Final Review Notes

CHEM 4AL Section 102 (Monday 2-6pm) GSI: Christine Chang ([email protected]) Office Hours: (Dead Week) Tuesday 4:30 – 5:30 pm and Thursday 3:00 – 4:00 pm

Some Related Notes Electronegativity

Recall that:

‐ Ionization energy: the energy needed to remove an electron from the atom ‐ Electron affinity: the negative of the energy released when an electron is gained by the

atom ‐ Electronegativity: the tendency of the atom to “hold” electrons closer to itself

(Defined mathematically as )

When two atoms in a molecule have differing electronegativities, a permanent dipole moment occurs. The more electronegative atom attracts electrons more than the less electronegative atom, creating partial negative and positive charges in the molecule.

Quantum Mechanics

Heisenberg Uncertainty

∆ ∆ħ2

∆ ∆ħ2

What is Quantum Mechanics?

‐ Quantum mechanics is physics at the “microscopic scale.” o As a system gets larger, it behaves more classically. For instance, a baseball

exhibits relatively little quantum mechanical behavior. ‐ Wave-particle duality: electromagnetic waves can act as particles, and particles of matter

can act as waves. ‐ Energies of particles can be discrete, or quantized. ‐ The wavefunction Ψ is the most complete description that can be given to a physical

system.


‐ Born postulate: The probability of finding a particle described by the wavefunction Ψ is: , ∗ | | with the normalization condition 1 ∗ satisfied.

Schrödinger Equation

Operators

‐ What is an operator?

o Some examples of operators: ∙ ∙ ∙

‐ We can define the eigenvalue of operator as:

Understanding the Schrödinger Equation

‐ We use the Schrödinger equation to describe a quantum system! ‐ How do we get the Schrödinger equation?

We want E (total energy) = T (kinetic energy) + V (potential energy).

For the electron, .

PE = Coulombic forces between two electrons

ħ2 4

‐ The Schrödinger equation predicts the quantization of energy!

o E is the energy eigenstate of the Hamiltonian.


Waves and Orbitals

Waves

‐ The state of a wavelike particle can be described using a wavefunction (Ψ). ‐ Waves have nodes, points at which the wavefunction is equal to zero.

o More nodes = higher energy!

‐ The possible location of an electron in an atom is described by orbitals, which are three-dimensional waves.

o Three-dimensional waves can have radial nodes and/or angular nodes. o In an atom, we name orbitals according to the following rules:

n = (total # of nodes) + 1 l = # angular nodes

(0, 1, 2, …) = (s, p, d, …) , 1, … , 1, ms = ±1

Increasing energy Increasing #

nodes 0

1

2

3

etc.


Quantum Numbers

We can describe an orbital using quantum numbers. These are listed in the table below.

Quantum Number

Name Value

Principal quantum number (# radial nodes) + (# angular nodes) + 1 Angular quantum number (# angular nodes) + 1

Magnetic quantum number {-l, …, 0, …, l } Spin quantum number ±½

Wavefunctions and Nodes

Recall that Ψ depends on r, θ, and φ. Separating Ψ into radial and angular parts:

, , ∙ ,

‐ At a node, Ψ = 0. ‐ At a radial node, R = 0. ‐ At an angular node, Y = 0.

Electron Density Diagrams

Where in the orbital will we be able to find an electron? To deduce this, we use electron density diagrams. Say the electron can be described by the wavefunction Ψ. We can then describe the probability of finding that electron in an orbital by looking at the value of |Ψ|2 for a given value of r.

How do we draw these diagrams? In class, we covered both |Ψ|2 and r2|Ψ|2.

Shielding

What causes shielding?

‐ Electrons carry a negative charge, and thus electrons repel each other. ‐ For multi-electron atoms, Zeff < Z.


Penetration

‐ In a multi-electron system, the electron density of the outer electron can penetrate the electron density of the inner electron.

‐ The 2s orbital penetrates the 1s better than the 2p orbital does. Thus, the 2s orbital is of a lower energy than the 2p orbital.

‐ Similarly, for 1s penetration, 3s > 3p > 3d, etc.

We can use these ideas to develop a better understanding of the periodic table.

The Periodic Table

Orbitals and How Electrons Occupy Them

We fill orbitals with electrons starting with the lowest energy orbitals. (This is called the Aufbau Principle.)

When filling orbitals with electrons, these rules are important:

‐ Pauli Exclusion Principle: Two electrons with the same spin cannot occupy the same quantum state.

‐ Hund’s Rule: Electrons will singly fill orbitals before doubly occupying them.

Exceptions: Cr, Nb, Mo

Periodic Trends

Trends in the various properties of elements can be observed on the periodic table. Some important trends include:

‐ Atomic radius: the size of the atom ‐ Ionization energy: the energy needed to remove an electron from the atom ‐ Electron affinity: the negative of the energy released when an electron is gained by the

atom


‐ Electronegativity: the tendency of the atom to “hold” electrons closer to itself

(Defined mathematically as )

Resonance Structures

What makes a Lewis structure “more significant”?

1. Satisfies the octet rule. Elements with d valence orbitals can accommodate more than an octet.

2. Maximizes the number of covalent bonds. 3. Formal charges are minimized and logically distributed.

Electronegative atoms favor negative, not positive, formal charges. Opposite formal charges should be as close together as possible, while same-sign

formal charges should be as far away as possible.

How do we draw Lewis structures?

1. Count the number of valence electrons in the molecule. For neutral atoms: use the periodic table. (i.e. C = 4 e-, P = 5 e-

) For each positive charge, subtract an electron from the count. For each negative charge, add an electron to the count.

2. Choose a central atom. 3. Attach the other atoms to the central atom. Try to use the guidelines for creating “more

significant” Lewis structures. Dots (electrons), lines/wedges/dashes (bonds)

4. Assign and clearly label formal charges on structures. Counting formal charges: (Group #) – (# bonds + # electrons)

i.e.

N: Group 5 – (2 e- +3 bonds) = 0 3H: Group 1 – (1 bond) = 0


Oxoacid strength

‐ What is a conjugate acid/base? Acid + Base → Conjugate Base + Conjugate Acid

‐ To examine the acid strength of an oxoacid (contains two or more oxygens), we can look at the resonance stabilization of the conjugate base.

‐ Question: which oxoacid is the most stable, H2SO4, H3PO4, or HClO4?

Valence Shell Electron Repulsion (VSEPR) Theory

What is VSEPR?

‐ VSEPR theory is a predictive theory for the geometric shapes molecules will most likely assume based on the number of bonds and lone electron pairs which are formed on atoms.

o Electron-electron repulsion: Bonds/lone pairs will want to be as far away from each other as possible; hence, the geometric configurations which allow for this can be used to predict molecular geometry.

‐ Steric number = (# atoms bonded to central atom) + (# lone e- pairs on the central atom) ‐ Lone pairs repel electrons more strongly than bonded electrons do, so they push the

angles in atoms.

Using VSEPR to Predict Molecular Geometries

1. Draw the Lewis structures of the molecule. We will use the most significant structure as the basis for the Lewis structure.

2. Assign the steric number to the structure. 3. Arrange the bonded atoms and lone pairs based on the steric number. 4. Deduce the molecular geometry.

Alternatively, you can use AXE notation. (A = central atom, X = bonded atom, E = electron pair.)


Introduction to Molecular Orbital (MO) Theory

Definition: Molecular orbital theory is a method for determining molecular structure. Instead of placing the electrons in bonds between two nuclei, we treat the electrons as existing around and being influenced by both of the nuclei equally.

i.e.

vs.

Lewis structures Molecular Orbitals

(In class we used the term MO-LCAO: molecular orbital linear combination of atomic orbitals.)

Conceptually, think of what happens when two atoms approach each other.

→ Overall, MO theory gives us a more descriptive picture of electron bonding and distribution than Lewis structures do!

Vocabulary:

BondOrder # #

Paramagnetic molecules have unpaired electrons in their molecular orbitals. Diamagnetic molecules have all paired electrons in their molecular orbitals.

The Highest Occupied Molecular Orbital (HOMO) is the molecular orbital with the highest energy which still contains electrons. The Lowest Unoccupied Molecular Orbital (LUMO) is the molecular orbital with the lowest energy which is absent of electrons.

Molecular Orbital (MO) Diagrams

How do we know how to label molecular orbitals?

→ Recall that the interactions between s orbitals result in σ MOs.

In σ MOs, the atomic orbitals directly overlap one another in a head-on approach.

In π MOs, the atomic orbitals interact via side-on bonding interactions.


Remember that Group 6 and 7 elements are exceptions to the typical energetic ordering of molecular orbitals!

Question: How do molecular orbital diagrams look like for bonding between two different molecules?

Before, we looked at homonuclear molecules. We will now move onto heteronuclear molecules.

First, we need to understand the factors governing how and when different atomic orbitals will interact.

1. The symmetries of the interacting atomic orbitals must be the same. We are creating more constructive interference, but also more destructive interference, and these ultimately cancel out and we will see no overall bonding or antibonding interactions. These are called nonbonding orbitals.

2. When ordering the atomic orbitals by energy, the more electronegative atoms will have orbitals lower in energy. This is because the energy of valence electron orbitals is obtained from the negative of the ionization energy.

3. The absolute energies of the atomic orbitals must be similar enough for interaction.

To illustrate these points, we can look at the MO diagram for hydrogen fluoride.

Summary: Drawing Molecular Orbital Diagrams

1. Draw the energy axis. 2. Position the valence atomic orbitals in order of their energy and fill them with electrons. 3. Determine whether either of your atoms is within Groups 6/7 on the periodic table (O, F

columns). If so, we will have to consider the exception case. 4. Draw the molecular orbitals in order of energy. 5. Fill the molecular orbitals with electrons using Hund’s Rule and the Pauli Exclusion

Principle.


More Uses for Molecular Orbital Diagrams

Molecular orbitals can also give us useful information about molecules, particularly about their bond length and bond energy.

Bond Length: By inspection, we can estimate the bond lengths of some atoms based upon periodic trends. The more electronegative an atom is, the more closely it holds its electrons, and the smaller its atomic radius. Thus, the bond length is shorter.

Using MO diagrams, we can also look at bond length by calculating the bond order. A higher bond order signifies a stronger bond, which results in a shorter bond length.

Bond Energy: A stronger bond requires more energy to break. Molecules with shorter bond lengths will have a stronger bonding interaction. Thus, in general, the bond energy is greater.

Hybridization

Definition: Hybridization is the mixing of atomic orbitals into new, hybrid orbitals for the description of bonding in a molecule. The hybrid orbitals reflect the atomic orbitals which contribute to the hybrid orbital, and their relative contributions.

i.e. sp orbitals result from the hybridization of one s and one p orbital, and thus have a 1:1 s:p contribution. (sp2 = 1:2, sp3

= 1:3)

Question: Why is hybridization useful?

Example 1. CH4

Let’s look at the “molecular orbital diagram”:

2p

2s

1s

C1s H+ 4


Notice how there are only two unpaired electrons. Thus, we would expect two covalent bonds to form, resulting in CH2, and meaning CH4 is an unstable molecule.

But in reality, the opposite is observed! (CH4 is stable, and CH2 is very unstable)

How can we explain the existence of CH4?

First, the 2s electron is excited.

Then, the 2s and 2p orbitals hybridize into four sp3 orbitals.

The four sp3 orbitals can then bond to the four H atoms to form covalent bonds which are identical in length and strength.

This is what we observe!

How to Hybridize Orbitals

1. Use VSEPR to determine the geometry of the molecule. 2. Determine the hybridization at each atom (sp3, sp2, sp). 3. Use unused p-orbitals to form π bonds.


Delocalized π-Systems

Aromaticity occurs when electrons are delocalized over a π-system, and lend stability to a molecule. Aromatic molecules have 4n+2 π-electrons. Antiaromatic molecules have 4n π-electrons.

Consider benzene:

We can illustrate the orbitals of benzene using a Frost circle.

How to Draw Frost Circles:

1. Draw the polygon with its point facing downwards, and draw a circle around the polygon. 2. Draw an energy axis. At each polygonal vertex, draw a line to represent a π molecular

orbital. 3. Fill the diagram with the correct number of electrons. (For benzene, there are 6.)

Introduction to Spectroscopy

What is Spectroscopy?

Spectroscopy is the interaction of electromagnetic radiation with atoms and molecules, used to elucidate information about atomic and molecular structure.

When microwave radiation is absorbed, transitions between rotational energy levels are generally observed.


When infrared radiation is absorbed, transitions between rotational & vibrational energy levels are observed.

When visible/ultraviolet radiation is absorbed, transitions between electronic, vibrational, & rotational energy levels are observed.

Thus, we often describe these types of spectroscopy as rotational, vibrational, and electronic spectroscopy, respectively.

The absorption/emission of radiation occurs when a change in the electric field is induced. This is important for our later discussion of selection rules.

The energy of the absorbed radiation is:

∆

The following table illustrates the different types of spectroscopy and the kind of information about the molecule that each method reveals.

Selection Rules

In order for a rotational transition to be allowed:

1) The molecule must have a permanent dipole moment which does not lie along the main rotation axis.

A permanent dipole moment occurs when a pair of nearby electric charges has charges of equal magnitude but opposite sign.

A temporary dipole moment includes weaker phenomena such as induced dipoles and London dispersion forces.


2) ∆ 1 3) ∆ 0

In order for a vibrational transition to be allowed:

1) The molecule’s dipole moment must vary during a vibration. For instance, stretching bond length will have an effect on the dipole moment

( ). Bending bonds to alter the dipole moment can also change the dipole moment. The total number of vibrational modes a molecule will have is equal to 3N – 5 for

linear molecules, or 3N – 6 otherwise. N is the number of atoms in the molecule. 3N degrees of freedom, minus 3 translational, minus 3 rotational (2 for

linear molecules) 2) ∆ 1

Rotational Spectroscopy

We can model rotational spectroscopy quantum mechanically using the rigid rotor approximation.

Rigid rotor:

The solution to the Schrödinger equation for the rigid rotor is

8 1

J = 0, 1, 2, …

I is the moment of inertia.


( )

When electromagnetic radiation is being absorbed, the molecule goes from quantum state J to J + 1. The energy difference between these two states can be written as

∆

8 1 2 1

4 1

Using E = hν, we can calculate the frequencies at which the absorption transitions occur:

4 1

Each energy level has a degeneracy given by

2 1

In rotational spectroscopy, according to the rigid rotor model, transitions must occur between adjacent levels (recall the selection rules).

Note the this model results in evenly spaced lines, separated by distances of 2B, where


8

Note that . This gives you B in units of Hz, or frequency. is in units of wavenumbers (cm-1).

Vibrational Spectroscopy

We can model vibrational spectroscopy quantum mechanically using the harmonic oscillator approximation.

The solution to the Schrödinger equation for the harmonic oscillator is

212

0, 1, 2, …

k is the spring (or force) constant, i.e. bond strength

** Often, is abbreviated as ω, AKA

the angular frequency

2 , where ν is the oscillation frequency ( ! Nu vs. V)

212

12

When electromagnetic radiation is being absorbed, the molecule goes from quantum state v to v + 1. The energy difference between these two states can be written as

∆

232

12

2


This satisfies the condition E = hν, with ν equal to

2

The degeneracy of each state is given by

1 !!

Beer-Lambert Law

The Beer-Lambert Law states that

log log

To find the relative absorbances of two different samples, you can take the ratio of the two absorbances.

loglog

Energy Potentials

Recall that we use the potential well for a harmonic oscillator as an approximation for an intermolecular potential energy curve.


Another model for the intermolecular potential energy well is a Morse potential,

Electronic Spectroscopy

Molecules can undergo electronic transitions as well as rotational and vibrational ones. Generally, the energy difference between the ground and excited electronic level is such that the radiation absorbed for the transition is in the ultraviolet/visible regions.

We represent the electronic states of a molecule as potential energy curves. Within the energy wells, lines representing vibrational states are present. Within each vibrational state, lines representing rotational states are present.


Vibronic transitions are the vibrational transitions in electronic spectra.

Here is a potential energy diagram of O2, showing the multiple electronic states and their associated vibrational states. Note that R, along the x-axis, is a measure of the internuclear distance.

How would you represent the transition from the ground to excited state visually?

Important guidelines for drawing any graphs:

Draw and label axes! Be sure to include units. Label any key points on the graph.

For potential energy diagrams, we will add:

Explicitly label the ground and excited states!


Label the potential energy minima, i.e. the lowest part of the well. Do not forget to include vibrational levels! (You do not need to draw rotational levels.) General idea: If you can label it, label it.

Transition Metal Chemistry

Question: What is a transition metal complex?

Transition metal complexes contain a transition metal center, and molecules (called ligands) bound to the metal center. Generally, they have the form [MLn]x+.

We say that ligands have a covalent type bond or a dative type bond.

What we need to know about ligands:

1. The charge of the ligand. i.e. The Cl ligand has a charge of -1.

2. The number of electrons donated by the ligand in its bond to the metal.

Some of the more common ligands and their electron donating count are listed below.


Crystal Field Theory

Definition: Crystal field theory models the effect that introducing ligands to a metal center will have on the energies of the metal d-orbitals.

The orbitals which overlap the ligands will be split such that they are higher in energy, whereas those which do not are split such that they are lower in energy.

Kinetic Theory of Gases

The ideal gas law states that pressure, volume, and temperature are related by the equation

or

where n is the moles of gas

N is the molecules of gas

In order to use the ideal gas law, we assume that the gas is composed of constantly-moving particles which (a) are sufficiently far apart to avoid intermolecular interactions, and (b) occupy zero volume.

Experimentally, most (sufficiently dilute) gases behave ideally at 1 atm and 0 °C to approximately 1%.

Some Things to Remember:

‐ The term kBT is a unit of energy. Note that each translational degree of freedom in a

particle contributes of energy to the particle.

‐ We derived the ideal gas law by considering the momentum change associated with a gas of density η striking the wall of a container with a speed of vx in the x-direction within a certain interval of time (Δt).

# 12

| | ∆

‐ The mean free path of molecules of diameter d in a gas of density η can be calculated using


1

√2

At higher temperatures and pressures, the ideal gas law is an increasingly inaccurate description of the behavior of gas particles!

Van der Waals Equation of State

To account for intermolecular interactions and molecular size, we present an improved version of the ideal gas law:

Note that a accounts for attractions between molecules, and b accounts for the volume taken up by each particle.

Intermolecular Potentials

We can represent the interactions between the atoms in a molecule using a potential energy curve.


The actual potential energy curves of molecules can be modeled using different equations. In class, we covered the Lennard-Jones potential, which models the energy curve using the equation

4

where ε represents the depth of the well

σ represents the size of the molecules

The minimum of the Lennard-Jones potential represents the preferred molecular diameter.

Introduction to Thermodynamics

Basic Principles

Thermodynamics is the study of the properties and relationships between the various properties of systems in equilibria.

Two important concepts in thermodynamics are work and heat, which refer to how energy is transferred between a system and its surroundings.

‐ Work (w) is defined as the transfer of energy resulting from an imbalance of forces between a system and its surroundings.

‐ Heat (q) is defined as the transfer of energy resulting from a difference in temperature between a system and its surroundings.

∆

where C is the heat capacity

The internal energy U is related to heat and work by

∆

The enthalpy of a system is expressed as

∆ ∆ ∆

Note that any ideal gas obeys the following relation:


We use thermodynamics to describe macroscopic systems.

Microscopic systems can be described using variables (r, p) and Schrödinger’s equation. Macroscopic systems can be described using variables (T, P, V, E, n, etc.).

Over time, if measuring macroscopic properties, we obtain some average value.

Macroscopic properties can be either intensive or extensive.

Intensive properties are determined by the intrinsic properties of the system and do not change as the size of the system changes.

Extensive properties change with the size of the system.

We relate macroscopic properties to each other using equations of state.

Definition: A microstate describes an instantaneous configuration of the microscopic variables of a system.

Laws of Thermodynamics

Thermodynamics is the study of the relationship between properties of the macroscopic systems in equilibrium. We define fundamental principles (“laws”) of thermodynamics to describe the energetics of changes between macroscopic, stationary states of the system.

Zeroth Law of Thermodynamics

Two systems in thermal equilibrium with a third system are also in thermal equilibrium with each other.

To define thermal equilibrium, consider two objects at different temperatures. When the two objects contact one another, a transfer of heat occurs from the object at a higher temperature to the object at a lower temperature.


First Law of Thermodynamics

The First Law is essentially a statement of the conservation of energy in a thermodynamic system.

The change in a system’s internal energy is equal to the heat supplied to the system minus the work done by the system.

∆

Second Law of Thermodynamics

The Second Law is a statement of the tendency of a thermodynamic system towards disorder.

The entropy of a system is a measure of the disorder. For an irreversible process, the entropy of the system plus its surroundings must increase.

For a reversible process, the entropy of the system plus its surroundings is constant.

Using the definition of entropy, we can define the Gibbs Free Energy:

Third Law of Thermodynamics

The Third Law is a statement about the behavior of a thermodynamic system in the zero temperature limit.

As T → 0 K, only the lowest-energy microstates of a system will be populated. o For systems with multiple minimum-energy microstates, the entropy approaches

a constant value. o For systems with only one minimum-energy microstate, the entropy approaches

zero.


Carnot Cycle

Thermodynamics can give insight into the conversion of heat into work. Heat engines withdraw energy as heat from a higher-temperature thermal reservoir, converts some of this energy to work, and discharges the rest of the energy as heat to lower-temperature thermal reservoir.

The Carnot cycle is an example of a thermodynamic cycle, which is where a system goes through a series of different states before returning to its initial state. In the Carnot cycle, we experience the following steps:

1) Reversible isothermal expansion: The gas expands at the hot temperature, Th. Because the process is isothermal, the temperature does not change during the

process. The gas absorbs heat energy and entropy from the high-temperature reservoir to

expand. 2) Reversible adiabatic (or “isentropic”) expansion: The gas expands without the gain or

loss of heat. Because the process is adiabatic, heat does not change during the process. The gas expands, doing work on its surroundings. The associated loss of energy

causes the gas to cool to the cold temperature, Tc. The entropy remains constant.

3) Reversible isothermal compression: The surroundings compress the gas at the cold temperature, Tc.

The surroundings do work on the gas, causing the gas to lose heat energy and entropy to the low-temperature reservoir and compress.

4) Reversible adiabatic (or “isentropic”) compression: The surroundings compress the gas without the gain or loss of heat.

The surroundings do work on the gas, which cause the internal energy to increase. This gain in energy heats the gas to the hot temperature, Th.


The entropy remains constant.

The Carnot cycle can be illustrated thusly:

Image source: Barclay Physics Wiki

Gibbs Free Energy and Equilibrium

The mathematical definition of Gibbs free energy (G) was given earlier:

In a chemical reaction at a constant temperature, the change in G is given as

∆ ∆ ∆

This change in G can elucidate the nature of a chemical process:

ΔGsystem > 0 for a non-spontaneous process. ΔGsystem = 0 for a reversible process. ΔGsystem < 0 for a spontaneous process.

Gibbs free energy is a measure of the maximum amount of non-expansion which can be removed from a closed system.


Image source: Harding at UCLA

We can calculate the ΔG° of a particular chemical reaction by using the free energy of formation and number of moles for the products and the reactants.

∆ ∆ , ∆ ,

The enthalpy of a reaction, ΔH°, can be calculated similarly.

Relation to Equilibrium Constant

In a reaction, the equilibrium constant K is defined as

For instance, if a reaction proceeds from aA + bB → cC + dD, we have

The equilibrium constant is related to the Gibbs free energy by

∆ ln

Equilibrium

Le Châtelier’s Principle

When a change is introduced to a chemical system at equilibrium, the equilibrium will shift to oppose the change.


In terms of concentrations,

∏

∏

We can write the same equation in terms of partial pressures.

∏

∏

To calculate ΔG°, ΔH°, or ΔS° of a particular chemical reaction, we can use the standard G/H/S of formation and number of moles for the products and the reactants.

∆ ∆ , ∆ ,

∆ ∆ , ∆ ,

∆ ∆ , ∆ ,

For a multistep reaction, we need to calculate the ΔG°, ΔH°, or ΔS° of each individual step and sum them at the end.

When dealing with systems at equilibrium, we have to consider that there are three important “time points” in that reaction.

1) Initial Time: This is your system at t0, happily at its initial state. The conditions during this point in time are the initial reaction conditions.

2) Change Time: This is when the system reacts to come to equilibrium. We will see a change in the reaction conditions.

3) Equilibrium Time: This is what your system looks like after equilibrium has been established.

Using these ideas, we can construct what are called ICE tables (initial, change, equilibrium) in order to simplify the process for us. This process is illustrated below, in the following example.


Acids and Bases

We have already learned some important concepts about acids and bases. Some vocabulary to keep in mind:

Acid + Base ⇄ Conjugate Acid + Conjugate Base

HA+ B- ⇄ HB + A-

Definitions

The first definition of an acid and base was made by Arrhenius, who said that acids produce hydrogen ions in aqueous solution, and bases produce hydroxide ions. The Arrhenius definition is limited to aqueous acids and bases.

In chemistry today, we mainly use two principal definitions of acids and bases.

By the Brønsted-Lowry definition of acids and bases:

Acids are proton (H+) donors. Bases are proton (H+) acceptors.

i.e. NH4+ + OH- ⇄ NH3 + H2O

NH4+ is a Brønsted acid, and OH- is a Brønsted base.

By the Lewis definition of acids and bases:

Acids are electron (e-) acceptors. Bases are electron (e-) donors.

i.e. BF3 + F- ⇄ BF4-

BF3 is a Lewis acid, and F- is a Lewis base.

The Acid Dissociation Constant (Ka)

Consider a generalized reaction for an acid in water:

HA(aq) ⇄ H+(aq) + A-(aq)


The equilibrium constant for this expression is:

H AHA

We call Ka the acid dissociation constant because it measures the rate at which the acid dissociates.

Note that Ka is often expressed in terms of pKa. The relation between Ka and pKa is:

p log

Acids and Acid Strength

We will examine the general equation for an acid below. (Note: This equation produces Ka as its equilibrium constant. Why?)

HA(aq) + H2O(l) ⇄ H3O+(aq) + A-(aq)

To measure acid and base strength we commonly use pH and pOH, where:

p log

p log

Acids can come in either the strong variety or the weak variety. Strong acids are acids in which the reaction equilibrium lies strongly to the right. In other words, they dissociate readily. Strong acids yield weak conjugate bases! Some common examples of strong acids include sulfuric acid, hydrochloric acid, and perchloric acid. Calculating the pH of a strong acid is relatively simple.

Weak acids are acids in which the reaction equilibrium lies far to the left. Thus, a weak acid does not dissociate very much in aqueous solution. Weak acids yield strong conjugate bases! Some common examples of weak acids include phosphoric acid, nitrous acid, and hypochlorous acid.

To calculate the pH of a weak acid, we need to use ICE tables.

Amphoteric Substances

Note that water is an amphoteric substance. In other words, water can act as both an acid and a base!


The autoionization for water is as follows:

2H2O(l) ⇄ H3O+(aq) + OH-(aq)

The equilibrium constant for this reaction is

H O OH H OH

Experimentally, [H+] and [OH-] are both equal to 1.0 × 10-7 M, which means that

Kw = 1.0 × 10-14

We can write that for an equilibrium expression,

p p 14 p

or

p p 14 p

Acid/Base Stability

Recall that an acid is stronger if its conjugate base is weaker. Thus, a more stable conjugate base gives rise to a stronger acid!

Buffers

A buffer is a solution which resists a change in its pH when either OH- or H+ is added.

May contain a weak acid and its salt (i.e. HF with NaF) or a weak base and its salt (i.e. NH3 and NH4Cl).

To calculate the pH of a buffered solution, we should use an ICE table.

Organic Acids

An organic acid is an acid with a carbon atom backbone. We often see organic acids containing the carbonyl (C=O) functional group.

Organic acids are usually weak acids. Some examples of organic acids include acetic acid and benzoic acid.


Note that in the examples of acetic acid and benzoic acid, though the acid contains several hydrogens, only the hydrogen attached to the –OH group is acidic. The other hydrogens in organic acids are not acidic and will not dissociate in an acid!

Extensive credit for these notes go to Zumdahl, Gray, and Oxtoby. (Chemistry, Chemical Bonds: An Introduction to Atomic and Molecular Structure, and Principles of Modern Chemistry)

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