indestructible, so a sample of matter can’t lose or gain mass because it doesn’t lose or gain atoms.

 

Law of constant composition

A compound always contains the same types of elements in the same relative proportions by mass. For example, water is always formed from hydrogen and oxygen and no other elements, and, water has 8 grams of oxygen for every gram of hydrogen. This law was known in Dalton’s day. It is explained by the idea that chemical reactions are groupings of atoms.

 

Law of multiple proportions

If two or more elements can combine to form two or more compounds, for a fixed amount of one of the elements, the other(s) will be present in the compounds in small whole number ratios. Huh? This is complicated, so we’ll try it one more time. Let’s limit the discussion to the simplest case. Suppose we have two compounds that are made from the same elements. They differ by the relative amounts of those elements. Not only that, but, if we make each of the compounds from the same amount of one of the elements, we find that the quantity (mass) of the other element needed will always be a small, whole number ratio. For example, carbon reacts with oxygen to form two compounds, carbon monoxide and carbon dioxide. If you start with the same amount of carbon in each case, the carbon dioxide requires twice as much oxygen as the carbon monoxide. The law of multiple proportions was Dalton’s own. He developed the theory to try to explain this body of observations. Dalton’s theory can be used to explain the carbon monoxide/dioxide situation: it takes twice as much oxygen to form carbon dioxide because each carbon atom needs two oxygen atoms whereas each carbon atom only needs one oxygen atom to make carbon monoxide. This seems really obvious to us because of the names (the di- and mono- prefixes give us a clue). However, the original name for carbon dioxide was “gas sylvestre” which is no help at all.

 

So, what is the difference between the law of constant composition and the law of multiple proportions? The law of constant composition compares the amounts of two elements in one compound while the law of multiple proportions compares the amounts of two elements in two compounds. Actually, by reducing one of the elements to unity, the law of multiple proportions finds a whole number ratio of the other one element in two compounds (and, therefore, is much more complicated).

 

Comparison Between The Law of Constant Composition and The Law of Multiple Proportions

 

The Law of Constant Composition

The Law of Multiple Proportions

Statement

A compound always contains the same elements in the same proportion by mass.

If two (or more) elements can combine to form two (or more) compounds, for a set amount of one of the elements in each compound, the other(s) will be present in a small whole number ratio by mass.

Example

Cupric oxide always contains copper and oxygen, and it is always 79.9% copper, by mass.

Copper and oxygen form two compounds: cuprous oxide and cupric oxide. If both compounds are made using 1.0 gram of oxygen, the cuprous oxide requires 8.0 grams of copper, and the cupric oxide requires 4.0 grams of copper. This is a two to one ratio.

The Difference

Relative amounts of two elements (copper and oxygen) in one compound (cupric oxide).

Relative amounts of one element (copper) in two compounds (cuprous and cupric oxides)—assuming a set amount of the other element (oxygen).

 

 

Modern Atomic Theory

Parts of the atom

The nucleus—the central portion of the atom containing most of the mass but least of its volume. It is composed of

Protons—positively charged subatomic particles. Each element has a unique number of protons.

Neutrons—neutral subatomic particles are called nuetrons. The atoms of an element may have different numbers of neutrons. If so, they are said to be isotopes of one another. For example, carbon has three different naturally occurring isotopes. All of the isotopes of carbon have six protons in their nuclei. One of the isotopes has six neutrons, one has seven, and one has eight.

 

Outside the nucleus (where the electrons live): the outer portion of the atom, containing least of the mass yet having most of the volume.

Electrons—very small subatomic particles with negative charge, move through this volume of space outside the nucleus. This volume of space is organized into shells, subshells, and orbitals. That involves quantum mechanics, which we will postpone as long as possible.

Atomic number, mass number, atomic weight, and charge

Atomic number—the number of proton in an atom of an element. For example, all of the atoms of the element iron have 26 protons, so the mass number of iron is 26. The atomic number is unique for each element. During nuclear reactions, an element may change into another. For clarity and as an aid to balancing nuclear reaction equations, the atomic number may be written as part of the atomic symbol. If so, it appears at the bottom left, as 26Fe.

Mass number—the number of protons and neutrons in an atom of a specific isotope of an element. For example, oxygen has an atomic number of eight. The isotope of oxygen having ten neutrons has a mass number of 18. The atomic symbol may include the mass number, if it is relevant. The mass number is written at the top left, as 18O.

Atomic weight—the average mass of the atoms of an element taking into account the masses of the various isotopes and their relative abundance. For example, oxygen has an atomic weight of 15.9994. This means that the average of the atoms’ masses is 15.9994 atomic mass units (amu). A proton has a mass of slightly more than one amu as does a neutron. An electron’s mass is so small that it would close to two thousand electrons to be as massive as a proton. Most of the naturally occurring atoms of oxygen have eight protons, eight neutrons, and eight electrons giving a mass of close to 16 amu. Many students assume that the mass number (always an integer) is a rounded form of the atomic weight (never an integer). NOPE. The atomic weight is an average while the mass number is a particle count. The atomic weight can be found on the periodic table. It is never written as part of an atomic symbol.

 


4Concept Check: What is that mass number of the isotope of zinc that has 37 neutrons?

Answer: The atomic number of zinc is 30 (found on the periodic table). The mass number is equal to the number of protons, 30, plus the number of neutrons, 37. Therefore, the mass number is 67.


 


4Concept Check: What is the atomic symbol for this isotope of zinc; include the atomic number and mass number.

Answer: zinc symbol is Zn with 67 mass number and 30 atomic number


Charge—an electrical charge is the characteristic of a sample of matter that determines how that sample will behave in an electro-magnetic field. There are three states of charge: positive, negative, and neutral (none). Two objects with the same charge will repel one another. Two objects that have opposite charges (one positive and one negative) will be attracted to one another. Atoms are neutral (have no charge) yet they are made up of positively and negatively charge particles (protons and electrons). The charge on the proton is exactly the same strength as the charge on the electron, so they cancel one another out. An ion is an atom that has a charge because it has lost or gained electrons (note that protons are not lost or gained). Electrons are negatively charged, so an atom that has lost electrons is a positively charged ion. Another name for a positively charge ion is a cation. An atom that has gained electrons is a negatively charged ion. Another name for a negatively charged ion is an anion. The charge is always written as part of the symbol and can be found at the upper right. Examples are Mg+2 and Br-1.

 


4Concept Check: What is the charge on a sulfur ion that has 18 electrons?

Answer: Sulfur has an atomic number of 16 (found on the periodic table). That means that the neutral atom has 16 protons. If the ion has 18 electrons, its charge is. Note that, since the protons are positively charged and the electrons are negatively charged, if we subtract the number of electrons from the number of protons, the algebraic sign will correspond to the charge of the ion.


 


4Concept Check: Write the symbol for this ion (include the charge only).

Answer: S-2


Subscripts:

This topic doesn’t really belong here, but, since we have been dealing with atomic symbols, we should include subscripts for clarity’s sake. The smallest particle of many elements is the atom. The atomic symbol identifies which of roughly one hundred elements, and it also may include information about the number of subatomic particles in that particular atom/ion. The smallest particle of the naturally occurring form of some elements is a group of atoms joined together. This atom group is known as a molecule. A number at the lower right of the atomic symbol tells how many atoms are in that molecule. For example, there are two naturally occurring forms of oxygen, one called simply oxygen and one called ozone. Oxygen molecule has two oxygen atoms joined together. Ozone has three oxygen atoms joined together. Their molecular symbols are O2 and O3, respectively.

If a substance consists of atoms that are joined together, its formula must include the subscript. If a particle has lost or gained electrons and has a charge, its formula must include that charge. The mass numbers and atomic numbers are only included in the symbol if that information is pertinent to the discussion.

Symbol Format

 atomic symbol format

 

 

Readers’ Digest Condensed Version of Quantum Mechanics

We can’t put it off any longer. Quantum mechanics is a theory that describes the behavior of the electrons in an atom. Quantum mechanics is fascinating and very rewarding to study. Unfortunately, it is also rather difficult to understand. Your freshman chemistry instructor will not expect you to understand quantum mechanics. However, he or she will expect you to be familiar with the terms and to be able to apply the major conclusions of the theory. Remember, theories are just tools. If quantum mechanics weren’t useful, we would not bother with it.

The major concepts:

This is a descriptive overview of the theory rather than a rigorous treatment. Quantum mechanics is based on the probability of finding an electron in a particular volume of space. This probability can be stated by a mathematical function. This function has four index numbers designated by the letters n, l, ml, and s. The principle quantum number, n, gives us an idea of how far, on average, the electron is likely to be from the nucleus and how much energy it has. The azimuthal quantum number, l, gives the shape of the volume of space the electron is likely to occupy and more specific information about its energy. The magnetic quantum number, ml, identifies which one of a set of volumes the electron occupies. The spin quantum number, ms, gives the magnetic properties of the electron in question and pinpoints which of two electrons. Together, the set of index numbers serve to locate the most probable volume that is likely to contain an electron with specific characteristics.

The set of quantum numbers is kind of like an electron’s address. Imagine electrons live in tiny little houses, two electrons per house. A set of quantum numbers would be an electron’s mailing address. The principle number, n, would be the state, but a state is a pretty big place. We can use l and ml to specify the town, then the street number of the electron’s address. This gives us a house where two opposite (boy and girl) electrons live. The ms quantum number, either up or down, tells which of the two electrons (Mr. or Mrs.). This gives us the most probable place to find the electrons, but just because we know the address doesn’t mean that the electrons are there. You aren’t always at home, either. This is just an analogy, and it isn’t a very good one because the electrons are not unique individuals with a set address.

Important terms:

Orbital—a volume that can hold at most two electrons is known as an orbital. The electrons in an orbital have the same values for the first three quantum numbers but they have different and opposite spin quantum numbers.

Subshell—a set of orbitals with the same shape and energy is called a subshell. The subshell is indicated by the value of the second quantum number, ml. The shapes of orbitals in a subshell are designated by letter names: s, p, d, and f. The s orbitals are spherical. The p orbitals are shaped like double teardrops. The d and f orbitals’ shapes are complicated. There is one s orbital per s subshell. There are three p orbitals per p subshell. There are five d orbitals per d subshell. There are seven f orbitals per f subshell. See the table below for the possible orbitals in the first four shells.

Shell—a set of subshells with about the same average distance from the nucleus is called a shell. All of the orbitals in a shell have the same principle quantum number, n. As the value for n increases, the energy and distance from the nucleus also increase. The value of n also sets the number of subshells and orbitals. See below.

Spin—the spin is a characteristic of an electron that is similar to the N or S pole of a magnet. A pair of electrons in an orbital must have opposite spins.

Ground state—when the atom has the lowest possible energy, its electrons are in the lowest energy orbitals. This is called the ground state.

 

Summary of Subshell Information

Value of n

Subshell Name

Subshell Shape

(Centered at the Nucleus)

Maximum # Electrons

1

1s

Sphere

2

2

2s

2p

Sphere

double teardrop

2

6

3

3s

3p

3d

Sphere

Double teardrop

Four leafed clover

2

6

10

4

4s

4p

4d

4f

Sphere

Double teardrop

Four leafed clover

Sea urchin?

2

6

10

14

 

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