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Lecture Notes

CHEM 142

Chapter 2

Atoms, Molecules, and Ions

2.2: Fundamental Chemical Laws

  • Lavoisier explained the true nature of combustion.
  • Law of Conservation of Mass: mass is neither created nor destroyed.
  • Law of Definite Proportion: a given compound always contains exactly the same proportion of elements by mass.
  • Law of Multiple Proportions: when two elemetns form a series of compounds, the ratios of the masses of the second element that combine with 1 gram of the first element can always be reduced to small integers.

2.3: Dalton’s Atomic Theory

Key elements of Dalton’s model:

  1. Each element is made up of tiny particles called atoms.
  1. The atoms of a given element are identical; the atoms of different elements are different in some fundamental way or ways.
  1. Chemical compounds are formed when atoms combine with each other. A given compound always has the same relative numbers and types of atoms.
  1. Chemical reactions involve reorganization of the atoms—changes in the way they are bound together. The atoms themselves are not changed in a chemical reaction.
  • Avagadro’s hypothesis: at the same temperature and pressure, equal volumes of different gases contain the same number of particles.

2.4: Cannizzaro’s Interpretation

Two main beliefs:

  1. Compounds contained whole numbers of atoms as Dalton postulated.
  1. Avaadro’s hypothesis is correct.

2.5: Early Experiments to Characterize the tom

The Electron

  • J. J. Thomson studied electrical discharges in partially evacuated tubes called cathode-ray tubes.
  • A cathode ray emanating from the negative electrode is emitted when a high voltage is applied to the tube.
  • This ray was hypothesized to be a stream of electrons.


  • Three types of radioactive emission were studied in the late 20th century: \(\gammma$ rays,\)\belta\(particles, and\)\alpha$$ particles.

The Nuclear Atom

  • Ernest Rutherford tested the plum pudding model by directing \(\alpha\) particles at a thin sheet of metal foil. The results disproved the plum pudding model.
  • The nuclear atom was instead proposed.

2.6: The Modern View of Atomic Structure: An Introduction

  • The nucleus is assumed to contain protons and neutrons.
  • Atomic number \(Z\) (number of protons)
  • Mass number \(A\) (number of protons and neutron)

2.7: Molecules and Ions

  • Covalent bonds - bonds share electrons, forming molecules.
  • Molecules can be represented by chemical formulas.
  • Positive ion - cation. Negative ion - anion.
  • Ionic bonding - attraction between oppositely charged ions.
  • Polyatomic ions - many atom ions.

2.8: An Introduction ot the Periodic Table

  • Most elements are metals - these have efficient conduction of heat and electricity, malleability, ductility, and a lustrous eappearance.
  • Metal atoms tend to lose electrons to form postiive ions.
  • Nonmetals appear in the upper right hand corner of the table (expect hydrogen).
  • Nonmetals bond to each other by forming covalent bonds.
  • Groups often have similar chemical properties.

2.9: Naming Simple Compounds

  • Binary ionic compounds contain a positive ion and a negative ion, written in that order.
  • The charge on the metal ion must be specified for metals that form more than one type of ionic compound.
  • The ion with the higher charge has a name ending in -ic, and the one with the lower charge has a name ending in ous. For example, \(Fe^{3+}\) is the ferric ion, whereas \(Fe^{2+}\) is the ferrous ion.
  • Polyatomic ions are assigned names that must be memorized.
  • When dissolved in water, certain molecules produce a solution containing free $$H^+$ ions (protons).
    • An acid is a molecule with one or more \(H^+\) ions attached to an anion.
    • If the anion deos not contain oxygen, the acid is named with the prefix hydro- and the suffix -ic.
    • If the anion contains oxygen, the acid is formed from the root name of the anion with -ic or -ous.

Chapter 12

Quantum Mechanics and Atomic Theory

12.0: The Nature of Energy

  • Energy: the capacity to do work or produce heat.
    • Work - a force acting over a distance.
  • Law of Conservation of Energy: energy can be converted from one form to another but can neither be created or destroyed.
    • Potential energy: energy due to position or composition. Attractive and repulsive forces, water behind a dam.
    • Kinetic energy: motion of the object. Calculated as \(KE = \frac{1}{2}mv^2\) (\(m\) is mass, \(v\) is velocity).
    • The energy in the universe is constant.
    • Energy can change from one form to another easily.
    • Frictional heating - transfer of energy from an object to its surface.
  • Temperature: reflects the random motions of the particles in a particular substance.
  • Heat: transfer of energy between two objects due to a temperature difference. Heat is not a substance contained in an object.
  • State function/state property: the state function refers to a property of the system that depends only on the present state; it does not depend on its past or future.
    • Energy is a state function. Work and heat are not state functions.

Chemical Energy

  • Universe = System + Surroundings
    • System - part of the universe we wish to focus attention on.
    • Surroundings - everything else.
  • Reactants and products of a reaction are part of the system.
  • Exothermic: reaction results in the evolution of heat; energy flows out of the system.
    • Released heat comes from the difference in potential energy between the products and the reactants. The energy gained by the surroundings equals the energy lost by the system.
    • Potential energy stored in chemical bonds is being converted to thermal energy (random kinetic energy) via heat.
  • Endothermic: heat flows into a system and the reaction absorbs energy from the surroundings.
    • e.g. nitric oxide: \(N_2(g) + O_2(g) + \text{energy} \rightarrow 2NO(g)\)
    • Products have higher potential energy (weaker bonds) than the reactants.

12.1: Electromagnetic Radiation

  • Electromagnetic radiation: one way energy travels through space.
    • Some examples of EMR - light from the sun, microwave energy, X rays, radio waves.
    • Electrical and magnetic fields simultaneously oscillate in planes perpendicular to each other.
  • Waves are characterized by wavelength, frequency, and speed.
    • Wavelength (\(\lambda\)): distance between two consecutive peaks or troughs in a wave.
    • Frequency (\(\nu\)): number of waves (cycles) per second that pass a given point in space.
  • Inverse relationship between wavelength: \(\lambda\nu = c\).
  • Hertz (Hz): unit cycles per second \(s^{-1}\).
  • Radiation is an important means of energy transfer.

12.2: The Nature of Matter

  • Energy can only be gained or lost in whole-number multiples of \(hv\), where \(h\) is Planck’s constant (\(6.626\times10^{-34}\) J s).
\[\Delta E = nhv\]

Modeling the change in energy for a system \(\Delta E\) with an integer \(n\), Planck’s constant \(h\), and the frequency of electromagnetic radiation \(\nu\).

  • Energy is quantized, rather than being continuous; it can only be transferred in units of size \(hv\).
    • Each ‘packet’ of energy is a quantum.
    • A system can transfer energy only in quanta.
    • Thus, energy possesses particulate properties.
  • Einstein: electromagnetic radiation itself is quantized. Electromagnetic radiation is a stream of particles (photons).
    • Energy of a photon: \(E_{\text{photon}} = hv = \frac{hc}{\lambda}\)
  • Photoelectric effect: electrons are emitted from the surface of metal when light strikes it.
\[KE_\text{electron} = \frac{1}{2}mv^2 = hv - hv_0\]

Kinetic energy of an electron given the mass \(m\) and the velocity of the electron \(v\), or the energy of the incident photon \(hv\) and the energy required to remove the electron the metal’s surface \(hv_0\).

\[m = \frac{E}{c^2}\]

Equation for mass \(m\) given energy \(E\) and the speed of light \(c\).

  • A beam of light can be thought to be a stream of particles, but photons do not have mass (i.e. do not exhibit mass in the same way classical particles do). A photon has mass only in a relativist sense; it has no rest mass.

Key Conclusions from Planck and Einstein’s work:

  • Energy is quantized, and transferred in discrete units called quanta.
  • Electromagnetic radiation exhibits both wave and particulate matter properties (‘dual nature of light’).
\[\lambda = \frac{h}{mv}\]

de Broglie’s equation: calculating the wavelength of a particle \(\lambda\) given the Planck constant \(h\) and the momentum \(mv\).

  • Diffraction: when light is scattered from a regular array of points or lines.
    • Color results from differences in how various wavelengths of visible light are scattered.
    • A regular array of atoms or ions in a crystal produces diffraction.
    • Diffraction patterns can only be explained in terms of waves; thus, particles have wave properties.
  • Constructive inference: waves are in phase, resulting in increased intensity.
  • Destructive interference: waves are out of phase; troughs and peaks coincide, resulting in decreased intensity.

Full circle: Electromagnetic radiation, which was thought to be a waveform, was found to exhibit particulate properties. The electron, which was thought to be a particle, was found to exhibit wave properties.

  • Matter and energy are not distinct. Energy is a form of matter, and all matter shows the same types of properties.
  • All matter exhibits both particulate and wave properties.
  • Larger ‘pieces’ of matter exhibit predominantly particulate properties (wavelength is too small to be observed). Small ‘pieces’ of matter (e.g. photons) exhibit predominantly wave properties. Intermediate-sized ‘pieces’ (e.g. electrons) show both particulate and wave properties of matter.

12.3: The Atomic Spectrum of Hydrogen

  • When a high-energy discharge is passed through a sample of hydrogen gas, the \(H_2\) molecules absorb energy, causing \(H-H\) bonds to break.
    • Resulting hydrogen atoms are excited; they contain excess energy and release it by emitting light.
    • This light produces the emission spectrum of the hydrogen atom.
  • Continuous spectrum: contains all lengths of visible light.
    • In contrast, when the hydrogen emission spectrum in the visible region is passed through a prism, only a few lines are visible. It is a line spectrum.
    • Only certain energies are allowed for the electron in the hydrogen atom; it is quantized.

12.4: The Bohr Model

  • Niels Bohr developed a quantum model for the hydrogen atom.
  • The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.
  • Classical physics tells us that a particle tends to move in a straight line and travels in a circle only if there is a force pushing it towards the center. Moreover, a charged particle under acceleration should radiate energy. The electron must emit light or lose energy as it accelerates around the nucleus, but this denies the existence of stable atoms. An atomic model based on classical physics is untenable.
  • Bohr assumed the hydrogen electron could exist only in stationary, non-radiating orbits. The angular momentum of the electron can occur only in certain increments.
\[E = -2.178 \times 10^{-18} J \left(\frac{Z^2}{n^2}\right)\]

Expression for energy levels available to the electron in the hydrogen atom. \(Z\) is the atomic number (\(Z=1\) for hydrogen); \(n\) is an integer. This equation applies to all one-electron species. When \(n=0\) the expression evaluates to 0; there is no interaction and thus no energy. The energy of an electron in any orbit is negative relative to this reference state.

  • The equation can be used to calculate energy changes when electrons change orbits.
  • A more negative energy means it is more tightly bound.
  • To calculate the change in energy when an electron changes state: \(\Delta E = \text{energy of final state} - \text{energy of initial state}\).
    • A negative \(\Delta E\) indicates that the atom has lost energy and is now in a more stable state. Energy is carried away from the atom by the production/emission of an atom.
  • The wavelength of the emitted photon can be calculated by \(\Delta E = h\left(\frac{c}{\lambda}\).
    • Use the absolute value of \(\Delta E\); if a negative value is used then \(\lambda\) will be negative, which produces a physically meaningless result.
  • Bohr model: the model correctly fits the quantized energy levels of the hydrogen atom as inferred from the emission spectrum; these correspond to allowed circular orbits for electrons. As the electron becomes more tightly bound, the energy becomes more negative relative to the zero-energy reference state. As the electron is brought closer to the nucleus, energy is released from the system.
\[\Delta E = E_\text{final} - E_\text{initial} = -2.178 \times 10^{-18}\text{J}\left(\frac{1}{n_\text{final}^2} - \frac{1}{n_\text{initial}^2}\right)\]
  • Bohr’s model seemed to be very promising; energy levels calculated by Bohr agreed with values obtained from the hydrogen emission spectrum.
    • However, Bohr’s model does not work with atoms other than hydrogen.
    • Bohr’s model is fundamentally incorrect.
    • The Bohr model is important regardless because observed quantization of energy in atoms can be explained by making simple assumptions.

12.5: The Quantum-Mechanical Description of the Atom

  • Werner Heisenberg, Louis de Broglie, and Erwin Schrodinger: developed wave mechanics/quantum mechanics.
    • de Broglie - the electron also shows wave properties;
    • Schrodinger - gave emphasis to the wave properties of the electron.
  • de Broglie applied the wave model to the Bohr atom by imagining the electron in the hydrogen atom as a standing wave.
  • Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will ‘fit’; all others form destructive interference.
    • Could explain quantization of the hydrogen atom..
\[\hat{H}\psi = E\psi\]

Schrodinger’s equation: \(\psi\) is the wave function (a function of three-dimensional coordinates), \(\hat{H}\) is the mathematical set of instructions called an operator.

  • A specific wave function for an electron is an orbital.
  • The wave function corresponding to the lowest energy for the hydrogen atom is the 1s orbital.
    • An orbital is not a Bohr orbit; the electron in the hydrogen 1s orbital is not moving around the nucleus in a circular orbit.
    • We do not know that the electron is moving; we cannot predict the electron’s motion using the 1s orbital function.
    • The wave function gives no information about the movements of the electron.
  • Werner Heisenberg discovered the Heisenberg uncertainty principle: there are fundamental limits to how precisely we can know the position and momentum of a particle at a given time.
\[\Delta x \times \Delta p \ge \frac{\hbar}{2}; \hbar = \frac{h}{2\pi}\]

Mathematical representation of Heisenberg’s uncertainty principle, where \(\Delta x\) is the uncertainty of the particle’s position, \(\Delta p\) is the uncertainty in the particle’s momentum, and \(\hbar\) is Planck’s constant divided by \(2\pi\).

  • From Heisenberg’s uncertainty principle, the minimum uncertainty \(\Delta x \cdot \Delta p = \frac{h}{4\pi}\).
    • Moreover, the more precisely we know a particle’s position, the less precisely we know its momentum, etc.
    • The limitation is small for large particles like baseballs, so it is unnoticed.
    • We cannot know the exact path of the electron as it moves around the nucleus.
    • Allows us to distinguish inherent uncertainty from measurement uncertainty.

12.8: The Physical Meaning of a Wave Function

  • What is a wave function, and what does it tell us about the electron to which it applies?
  • The square of the function evaluated at a particular point in space indicates the probability of finding an electron near that point.
  • The quotient \(\frac{N_1}{N_2}\) is the ratio of the probabilities of finding the electron in the infinitesimally small volume elements \(dv\) around two points; if the ratio is 100, then the electron is 100 times more likely to be found at position 1 than at position 2.
  • The square of the wave function can be represented as a probability distribution.
  • We are interested in knowing the total probability of finding the electron in the hydrogen atom at a distance from the nucleus. Radial probability distributions (\(4\pi r^2 R^2\) vs \(r\), where \(R\) is the radial component of the wave function) show the probability of finding the electron in each spherical shell.
    • The probability of finding an electron at a particular position is greatest near the nucleus, but the volume of the spherical shell increases with distance from the nucleus. These two forces are summed in the RPD.
    • The maximum radial probability is the same as the radius of the innermost orbit in the Bohr model; thus it is called the Bohr radius \(a_0\).
  • The size of the orbital cannot be precisely defined since the probability never becomes 0. The hydrogen \(1s\) orbital has no distinct size.
  • The normally accepted definition of the size of a hydrogen \(1s\) orbital is the radius that encloses 90% of the total electron probability.

12.9: The Characteristics of Hydrogen Orbitals

Quantum Numbers

  • Many orbitals (wave functions) satisfy the Schrodinger equation for a hydrogen atom.
  • Each of the orbitals is characterized by a set of quantum numbers.
    • Principal quantum number (\(n\)) relates to the size and energy of the orbital. Takes integer values. An increase in \(n\) means higher energy because the energy is less tightly bound to the nucleus; the energy is less negative.
    • Angular momentum quantum number (\(l\)) relates tot he angular momentum of an electron in a given orbital. Takes integer values from 0 to \(n-1\) for each value of \(n\). \(0 \implies s, 1 \implies p, 2\implies d, 3\implies f, 4\implies g\).
    • Magnetic quantum number (\(m_l\)) relates to the orientation of space of angular momentum associated with the orbital. Takes integral values between \(l\) and \(-l\), including 0.

Orbital Shapes and Energies

  • The meaning of an orbital is illustrated most clearly by a probability distribution; each orbital in the hydrogen atom has a unique probability distribution.
  • \(2s\) and \(3s\) orbitals contain areas of high probability separated by areas of zero probability.
    • Areas of zero probability are nodal surfaces, or nodes.
    • The number of nodes increases as \(n\) increases.
    • For \(s\) orbitals, the number of nodes is given by \(n-1\).
  • \(p\) orbitals have two lobes separated by a node at the nucleus.
  • The energy of a particular orbital for hydrogen is determined by the value of \(n\); all orbitals with the same \(n\) has the same energy - they are degenerate.
  • Hydrogen’s electron can occupy any of its atomic orbitals; in its lowest energy state, though, the electron resides in the \(1s\) orbital.
    • If energy is put into the atom, the electron can be transferred into a higher-energy orbital - this produces an excited state.

Key Notes About the Hydrogen Atom

  1. In the quantum mechanical model the electron is described as a wave. This representation leads to a series of wave functions (orbitals) that describe the possible energies and spatial distributions available to the electron.
  2. In agreement with the Heisenberg uncertainty principle, the model cannot specify the detailed electron motions. Instead, the square of the wave function represents the probability distribution of the electron in that orbital. This approach allows us to picture orbitals in terms of probability distributions, or electron density maps.
  3. The size of an orbital is arbitrarily defined as the surface that contains 90% of the total electron probability.
  4. The hydrogen atom has many types of orbitals. In the ground state the single electron resides in the \(1s\) orbital. The electron can be excited to higher-energy orbitals if the atom absorbs energy.

12.10: Electron Spin and the Pauli Principle

  • A fourth quantum number was needed to account for details of the emission spectra of atoms.
  • Electron spin quantum number (\(m_s\)) can only hold two values, \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
  • Pauli exclusion principle: in a given atom no two electrons can have the same set of four quantum numbers (\(n\), \(l\), \(m_l\), \(m_s\)).
    • Electrons in the same orbital have the same values of \(n\), \(l\), and \(m_l\); thus, an orbital can hold only two electrons, and they must have opposite spins.

12.11: Polyelectronic Atoms

  • The quantum mechanics model provides a description of the hydrogen atom that agrees well with experimental data.
  • How does the model apply to polyelectronic atoms (atoms with more than one electron)?
  • Three energy contributions in a Helium atom:
    1. Kinetic energy of electrons as they move around the nucleus
    2. Potential energy of attraction between the nucleus and the electrons
    3. Potential energy of repulsion between thet wo electrons
  • Electron correlation problem: we cannot rigorously account for the effect a given electron has on the motions of the other electrons in an atom.
    • Nevertheless, we can make approximations. Simplest approximation: each election is treated as if it were moving in a field of charge that is the net result of the nuclear attraction and average repulsions of all other electrons.
    • The effect of electron repulsion can be thought of as reducing the nuclear charge.
    • Apparent/effective nuclear charge: \(Z_\text{eff}\). This is the charge ‘experienced’ by each electron.
    • In general, \(Z_\text{eff} = Z_\text{actual} - (\text{effect of electron repulsions})\), where \(Z_\text{actual}=Z\), the atomic number (number of protons).
  • Self-consistent field (SCF) method: an electron is assumed to moving in a potential energy field that is the result of both the nucleus and the average electron density of all other electrons in the atom. The many-electron Schrodinger equation can be separated into a set of one-electron equations that are solved by computers.

12.12: The History of the Periodic Table

  • Originally constructed to represent patterns observed in chemical properties of the elements.
  • Johann Dobereiner - attempted to form a model of triads.
  • John Newlands - arranged elements into octaves; properties repeat for every 8th element.
  • Dmitri Ivanovich Mendeleev - conceived the present periodic table and demonstrated its usage in predicting the existence and properties of unknown elements.

12.13: The Aufbau Principle and the Periodic Table

  • We can use the quantum mechanical model of the atom to show how electron arrangements in the atomic orbitals of various atoms account for the organization of the periodic table.
    • Assuming all atoms have orbitals similar to those that have been described for the hydrogen atom.
  • Aufbau Principle: As protons are added one by one to the nucleus to build up elements, electrons are similarly added to the atomic orbitals.
    • Hydrogen has one electron, which occupies the \(1s\) orbital in its ground state; the configuration is written as \(1s^1\).
    • Helium has two electrons; electrons are in the \(1s\) orbital with opposite spins; \(1s^2\) configuration.
    • Lithium has three electrons; two electrons are in the \(1s\) orbital and the other is in the \(2s\) orbital; \(1s^22s^1\) configuration.
    • Carbon has six electrons; \(1s^22s^22p^12p^1\)/\(1s^22s^22sp^2\) configuration.
    • Sodium has eleven electrons; \(1s^22s^2p^63s^1\) configuration. To avoid writing inner-level electrons, this is abbreviated as \([Ne]3s^1\), where \([Ne]\) represents the electron configruation of neon.
  • Hund’s Rule: the lowest-energy configuration for an atom is the one having the maximum number of unpaired electrons allowed but the Pauli principle in a particular set of degenerate orbitals.
  • Valence electrons are electrons in the outermost principal quantum level of an atom. Other inner electrons are the core electrons.
  • Elements in the same group have the same valence electron configuration.

Ionization Energy

  • Energy required to move an electron from a gaseous atom or ion: \(X(g) \rightarrow X^+ (g) = e^-\) (assuming the atom or ion is in ground state.)
  • Ionization potential is given in units of electron-volts per atom (\(1 eV = 1.602\times 10^{-19} J\).
  • Ionization energy of an electron gives information about the energy of the orbital it occupies.
  • Koopmans’ theorem: the ionization energy of an electron is equal to the energy of the orbital from which it came.
    • Assumes that electrons left behind in the resulting ion will not reorganize in response to the removal of the electron.
    • Ionization energies provide information helpful in testing the orbital model of the atom.
  • Energy required to remove electrons from aluminum atoms in gaseous state:
\[Al(g) \rightarrow Al^+(g) + e^- \implies I_1 = 580 kJ/mol\] \[Al^{+}(g) \rightarrow Al^{2+}(g) + e^- \implies I_2 = 1815 kJ/mol\] \[Al^{2+}(g) \rightarrow Al^{3+}(g) + e^- \implies I_2 = 2740 kJ/mol\] \[Al^{3+}(g) \rightarrow Al^{4+}(g) + e^- \implies I_2 = 11600 kJ/mol\]
  • The highest-energy electron (least tightly bound) is removed first.
    • Energy required to move this: first ionization energy (\(I_1\)).
    • \(I_1\) is much smaller than \(I_2\) (second ionization energy) because of charge; the frist electron is removed from a neutral atom whereas the second is removed from a \(1+\) ion.
  • As we go across a period from left to right, the first ionization energy increases.
  • Electrons in the same principal quantum level are not expected to shield each other very well. We do not expect electrons to completely shield each other from increasing nuclear charge as the number of protons in the nucleus increases.
  • Electrons are bound more firmly when going from left to right.
  • First ionization energy values decrease in going down a group.
    • Electrons being removed are farther from the nucleus; the electron is easier to remove.

Electron Affinity

  • Electron affinity - the energy change associated with the addition of an electron to a gaseous atom: \(X(g) + e^- \to X^- (g)\).
  • Atoms in the first 20 elemtns that form stable negative ions have negative (exothermic) electron affinities.
    • The more negative the energy, the greater the quantity of energy released.
    • Electron affinities generally become more negative from left to right.

Atomic Radius

  • Neither the size of an atom nor an orbital can be specified exactly.
  • Arbitrary choices are used to obtain values for atomic radii.
    • Measure distance between atoms in chemical compounds.
  • The atomic radius decreases in going from left to right across a period.
    • Increasing effective nuclear charge (decreasing shielding) in going from left to right; valence electrons are drawn closer to the nucleus, decreasing the size of the atom.
  • Atomic radius increases down a group because of increases in the orbital sizes of successive principal quantum levels.

12.16: The Properties of a Group: The Alkali Metals

Information Contained in the Periodic Table

  1. Members of each group exhibit similar chemical properties that change in a regular way.
    • Quantum mechanics allows us to understand similarities in the properties of atoms from the identical valence electron configurations.
    • Number and type of valence electrons primarily determine an atom’s chemistry.
  2. The electron configuration of a representative element is very valuable. Predicted electron configurations for transition metals are sometimes incorrect. Memorize chromium and copper.
  3. Certain groups in the periodic table have important names. 1A: Alkali metals; 2A: Alkaline earth metals; 7A: Halogens, 8A: Noble Gases.
  4. Most fundamental classification of elements is into metals and non-metals.
    • Metals tend to give up electrons to form a positive ion (metals have low ionization energies).
    • Nonmetals tend to gain electrons to form an anion when reacting with a metal. Nonmetals have large ionization energies and most have negative electron affinities.

The Alkali Metals

  • Hydrogen behaves as a nonmetal because of its very small size.
  • When we move down the group, the first ionization energy decreases and the atomic radius increases.
  • Smooth decrease in melting point and boiling point in going down Group 1A.

Chapter 13

General Concepts of Bonding

13.1: Types of Chemical Bonds

  • We can study various properties of bond, like the energy required to break a bond (bond energy).
  • Spectroscopy: the study of the interactions of electromagnetic radiation with matter.
  • Systems behave in ways that achieve the lowest possible energy.
  • Ionic bonding - ionic substances are formed when an atom that loses electrons relatively easily reacts with an atom that has a high affinity for electrons.
\[V=\frac{Q_1Q_2}{4\pi \in _0r}=2.31\times 10^{-19}\:\text{J}\:\text{nm}\:\left(\frac{Q_1Q_2}{r}\right)\]

Coulomb’s law - used to calculate the energy of interaction between a pair of ions. \(V\) is in units of Joules, \(r\) is the distance between the ion centers in nanometers, \(Q_1\) and \(Q_2\) are the numerical ion charges, and \(\in_0\) is teh permittivity of the vacuum.

  • The ion pair has lower energy than the separated ions.’
  • Coulomb’s law can also be used to calculate the repulsive energy when two like-charged ions are being brought together.
  • For two closely spaced hydrogen atoms, there are proton-proton repulsion, electron-electron repulsion, and proton-electron attraction terms.
  • Equilibrium internuclear distance - the distance at which energy is at a minimum, also known as bond length.
  • Four key components of an energy profile:
    1. The energy terms involved are the potential energy that results from the attractions and repulsions among the charged particles and the kinetic energy caused by the motions of the electrons.
    2. The zero reference point for energy is defined for the atoms at infinite separation.
    3. At very short distances the energy rises steeply because of the great importance of the internuclear repulsive forces at these distances.
    4. The bond length is the distance at which the system has minimum energy, and the bond energy corresponds to the depth of the “well” at this distance.
  • In the \(H_2\) molecule the electrons reside primarily in the space between the two nuclei where they are attracted simultaneously by both protons.
  • Bonds should be thought in terms of forces: bonding in the hydrogen molecules is conducted by electrons shared in the nuclei - covalent bonding.
  • Polar covalent bonds - electron sharing is unequal across atoms.
  • When a sample of \(HF\) molecules is placed in an electric fiedl, the molecules roient themselves with the fluoride end closest to the positive pole and the hydrogen closer to the negative pole; this implies the charge distribution \(H_{\delta+} - F_{\delta-}\).

13.2: Electronegativity

  • Electronegativity: the ability of an atom in a molecule to attract shared electrons to itself.
  • Linus Pauling’s model: compare the measured \(H-X\) bond with the “expected” \(H-X\) bond energy.
  • Leland C. Allen’s model: calculate the electronegativity baed on the average ionization energies of the valence electrons for a given item; electronegativity is a property of an isolated atom.
  • Electronegativity increases from left to right across a period and decreases down a group.
Electronegativity Diff. in the Bonding AtomsBond Type
IntermediatePolar Covalent

13.3: Bond Polarity and Dipole Moments

  • When placed in an electric field, molecules have a preferential orientation.
  • A molecule like HF that has a center of positive charge and a center of negative charge is dipolar and possesses a dipole moment.
\[\mu = QR\]

The dipole moment \(\mu\) given the magnitude of charge \(Q\) and the distance of separation \(R\), in units of coloumb meter or debye.

  • Dipole moment gives information about its bonding and electron distribution.
  • Electrostatic potential diagram.
  • Polyatomic molecules can also exhibit dipolar behavior.
  • In some cases, bond polarities in moleculs oppose and cancel each other.

13.4: Electron Configurations and Sizes

  • Quantum mechanics helps us understand what constitutes a stable compound.
  • A large number of stable compounds have noble gas arrangements of electrons.
  • Non-metallic electrons form covalent bonds with nonmetals or take electrons from metals to form ions.
  • Two nonmetals in a covalent bond share electrons in a way that completes the valence electron configurations of both atoms (i.e. both obtain noble gas electron configurations).
  • Nonmetal and representative group metal in a binary ionic compound form ions such that the valence electron configruation of the nonmetal is completed and the valence orbitals of the metal are emptied.

Predicting Formulas of Ionic Compounds

  • Ionic compound - usually in reference to the solid state of that compound.
    • Packed in a way that minimizes \(-\) to \(-\) and \(+\) to \(+\) repulsions and maximizes \(+\) to \(-\) attractions.
  • Chemical compounds are always electrically neutral.

Sizes of Ions

  • Ion size determines the structure and stability of ionic solids, the properties of ions in an aqueous solution, and the biological effect of ions.
  • Ionic radii - measured distances between ion centers in ionic compounds.
  • Ion size increases down a group.
  • Isoelectronic ions - ions containing the same number of electrons.
    • Across an isoelectronic set of ions, as the number of protons increases, the electrons experience greater attraction and become smaller.

13.5: Formation of Binary Ionic Compounds

  • Metals and nonmetals react by transferring electrons to form mutually attractive cations and anions.
  • Lattice energy - the change in energy that takes place when separated gaseous ions are packed together to form an ionic solid: \(M^+(g) + X^-(g) \to MX(s)\).
  • Lots of energy is released when ions combine to form a solid.

Lattice Energy Calculations

  • Lattice energy can be represented by a modified form of Coloumb’s law.
\[\text{lattice energy} = k\left(\frac{Q_1Q_2}{r}\right)\]

Modified Coloumb’s law, where \(k\) is the proportionality constant depending on the structure of the solid and the electron configurations of the ions, \(Q_1\) and \(Q_2\) are the charges of the ions, and \(r\) is the shortest distance between centers of the cations and anions.

13.6: Partial Ionic Character of Covalent Bonds

  • When atoms with different electronegativities react to form molecules, the electrons are not shared equally - the possible result is a polar covalent bond or a complete transfer of electrons.
  • There are no ionic bonds between discrete pairs of atoms. Calculate percent ionic character of binary compounds in the gas phase.
  • No bond reaches 100% ionic character; no individual bonds are completely ionic.
  • More than 50% ionic character compoudns are considered to be ionic solids.
  • Many substances contain polyatomic ions.
  • Any compound that conducts an electric current when melted will be classified as ionic.
  • Salt - used interchangably with ionic compound.

13.7: A Model for the Covalent Chemical Bond

  • What is a chemical bond? Forces that cause a group of atoms to behave as a unit.
  • Bonds occur because systems seek the least possible energy. Bonds occur when collections of atoms are more stable in bonds than in separated form.
  • We can interpret molecular stability in terms of the chemical bond.
  • The concept of a bond is a human invention - bonds provide a method to divide energy evolved when a stable molecule is formed from its component atoms.
  • A bond is a quantity of energy obtained from the molecular energy of stabilization.
  • Bonding model provides a framework to systematize chemical behavior by thinking of molecules as collections of common fundamental components.
  • The bonding model is physically sensible; atoms can form stable groups by sharing electrons.
  • Some molecular properties require thinking of the molecule as a whole, with electrons free to move through the entire molecule - delocalization of electrons.

13.8: Covalent Bond Energies and Chemical Reactions

  • Establish the sensitivity of a particular type of bond to its molecular environment.
  • Measure the average of individual bond disassociation energies.
  • Single, double, triple, and general multiple bonds exist.

Bond Energy and Enthalpy

  • Bond energy values can be used to calculate approximate energies for reactions.
  • For bonds to be broken, energy must be added to the system (exothermic process). The formation of a bond must release energy (exothermic process).
\[\Delta H = \sum D \text{ (bonds broken)} - \sum D \text{ (bonds formed)}\]

Enthalpy change calculation. \(\sum\)i s the sum of terms, \(D\) is the bond energy per mole of bonds.

  • We must make certain approximations; average bond energies apply regardless of the molecular environment, and we ignore the difference between enthalpy and internal energy.

13.9: The Localized Electron Bonding Model

  • A model to describe covalent bonds: localized electron (LE) model, used to analyze complicated molecule and to interpret chemical phenomena.
  • A molecule is composed of atoms that are bound together by using atomic orbitals to share electron pairs.
  • Electron pairs are assumed to be localized on a particular atom or in space between two atoms; pairs of electrons localized in an atom are lone pairs, and pairs in the space between are bonding pairs.
  • Three parts:
    • Descriptions of the valence electron arrangement in the molecule using Lewis structures.
    • Prediction of the geometry of the model using the valence shell electron pair repulsion model.
    • Description of the type of atomic orbitals used by the atom to share electrons or hold lone pairs.

13.10: Lewis Structures

  • A Lewis structure of a molecule represents the arrangement of valence electrons among the atoms in the molecule.
  • In the most stable compounds, atoms achieve noble gas electron configurations.
  • When metals and nonmetals react to form solid binary ionic compounds, electrons are transferred.
  • Only the valence electrons are included when writing Lewis structures.
  • Octet rule: eight electrons are needed to fill each \(ns\) and \(np\) orbital set.
  • Steps to writing a Lewis structure:
    1. 1 Sum the valence electrons from all the atoms. Do not worry about keeping track of which electrons come from which atoms. It is the total number of electrons that is important.
    2. Use a pair of electrons to form a bond between each pair of bound atoms.
    3. Arrange the remaining electrons to satisfy the duet rule for hydrogen and the octet rule for the second-row elements.

13.11: Resonance

  • Sometimes more than one valid Lewis structure is possible for a molecule.
  • Consider the nitrate ion \(NO_3^-\); although three Lewis structures exist, the true Lewis structure is the superposition of all three.
  • Resonance - when more than one valid Lewis structure can be written for a particular molecule.
  • Resonance structure - resulting electron structure of the molecule given by the average of the resonance structures.
  • Although the localized electron model postulates that electrons are localized between a pair of atoms, nature does not operate this way. Electrons are actually delocalzied.
  • Resonance compensates for the defective LE model assumption.

13.12: Exceptions to the Octet Rule

  • LE model is simple and successful, but the octet rule does not apply to all molecules.
  • Pattern observed for elements in Period 3 and beyond, and can hold more than 8 electrons. The classical explanation is that the \(3d\) orbitals can be used to accomodate more electrons.
  • Odd-electron molecules: nitric oxide, for instance. Requires a more sophisticatred model than Lewis structures.
  • Formal charge: we can estimate the charge on each atom in the various possible Lewis structures to deal with ions and molecules that can have many possible Lewis structures.
    • Count both of the shared electrons as belonging to electronegativity of a bond.
    • Lone pair electrons belong entirely to an atom.
    • Shared electrons are divided equally between sharing atoms.
  • Two schools of thought on using fromal charges to identify the closest resonance structures to the actual electronic structure
    • “Atoms will try to achieve minimum formla charges.”
    • “The octet rule is primary.”
  • Valid Lewis structures may not be correct.

13.13: The VSEPR Model

  • Valence Shell Electron-Pair Repulsion model: assumes that the structure around a given atom is determined principally by minimizing electron-pair repulsions.
  • Bonding and nonbonding pairs around a given atom should be positioned as far apart as possible.
  • Lone pairs require more room than bonding pairs and tend to compress the angles between the bonding pairs.
  • A double bond should be counted as one effective pair in using the VSEPR model.

Chapter 3


3.1: Atomic Masses

  • Atomic mass unit - one-twelfth the mass of carbon-12.
  • Mass spectrometers can be used to compare the masses of atoms.
    • Atoms or molecules are passed through a beam of high-speed electrons.
  • Atomic mass is a weighted average of all isotopes.

3.2: The Mole

  • It is most convenient to define the mole as the number equalt ot he number of carbon atoms in exactly 12 grams of pure carbon-12.
  • Avagadro’s number
  • The mole is defined such that a sample of a natural element with a mass equal to the element’s atomic mass expressed in grams contains 1 mole of atoms.

3.3: Molar Mass

  • A chemical compound is a collection of atoms. To convert between mole quantities and mass, we use molar mass - the mass of 1 mole of an element.
  • Molar mass and molar weight are equivalent.
  • The term “formula weight” is used for ionic compounds instead of “molar mass” and “molecular weight”.

3.4: Percent Composition of Compounds

  • Composition in terms of masses of elements.

3.5: Determining the Formula of a Compound

  • The formula is obtained by decomposing an element or by reacting it with oxygen to produce substances like \(CO_2\), \(H_2O\), and \(N_2\).
  • The formula represents the mole/number ratios.
  • Empirical formula - simplest whole-number ratio of various types of atoms in a compound.
  • Molecular formula - a multiple of the empirical formula.

3.6: Chemical Reactions

  • Chemical change - reorganization of atoms in one or more substances.
  • Reactants - left side of the arrow, form the products - right side of the arrow.
  • Chemical equations must be balanced.
  • Chemical equations often inclue physical states of reactants and products - (s) for solid, (l) for liquid, (g) for gas, and (aq) for dissolved in water - an aqueous solution.
  • A balanced chemical equation gives you a lot of information.

3.7: Balancing Chemical Equations

  • An unbalanced chemical equation is of little use.
  • Atoms must be conserved in a chemical reaction.
  • The formulas of compounds must never be changed when writing a chemical equation.

3.8: Stoichiometric Calculations - Amounts of Reactants and Products

  • Coefficients represent numbers of molecules, not masses of molecules.
  • “What mass of oxygen will react with 96.1 grams of propane?” - firstly, write the balanced chemical equation for the reaction. Obtain the mole ratio and utilize mole-gram conversions.

3.9: Calculations Involving a Limiting Reactant

  • When chemicals are mixed together, reactants may ‘run out’.
  • Limiting reactant/reagant - a reactant runs out because there are not enough moles to react with other reactants.
  • Theoretical yield - amount of a given product formed when the limiting reactant is completely consumed.
  • Side reactions and other complications limit how much of the limiting reagant can be consumed, forming the actual yield.
  • Percent yield is calculated as \(\frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%\).

Chapter 4

Types of Chemical Reactions and Solution Stochiometry

4.1: Water, the Common Solvent

  • Water is a crucial substance on Earth.
  • Water can dissolve many substances. What happens when a solid dissolves?
    • A water molecule has an \(H-O-H\) angle of about 105 degrees.
    • The water molecule is polar because of unequal electron sharing.
  • Hydration - negative ends are attracted to positively charged cations and positive ends are attracted to negatively charged anions.
  • Ionic substances (salts) dissolved in water break up into individual cations and anions.
  • (aq) - indicates that the ions are hydrated by unspecified numbers of water molecules.
  • Water also dissolves nonionic substances - ethanol, etc.
    • The ethanol molecule contains a polar \(O-H\) bond like in water, making it compatible with water.
    • Pure water does not dissolve animal fat because fat molecules are nonpolar and do not interact with polar water molecules.
  • Predicting solubility - “like dissolves like”.

4.2: The Nature of Aqueous Solutions - Strong and Weak Electrolytes

  • A solution is a homogenous mixture. Its composition can be varied by changing the amount of dissolved substances.
  • What happens when a substance (solute) is dissolved in liquid water (solvent)?
  • Electrical conductivity - ability to conduct an electric current.
  • Strong, weak, and nonelectrolytes

Strong Electrolytes

  • Several classes: soluble salts, strong acids, and strong bases.
  • A salt is an array of cations and anions that separate and become hydrated when the salt dissolves.
  • Solubility - measured in terms of mass of solute that dissolves per given volume of solvent, or in terms of number of moles of solute that dissolve in a given volume of solution.
  • Acid - substance that produces \(H^+\) ions (protons) when it is dissolved in water.
    • Hydrochloric acid, nitric acid, and sulfiric acid are aqueous solutions.
    • A strong acid completely dissociates into its ions.
    • In sulfiric acid, only the first hydrogen ion is completely dissociated.
  • Base - soluble compounds containing the hydroxide ion . Sodium hydroxide, potassium hydroxide.

Weak Electrolytes

  • Substances that produce relatively few ions when dissolved in water. These are often weak acids and weak bases.
  • Main acidic component of vinegar - acetic acid.
  • Formulas for acids are written with acidic hydrogen atom or atoms listed first.


  • Substances that dissolve into water but do not produce any ions.
  • Ethanol: dissolves, but does not break into hydrogen ions.

4.3: The Composition of Solutions

  • Chemical reactions often take place when two solutions are mixed.
  • We must know the nature of the reaction and the amount of chemicals present in the solutions.
  • Molarity: moles of solute per volume of solution (liters).
  • Standard solution: a solution whose concentration is accurately known.
  • Dilution - water is added to achieve the desired molarity of a particular solution.
    • Moles of solute after dilution is the same as the moles of the solute before dilution.

4.4: Types of Chemical Reactions

Reactions are divide dinto one of the following main groups: precipitation reactions, acid-base reactions, and oxidation-reduction reactions.

4.5: Precipitation Reactions

  • When two solutions are mixed, sometimes an insoluble substance forms.
  • Precipitation reaction - the resulting solid is the precipitate.
  • In most cases, when a solid containing ions dissolves in water, the ions separate and move independently.
  • When dealing with the chemistry of an aqeous solution: first focus on the actual components of the solution before any reaction occurs, then figure out how the components interact with each other.
  • Think about solid products in terms of ion interchange.

Rules for the Solubility of Salts in Water

  • Most nitrate salts are soluble.
  • Most salts of sodium, potassium, and ammoniuim are solouble.
  • Most chloride salts are soluble, except for \(AgCl\), \(PbCl_2\), and \(Hg_2 Cl_2\).
  • Most sulfate salts are soluble, except for \(BaSO_4\), \(PbSO_4\), and \(CaSO_4\).
  • Most hydroxide salts are only slightly soluble, except for \(NaOH\), \(KOH\), and \(Ca(OH)_2\), which are soluble.
  • Most sulfate, carbonate, and phosphate salts are only slightly soluble.

4.6: Describing Reactions in Solution

  • Consider equations used to represent reactions in a solution.
  • The molecular equation shows the reactants and products of the solution, but does not show what actually occurs in the solution.
  • Ionic equation - an equation written with the individual ions implied byt he molecular equation. This better represents the actual forms of the reactants and products in the solution.
  • Only some ions participate in reactions.
    • Spectator ions - ions that do not participate directly in a reaction in solution.
    • net ionic reaction - an ionic equation without spectator ions.

Three Types of Equations

  • Molecular equation
  • Complete ionic equation (all ions in reactants and products)
  • Net ionic equation

4.7: Selective Precipitation

  • Selective precipitation - separate cations by precipitating them one at a time.
  • We can use the fact that salts have different solubilities to separate mixtures of ions.
  • Qualitative analysis - mixtures of ions are separated and identified.

4.8: Stoichiometry of Precipitation Reactions

  • We must determine which reactant is limiting, since the reactant that is consumed first will limit the amounts of products formed.
  • It is sometimes difficult to tell which reaction will occur when two solutions are mixed.
  • Always write down species present in the solution; then, obtain the moles of reactants.
  1. Identify the species present in the combined solution and determine which reaction occurs.
  2. Write the balanced equation for the reaction.
  3. Calculate the moles of reactants.
  4. Determine which reactant is limiting.
  5. Calculate the mole of product or products, as required.
  6. Convert to grams or other units, as required.

4.9: Acid-Base Reactions

  • An acid is a substance that produces \(H^+\) ions in water; a base is a substance that produces \(OH^-\) ions.
  • Acid - proton donor. Base - proton acceptor.
  • The hydroxide ion is such a strong base that for purposes of stoichiometry it is assumed to react completely with any weak acid dissolved inw ater.
  • Acid-base reactions - neutralization reaction.
  • Acid base titration - example of volumetric analsyis.
    • Titrant solution is delivered from a buret.
    • Point in which titrant has been added to react exactly with substance being determined - equivalence/stoichiometric point.
  • Write down components of the reaction one by one.

4.10: Oxidation-Reduction Reactions

  • Many substances are ionic.
  • Reactions in which one or more electrons are transferred are oxidation-reduction/redox reactions.
  • Many important chemical reactions involve oxidation and reduction.
    • Most reactions used for energy production are redox reactions.

Oxidation States

  • Oxidation states (or oxidation numbers) provide a way to keep track of electrons in redox reactions.
  • Governed by a set of rule describing how to divvy shared electrons in compounds containing covalent bonds.

Key Rules:

  1. The oxidation state of an atom in an element is 0.
  2. The oxidation state of a monatomic ion is the same as its charge.
  3. In a covalent compound with nonmetals, hydrogen is assigned an oxidation state of +1.
  4. In covalent compounds, oxygen is assigned an oxidation state of -2. In peroxides (compounds with \(O_2^{2-}\)), each oxygen is assigned an oxidation state of -1.
  5. In binary compounds, the element with the greater attraction for the electrons is assigned a negative oxidation state equal to its charge in its ionic compounds.
  6. The sum of oxidation states must be 0 for a neutral compound, and equal to the overall charge for an ionic species.

Characteristics of Redox Reactions

  • Redox reactions are characterized by a transfer of electrons.
  • Formal transfer of electrons
    • Oxidized: loses electrons; oxidation state increases; reducing agent
    • Reduced: gains electrons; oxidation state decreases; oxidizing agent
  • Oxidizing agent - electron acceptor. Reducing agent - electron donor.

4.11: Balancing Oxidation-Reduction Equations

  • Oxidation-reduction reactions are often complicated, which means it can be difficult to balance their equations by simple inspection.

The Oxidation States Method

  • We want to balance equations using changes in the oxidation state. Begin by specifying the oxidation states.
  1. Assign the oxidation states of all atoms.
  2. Decide which element is oxidized and determine the increase in oxidation state.
  3. Decide which element is reduced and determine the decrease in oxidation state.
  4. Choose coefficients for the species containing the atom oxidized and the atom reduced such that the total increase in oxidation state equals the total decrease in oxidation state.
  5. Balance the remainder of the equation by inspection.

The Half-Reaction Method

  • For redox reactions that occur in aqueous solution, it is useful to separate the reaction into two half-reactions: an oxidation half-reaction and a reduction half-reaction.
  • Balance the equations for the half-reacitons separately; then add them to obtain the overall balanced equation.

4.12: Simple Oxidation-Reduction Titrations

  • Redox reactions are commonly used for volumetric analytical procedures.
  • Potassium permanganate, potassium permanganate, potassium dichromate, cerium hydrogen sulfate.
  • An oxidizing agent can undergo several different reactions.

Chapter 5


5.3: The Ideal Gas Law

  • Boyle’s law: \(V = \frac{k}{P}\).
  • Charles’ law: \(V = bT\).
  • Avagadro’s law: \(V = an\).
  • Combine into \(V = R \left(\frac{Tn}{P}\right)\).
    • \(R\): combined proportionality constant called the universal gas constant.
    • \(R\) is 0.08206 L atm \(K^{-1} \text{mol}^{-1}\).
  • Ideal Gas Law: \(PV = nRT\).
  • The ideal gas law is an empirical equation - it is derived from experimental measurements on gas properties.
  • It is best understood as a limiting law - behavior that real gases approach at low pressures and high temperatures.
  • Temperature must always be converted to the Kelvin scale.

Gas Stoichiometry

  • \(V\) in the ideal gas law - the molar volume of an ideal gas.
  • 0 degrees Celsius and 1 atm - standard temperature and pressure.

Molar Mass

  • Calculation of molar mass from measured density.
\[n = \frac{\text{grams of gas}}{\text{molar mass}} = \frac{\text{mass}}{\text{molar mass}} = \frac{m}{\text{molar mass}}\] \[P = \frac{dRT}{\text{molar mass}} \implies \text{molar mass} = \frac{dRT}{P}\]
  • If density of a gas at a given temperature and pressure is known, molar mass can be calcualted.

5.5: Dalton’s Law of Partial Pressures

  • For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.
  • It is the total number of moles of particles that is important.
  • The volume of an individual gas particle must not be important. The froces among the particles must not be important.
  • Mole fraction - ratio of the number of moles in a component of a mixture to the total number of moles in the mixture.
  • The partial pressure of a component of a gaseous mixture is equal to the mole fraction of that component multiplied by the total pressure.

Chapter 15

Chemical Kinetics

15.1: Reaction Rates

  • Chemical kinetics deals with the speed at which changes occur. Speed/rate of a process is change in a quantity over a period of time. in concentration of a reactant or product per unit time
  • Reaction rate of a chemical reaction - change in concentration of reactant or product per unit time.
  • Any rate expression involving a reactant will include a negative sign such that we work with positive rates.
  • Stoichiometry determines relative rates of consumption of reactants and generation of products.

15.2: An Introduction to Rate Laws

  • Chemical reactions are reversible.
  • Reverse reaction can also occur.
  • Under the condition that the reverse reaction is negligible, the reaction rate depends only on the concentration of the reactants. Rate law - shows how rate depends on the concentrations of reactants. Proportionality constant \(k\) (rate constant) and \(n\) (order of reactant) must be determined experimentally.

Types of Rate Laws

  • Differential rate law/rate law - how rate depends on concentration.
  • Integrated rate law - how concentration depends on time.
  • We can work backwards from the rate law to find steps by which the reaction occurs.

15.3: Determining the Form of the Rate Law

  • First order: when the reactant is halves, the rate is also halved.
  • Method of initial rates: intiial rate is instantaneou rate determined after the reaction begins.
  • Overall reaction order - sum of the orders.

15.4: The Integrated Rate Law

  • Rate laws express rate as a function of reactant concentrations.
  • Instead, express reactant concentrations as a function of time.

First-Order Rate Laws

  • First-order reaction - if the concentration of a reactant doubles, the concentration of the product doubles too.

Half Life of a First Order Reaction

  • Time required for a reactant to reach half of its original concentration - \(t_{1/2}\).
  • Half life does not depend on concentration.

Second-Order Rate Laws

  • For a second order reaction, half-life depends on \(k\) and \([A]_0\); for a first-order reaction it depends only on \(k\).

Zero-Order Rate Laws

  • Zero order reaction: \(Rate = k[A]_0 = k(1) = k\)
  • Most often encountered when a substance like a metal surface or an enzyme is required for the reaction to occur.
  • Rate is a constant because it is controlled by waht happens on the surface rather than the reactant.

Integrated Rate Laws with MOre Than One Reactant

  • Special techniques are required to deal with more complicated reactions.
  • Pseudo-first-order-rate law: simplify a complicated rate law.
  • Kinetics of complicated reactions can be studied by observing one reactant at a time.

15.5: A Summary of Rate Laws

  • To simplify rate laws for reactions, assume only the forward reaction is important.
  • Differential rate law - rate vs concentration. Integrated rate law - concentration vs time.
  • Experimentally determine type of rate law and write the other law.
  • Method of initial rates

15.6: The Steady-State Approximation

  • Concentration of intermediate remains constant as the reaction proceeds.