Gen Chem Ch 1
Element Q consists of 3 different isotopes: A, B, and C. isotope A has an atomic mass of 40amu and accounts for 60% of naturally occurring Q. isotope B has an atomic mass of 44 amu and accounts for 25% of Q. finally, isotope C has an atomic mass of 41amu and accounts for 15% of Q. What is the atomic weight of element Q?
0.6(40amu)+ 0.25(44 amu)+ 0.15(41 amu) = 24.00 amu+ 11.00 amu+ 6.15 amu= 41.15 amu atomic weight of Q= 41.15 g/mol.
what are the lowest s, p, d, and f subshells?
1s, 2p, 3d, 4f
determine the number of protons, neutrons and electrons in a nickel-58 atom and in a nickel-60 +2 cation
58^Ni has an atomic number of 28 and a mass number of 58. Therefore 58^Ni will have 28 protons, 28 electrons , and 58-28 or 30 neutrons 60^Ni^2+ has the same number of protons. However it has lost 2 electrons: 26 electrons Also the mass unit is 2 units higher than that for 58^Ni: 32 neutrons
Avogardo's number
A mole is a number of "things" (atoms, ions, molecules) equal to Avogardo's number. For example, the atomic weight of carbon is 12.0 g/mol, which means that the avg carbon atom has a mass of 12.0amu (C-12 is far more abundant than C-13 or 14), and 6.02x10^23 carbon atoms have a combined mass of 12.0g.
Isotopes
Atoms that share an atomic number but have different mass numbers. convention [format] to show both the atomic number (Z) and the mass number (A) of atom X is pictured.
Bohr model (structure)
Bohr came to describe the structure of the hydrogen atom as a nucleus with 1 proton forming a dense core, around which a single electron revolved in a defined pathway (*orbit*) at a discrete energy value. If one could transfer an amount of energy exactly equal to the difference between one orbit and another, this could result in the electron "jumping" from one orbit to a higher-energy one. These orbits had increasing radii, and the orbit with the smallest, lowest-energy radius was defined as the *ground* *state* (n=1). Bohr likened his model of the hydrogen atom to the planets orbiting the sun, in which each planet traveled along a roughly circular pathway at set distances- and energy values- from the sun. Bohr's Nobel Prize winning model was reconsidered over the next two decades but remains an important conceptualization of atomic behavior. In particular, remember that we now know that electrons are not restricted to specific pathways, but tend to be localized in certain regions of space. The Bohr model is useful for explaining the atomic emission and absorption spectra of atoms.
Bohr took the equation L= nh/2π then related the permitted angular momentum values to the *energy* *of* *the* *electron* to obtain:
E= -(R_H)/n^2. Where R_H is the experimentally determined *Rydberg* *unit* *of* *energy*, equal to 2.18x10^-18 J/electron. Therefore like angular momentum, the energy of the electron changes in discrete amounts with respect to the quantum number. A value of zero energy was assigned to the state in which the proton and electron are separated completely, meaning that there is no attractive force between them. Therefore, the electron in any of its quantized states in the atom will have an attractive force toward the proton; this is represented by the negative sign. Ultimately, the only thing the energy equation is saying is that the energy of an electron increases- becomes less negative- the farther out from the nucleus that it is located (increasing n). This is an important point: while the magnitude of the fraction is getting smaller, the actual value it represents is getting larger (becoming less negative). At first glance, it may not be clear that the energy (E) is directly proportional to the principal quantum number (n). Take notice of the negative sign, which causes the values to approach zero from a more negative value as n increases (thereby increasing the energy). Negative signs are as important as a variable's location in a fraction when it comes to determining proportionality.
The energy associated with a change in the principal quantum number from a higher intial value n_i to a lower final value n_f is equal to the energy of the photons predicted by Planck's quantum theory. Combining Bohr's and Planck's calculations we can derive:
E= hc/λ= -R_H[1/n_i² - 1/n_f²] This complex looking equation essentially says: the energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower energy final state. This equation is nothing new. It is simply derived from the conservation of energy by setting the energy of a photon (E=hf=hc/λ) equal to the energy of the electron transition (from E=-R_H/n²). Note that unlike other equations, this is initial minus final; the negative sign in the equation accounts for absorption and emission, and a negative E corresponds to absorption.
*parallel* *spins*.
Electrons in different orbitals with the same m_s values are said to have *parallel* *spins*.
mass number (A)
Every atom has a characteristic mass number (A), which is the sum of the protons and neutrons in the atoms nucleus. A given element can have a variable number of neutrons; thus while the atoms of the same element always have the same atomic number, they do not necessarily have the same mass number.
Hund's rule
In subshells that contain more than one orbital, such as the 2p subshell with its 3 orbitals, the orbitals will fill according to hunds rule, which states that w/n a given subshell, orbitals are filled such that there are a max number of half filled orbitals with parallel spins. e-s prefer to have their own orbital before being forced to double up with another electron. Of course, the basis for this preference is electron repulsion: electrons in the same orbital tend to be closer to each other and thus repel each other more than e-s placed in different orbitals An important corollary from Hund's rule is that half-filled and fully filled orbitals have lower energies (higher stability) than other states. This creates two notable exceptions to electron configuration that are often tested on the MCAT: chromium (and other elements in this group) and copper (and other elements in this group). Chromium (z=24) should have the electron configuration [Ar]4s²3d⁴ according to the rule established earlier. However, moving one electron from the 4s subshell to the 3d subshell allows all the 3d subshells to be half-filled: [Ar] 4s¹3d⁵. While moving the 4s electron up to the 3d-orbital is energetically unfavorable, the extra stability from making the 3d subshell half-filled outweighs the cost. Similarly with copper: [Ar]4s¹3d¹⁰> [Ar]4s²3d⁹, a full d subshell outwighs the cost of moving an electron out of the 4s subshell. Similar shifts can be seen with f subshells, but they are never observed for the p subshell; the extra stability doesnt outweight the cost.
According to Hund's rule, what is the orbital diagram for iron?
Iron has an atomic number of 26. As determined earlier, its electron configuration is [Ar]4s²3d⁶. The electrons will fill all of the subshells except for 3d, which will contain 4 orbitals with parallel (upward) spin and one orbital with electrons of both spin directions
Planck Relation and Constant
Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta. The *energy* of a quantum, he determined is given by the planck relation. E=hf. Where h is a proportionality constant known as *Planck's* *constant* equal to 6.626 x10^-34 J*s, and f (sometimes designated by the Greek letter nu, ν) is frequency of the radiation The speed of light (or any wave) can be calculated using ν=fλ. the speed of light, c, is 3*10^8 m/s. This equation can be incorporated into the equation for quantum energy to provide different derivations
What is the electron configuration of Fe³⁺?
The electron configuration of iron is [Ar]4s²3d⁶. Electrons are removed from the 4s subshell before the 3d subshell because it has a higher principal quantum number(4s= (n+l)= 4+0=4 vs 3d=(n+l)=3+2=5). Therefore, Fe³⁺ has a configuration [Ar]3d⁵ NOT [Ar]4s²3d³
valence electrons
The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called *valence* *electrons*; they are much more likely to become involved in bonds with other atoms bc they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom. the sharing of these valence electrons in covalent bonds allow elements to fill their highest energy level to increase stability.
Lyman series
The group of hydrogen emission lines corresponding to transitions from energy levels n > or = 2 to n=1 is known as the Lyman series. The Lyman series includes larger energy transitions than the Balmer series; it therefore has shorter photon wavelengths in th UV region of the electromagnetic spectrum [bc E=hc/λ]
Balmer series
The group of hydrogen emission lines from energy levels n> or =3 to n=2 is known as the Balmer series, and includes 4 wavelengths in the visible region.
What is the electron configuration of osmium (Z=76)?
The noble gas that comes just before osmium is xenon (Z=54) therefore, the electron configuration can begin with [Xe]. Continuing across the periodic table, we pass through the 6s subshell (cesium and barium), the 4f subshell, and into the 5d subshell. Osmuis is the sixth element in the 5d subshell so the configuration is: [Xe]6s²4f¹⁴5d⁶
Paramagnetic
The presence of paired or unpaired electrons affects the chemical and magnetic propetires of an atom of molecule. Materials composed of atoms with unpaired electrons will orient their spins in alignment with a magnetic field and thus be weakly attracted to the magnetic field. These materials are considered paramagentic. Remember that *para*magnetic means that a magnetic field will cause *para*llel spins in unpaired electrons and therefore cause an attraction.
Azimuthal (angular momentum) quantum number.
The second quantum number. is designated by the letter l. The second quantum number refers to the shape and number of *subshells* within a given principal energy level (shell). The azimuthal quantum number is very important bc it has important implications for chemical bonding and bond angles. The value of n limits the value of n in the following way: for any given value of n, the range of possible values for l is 0 to (n-1). for ex, within the first principle energy level n=1 the only possible value for l is 0 . A simpler way to remember this relationship is that the n-value also tells you the possible # of subshells. Therefore theres only one subshell (l=0) in the first principal energy level; there are two subshells (l=0 and 1) within the second principal energy level; there are 3 subshells (l=0,1, and 2) within the 3rd principal energy level. For any principal quantum number, n, there will be n possible values for l ranging from 0 to (n-1).
Which e-s are the valence electrons of elemental vanadium, elemental selenium, and the sulfur atom in a sulfate ion?
Vanadium has 5 valence electrons: two in its 4s subshell and three in its 3d subshell. Selenium has 6 valence electrons: two in its 4s subshell and four in its 4p shubshell. Selenium's 3d e-s are not part of its valence shell. Sulfur in a sulfate ion has 12 valence elections. its original 6 plus 6 more from the oxygens which it is bonded. Suflurs 3s and 3p subshells can contain only 8 of these 12 e-s; the other 4 e-s have entered the sulfur atoms 3d subshell, which is normally empty in elemental sulfur.
Neutrons
are neutral. no charge. a neutrons mass is only slightly larger than that of the proton, and together the protons and neutrons of the nucleus make up almost the entire mass of an atom
Atomic Emission Spectra and equation for the electromagentic energy of photons
at room temp, the majority of atoms in a sample are in the ground state. However, electrons can be excited to higher energy levels by heat or other energy forms to yield excited states. bc the lifetime of an excited state is brief, the electrons will return rapidly to the ground state, resulting in the emission of discrete amounts of energy in the form of photons. The electromaagnetic energy of these photons can be determined using the following equation: E=hc/λ where h is planck's constant, c is the speed of light in a vacuum (3*10^8 m/s) and λ is the wavelength of the radiation. Note this equation is just a combination of E=hf and c=fλ. The e-s in an atom can be excited to different energy levels. When these e-s return to their ground states, each will emit a photon with a wavelength characteristic of the specific energy transition it undergoes. As described above, these energy transitions do not form a continuum, but are quantized. Thus the spectrum is composed of light at specified frequencies.
atomic mass/ mass number
atomic mass of an atom(in amu) is nearly equal to its *mass* *number*. The sum of protons and neutrons (in reality some mass is lost as binding energy). Atoms of the same element with varying mass numbers are called *isotopes*. because isotopes have the same number of protons and electrons, they generally exhibit similar chemical properties.
(n+l) rule
can be used to rank subshells by increasing energy. This rule states that the lower the sum of the values of the first and second quantum numbers (n+l), the lower the energy of the subshell. This is a helpful rule for Test Day. If 2 subshells possess the same (n+l) value, the subshell with the lower n value has a lower energy and will fill with electrons first.
Paschen series
corresponds to transitions from n> or 4 to n=3. Energy is inversely proportional to wavelength. E=hf=hc/λ
principal quantum number.
denoted by the letter n. This is the quantum number used in Bohr's model that can theoretically take on any positive integer value. The larger the integer of n, the higher the energy level and radius of the electrons *shell*. within each shell there is a capacity to hold a certain number of electrons given by: Max # if e-s w/n a shell= 2n² The difference in energy between two shells decreases as the distance from the nucleus increases bc the energy difference is a function of [1/n_i² - 1/n_f²]. The energy difference between the n=3 and n=4 shells (1/9-1/16) is less than the energy difference between the n=1 and n=2 shells (1/1-1/4). Remember, a larger integer value for the principal quantum number indicates a larger radius and higher energy, similar to gravitational potential energy in physics.
Aufbau or building up principle
electrons fill from lower to higher energy subshells, and each subshell will fill completely before electrons begin to enter the next one.
orbitals
electrons move rapidly and are localized within regions of space around the nucleus called *orbitals*
Atomic number (Z)
equal to the # of protons found in an atom of that element. As such it acts as a unique identifier for each element bc elements are defined by the number of protons they contain. For ex, all atoms of oxygen contain eight protons. While all atoms of a given element have the same atomic number, they do not necessarily have the same mass *[isotopes]*
Application of the (n+1) rule: which will fill first, the 5d subshell or the 6s subshell?
for 5d, n=5 and l=2 so (n+l)=7. For 6s, n=6 and l=0 so (n+l )= 6 Therefore the 6s subshell has lower energy and will fill first
Electron configuartion
for a given atom or ion, the pattern by which subshells are filled as well as the number of electrons w/n each principal energy level and subshell are designated by its electron configuration. Electron configuration use spectroscopic notation wherein the first number denotes the principal energy level, the letter designates the subshell, and the superscript gives the number of electrons in that subshell. For ex, 2p⁴ indicates that there are four electrons in the second (p) subshell of the second principal energy level. This also implies that the energy levels below 2p (that is, 1s and 2s) have already been filled. Remember that the shorthand used to describe the electron configuration is derived directly from the quantum numbers.
protons
found in the nucleus of the atom. Each proton has an amount of charge equal to the fundamental unit of charge (e= 1.6x 10^-19C), and we denote this fundamental unit of charge as "+1 e" or simply "+1" for the proton. Protons have a mass of approximately amu.
half-life
half-lifes of different isotopes corresponds with stability; generally more long lasting isotopes are more abundant- therefore helps determine the relative proportions of these different isotopes.
quanta
in 1910, Ernest Rutherfor provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the atoms volume. 11 years earlier, Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta
Bohr model (equation derivation)
in 1913. Danish physicist Niels Bohr used the work of Rutherford and Planck to develop his model of the electronic structure of the hydrogen atom. Starting from Rutherford's findings, Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit. He postulated that the centripetal force acting on the electron as it revolved around the nucleus was created by the electrostatic force between the positively charged proton and negatively charged electron. Bohr used Planck's quantum theory to correct certain assumptions that classical physics made about the pathways of electrons. classical mechanics postulates that an object revolving in a circle, such as an electron may assume an infinite number of values for its radius and velocity. The angular momentum (L=mvr) and kinetic energy (K= 1/2mv^2) of the object could therefore take on any value. However, by incorporating Planck's quantum theory into his model, Bohr placed restrictions on the possible values on the angular momentum. Bohr predicted that the possible values for the *angular* *momentum* of an electron orbiting a hydrogen nucleus could be given by: L= nh/2π where n is the principal quantum number, which can be any positive integer and h is Planck's constant. bc the only variable is the principal quantum number, the angular momentum of an electron changes only in discrete amounts with respect to the principal quantum number. Note the similarities between quantized angular momentum and Planck's concept of quantized energy (E=hf)
absorption spectrum
in addition to a unique admission spectrum, every element possesses a characteristic absorption spectrum. Not surprisingly, the wavelengths of absorption correspond exactly to the wavelengths of emission bc the difference in energy levels remain unchanged. Identification of elements in the gas phase requires absorption spectra. absorption is the basis for the color of compounds. We see the color of the light that it not absorbed by the compound.
Atomic weight
in nature almost all elements exist as two or more isotopes, and these isotopes are usually present in the same proportions in any sample of a naturally occurring element. the weighted average of these different isotopes is referred to as the *atomic* *weight* and is the number reported on the periodic table. For example chlorine has 2 naturally occurring isotopes: Cl-35 and Cl-37. Cl-35 is about 3x more abundant than 37. Therefore the atomic weight is closer to 35 than 37 (35.5) When an element has 2 or more isotopes, no one isotope will have a mass exactly equal to the element's atomic weight. Bromine, for example, is listed in the periodic table as having a mass of 79.9 amu. This is an avg of the two naturally occurring isotopes, bromine-79 and bromine-81, which occur in almost equal proportions. There are no bromine atoms with an actual mass of 79.9 amu The utility of the atomic weight is that it represents both the mass of the "average" atom of that element, in amu, and the mass of one mole of the element, in grams.
Heisenberg uncertainty principle
it is impossible to simultaneously determine, with perfect accuracy, the momentum and position of an electron. If we want to assess the position of an electron an electron has to stop; if he want to assess its momentum, the electron has to be moving
orbitals and the periodic table
looking at the 2p block in the periodic table, 2p contains 3 orbitals. If each orbital can contain 2 electrons, then 6 electrons can be added during the course of filling the 2-p orbitals. As atomic number increases, so does the number of electrons (assuming the species is neutral). Therefore, it should be no surprise that the p block contains 6 groups of elements. The s block contains 2 elements in each row of the periodic table, the d contains 10 and the f contains 14.
diamagnetic
materials consisting of atoms that have all paired electrons will be slightly repelled by a magnetic field and are said to be diamagnetic. Given sufficiently strong magnetic fields beneath an object any diamagnetic substance can be made to levitate.
Atomic mass vs Atomic weight
mnemonic: atomic *mass* is nearly synonymous with *mass* number. Atomic *weight* is a *weighted* average of naturally occurring isotopes of that element.
Electrons
move through the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal in magnitude to that of a proton, but with the opposite sign [neg], denoted by "-1e" or simply "-e". The mass of an electron is approximately 1/2000 of a proton. bc subatomic particles masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses. Electrons move around the nucleus at varying distances, which correspond to varying levels of electrical potential energy. The electrons closer to the nucleus are at lower energy levels, while those that are further out (in higher *shells*) have higher energy. The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called *valence* *electrons*; they are much more likely to become involved in bonds with other atoms bc they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom
anion
neg charged atom; caused by gaining electrons
Pauli exclusion principle
no two electrons in a given atom can possess the same set of four quantum numbers. The position and energy of an electron described by its quantum numbers is known as its energy state. The value of n limits the values of l, which limits the values of m_l. For a given value of n, only particular values of l are permissible; given a value of l, only particular values of m_l are permissible. The values of the quantum numbers qualitatively give info about the orientation of the orbitals. Think of the quantum numbers as becoming more specific as one goes from n to m_s. n= state l= city m_l= street m_s= house
ground state
of an atom is the state of lowest energy, in which all electrons are in the lowest possible orbitals. In Bohr's model, the electron was promoted to an orbit with a larger radius (higher energy), the atom was said to be in the excited state.
cation
postively charged atom; caused by losing electrons
spectroscopic notation
refers to the shorthand representation of the principal and azimuthal quantum numbers. the principle quantum number remains a number, but the azimuthal quantume number is designated by a letter: the l=0 subshell is called s; the l=1 subshell is called p; the l=2 subshell is called d and the 1=3 subshell is called f. Thus an electron in the shell n=4 and subshell l=2 is said to be in the 4d subshell. Within each subshell there is a capacity to hold a certain number of electrons given by: maximum number of electrons within a subshell= 4l+2 where l is the azimuthal quantum number. The energies of the subshells increases with increasing l value, however, the energies of subshells from different principal energy levels may overlap. For ex, the 4s subshell will have a lower energy than the 3d subshell.
Spin quantum number.
the fourth quantum number is called the spin quantum number and is denoted by m_s. In classical mechanics, an object spinning about its axis has an infinite number of possible values for its angular momentum. However, this does not apply to the electron, which has two spin orientations designated +1/2 and -1/2. Whenever 2 electrons are in the same orbital, they must have opposite spins. In this case, they are often referred to as as being *paired*. Electrons in different orbitals with the same m_s values are said to have *parallel* *spins*.
atomic mass unit
the mas of one proton is approximately one amu. The size of the atomic mass unit is defined as exactly 1/12 the mass of the carbon 12 atom, approximately 1.66x10^-24g. bc the carbon 12-nucleus has 6 protons and 6 neutrons, an amu is approximately equal to the mass of a proton or neutron. The difference in mass between protons and neutrons is extremely small; in fact it is roughly equal to the mass of an electron.
magnetic quantum number
the third quantum number. designated by m_l. The magnetic quantum number specifies the particular *orbital* within a subshell where an electron is most likely to be found at a given moment in time. Each orbital can hold a max value of 2 electrons. The possible values of m_l are the integers between -l and +l including 0. For example, the s subshell, with l=0 limits the possible m_l values to 0, and bc there is a single value of m_l there is only one orbital in the s subshell. The p subshell, with l=1 limits the possible m_l values to -1, 0, and +1. and bc there are 3 values for m_l there are 3 orbitals in the p subshell. The d subshell has 5 orbitals (-2 to +2) and the f subshell has seven orbitals (-3 to +3). the shape of the orbitals like the number of orbitals, is dependent on the subshell in which they are found. the orbitals in the s subshell are sphereical while the 3 orbitals in the p subshell are dumbell shaped and align along the x, y, and z axes. In fact, the p orbitals are often referred to as px, py, and pz.
quantized energy analogy
think of the concept of quantized energy as being similar to the change in gravitational potential energy that you experience when you ascend or descend a flight of stairs. Unlike a ramp, on which you could take an infinite number of steps associated with a continuum of potential energy changes, a staircase only allows you certain changes in height, and as a result, allows only certain discrete (quantized) changes of potential energy
excited state
when at least one electron has moved to a subshell of higher than normal energy. All systems tend toward minimal energy; thus on the MCAT, atoms of any element will generally exist in the ground state unless subjected to extremely high temperatures or irradiation. mnemonic: as electrons go from a lower energy level to higher energy level they get *AHED* -Absorb light -Higher potential -Excited -Distant (from the nucleus)
line spectrum or atomic emission spectrum
where each line on the emission spectrum corresponds to a specific electron transition. Bc each element can have its electrons excited to a different set of distinct energy levels, each possesses a unique *atomic* *emission* *spectrum*, which can be used as a fingerprint for the element. one particular application is the analysis of stars and planets: while a physical sample may be impossible to procure, the light from a star can be resolved into its component wavelengths which are then matched to the known line spectra of the elements. emissions from electrons dropping from an excited state to a ground state give rise to fluorescence. What we see is the color of the emitted light.
