CHEM 104 General Chemistry for Majors Thermodynamics the study of the transformations of energy from one form into another System and Surroundings
System – region of interest to the observer
Surroundings – the rest of the universe (!) Types of Systems
Can exchange both Can exchange energy Can exchange neither matter and energy but not matter with energy nor matter with with the surroundings the surroundings the surroundings Work and Internal Energy
Generally, work is a motion against an opposing force, …however this is not always in the literal everyday language sense
Work always has the units of energy – kg • m2 •s-2
For moving an object against an opposing force, Work = opposing force × distance
Work is the transfer of energy to (or from) a system by force acting through a distance
Internal energy (U) is the total store of energy of a system
The absolute value of internal energy of a system is unknowable; therefore we only deal with changes in internal energy (∆U)
Expansion work
Expansion work involves change in volume
Gas expanding against a piston in a cylinder is a convenient example of expansion work Isothermal Reversible Expansion
A process is reversible if its direction can be reversed by an infinitely small change in a variable Heat
Heat (q) is the energy transferred as a result of a temperature difference When energy is only transferred as heat, ∆U = q Let us agree to that for heat entering the system: q > 0 and for heat leaving the system: q < 0
•Exothermic process: q < 0 •Endothermic process: q > 0 •Thermoneutral process: q = 0
Heat Capacity
• Heat capacity is an extensive property
C = q/∆T
• Specific heat capacity (Cs) is the heat capacity per mass unit; molar heat capacity (Cm) is the heat capcity per mole
q = mCs∆Tor q = nCm∆T
The First Law of Thermodynamics
The internal energy of an isolated system is constant ∆U = q + w State and Process Functions
• A state function defines a property of the state of the system and does not depend on the path taken. The change in the state function only depends on the starting and the end states. • A process function defines transition between states of the system.
U from translation, rotation, vibration
• Utranslation = 3/2 × nRT
• Urotation = nRT (for linear molecules)
or
• Urotation = 3/2 × nRT (for nonlinear molecules)
• At room temperature, the vibrational contribution is small (it is of course zero for monatomic gas at any
temperature). At some high temperature, it is (3N-5)nR for linear and (3N-6)nR for nolinear molecules (N = number of atoms in the molecule.
Enthalpy
H = U + PV Enthalpy is a state function At constant pressure: ∆H = ∆U + P∆V ∆H = q
At constant pressure, the change in enthalpy is equal to the heat releases or absorbed by the system. Exothermic: ∆H < 0 Endorthermic: ∆H > 0 Thermoneutral: ∆H = 0 Isobaric (Cp) and isochoric (Cv) heat capacity
Cv = ∆U/∆T
Cp = ∆H/∆T
For an ideal gas:
Cp = Cv + nR
Cp,m = Cv,m + R Consider that, at constant pres sure, transfer of heat to an ideal gas system results in work done by the system Heat capacities of ideal gases
We can calculate the isobaric and isochoric heat capacities of ideal gases for monatomic, linear, and nonlinear molecules.
Example to the right:
I2 molecule
Enthalpy of Physical Change
For phase transfers at constant pressure
Vaporization: ∆Hvap = Hvapor –Hliquid
Melting (fusion): ∆Hfus = H liquid –H solid
Sublimation: ∆Hsubl = H vapor –H solid
For the same temp: ∆Hsubl = ∆Hvap + Hfus
∆Hforward = -∆Hreverse
Consequences of being a state function
Heating Curve
Enthalpy of chemical change (reaction)
Enthalpy of reaction is the heat released or absorbed as a result of a chemical reaction
∆Hrxn = ΣHproducts – ΣHreactants
∆Hrxn = ∆Urxn + ∆ngasRT
Standard reaction enthalpy (∆Ho) refers to reactions where all products and reactants are in their standard state Why bother with standard states? Hess’s law
The overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction can be divided 0 Enthalpy of combustion (∆H c) – change in enthalpy of a mole of substance upon combustion under standard conditions Various measures of ∆Hc and CO2 content of fuels
Fuel FW kJ/mol kJ/g molCO2/mol molCO2/kg molCO2/MJ Hydrogen 2 -286 -143 0 0 0
Methane 16 -890 -55.6 1 63 1.12
Isooctane 114 -5461 -47.9 8 70 1.46
Benzene 78 -3268 -41.9 6 77 1.84
Methanol 32 -726 -22.7 1 31 1.38
Ethanol 46 -1368 -29.7 2 43 1.46
Carbon 12 -394 -32.8 1 83 2.54
Biodiesel 298 -11962 -40.1 19 64 1.59
NIST Chemistry webbook: http://webbook.nist.gov/chemistry/ 0 Standard enthalpy of formation (∆H f) of a substance is the standard enthalpy of formation of this substance
from the elemental compounds at standard conditions Born-Haber cycle is an application of Hess’s law Variation of enthalpy with temperature
0 0 ∆H (T2) = ∆H (T1) + (T2 –T1) ∆Cp
∆Cp = ΣnCp,m(products) - ΣnCp,m(reactants)
ENTROPY
A spontaneous process has a tendency to occur without being driven by an external influence; does not have to be fast
Entropy is a measure of disorder (probability?) Entropy is a state function
The 2nd law: The entropy of an isolated system increases in the course of any spontaneous change Changes in physical state and entropy (changes)
During the phase transition, the temperature remains constant
At the temperature of phase transition, the transfer of heat is reversible
For P = const, qtransition = ∆Htransition
Ergo: ∆Stransition = ∆Htransition /Ttransition 0 -1 -1 ∆S transition – standard entropy of transition (J mol K )
The Third Law of Thermodynamics
The entropies of all perfect crystal approach zero as the absolute temperature approaches zero Statistical entropy
S = k ln(W), where W is the number of different microstates for the macrostate
The statistical definition of entropy is equivalent to that derived from macroscopic observations
0 Standard molar entropy (S m)
S(T) = S(0) + ∆S(0ÆT)
∆S(0ÆT) must account for phase transitions
Standard reaction entropy
0 0 0 ∆S rxn = ΣnS m(products) - ΣnS m(reactants)
0 For reactions in which the amount of gas increases, ∆S rxn is usually positive (and vice versa).
Also, generally, the increase in the number of particles in (ideal) solution or gas phase leads to increase in entropy. Global changes in entropy
The 2nd law refers to the isolated system. In order to determine whether the process is spontaneous, we need to know the change in entropy for both the system and the surroundings.
∆Stot = ∆S + ∆Ssurr
(Dynamic) Equilibrium
A system is at equilibrium when it has no tendency to change in either direction. Microscopic processes continue, but there is no net change. In other words, neither the forward nor the reverse process is spontaneous, which means….
∆Stot = 0
Gibbs free energy
Allows us to determine spontaneity considering the system alone May be thought to quantify the maximum amount of non- expansion work the system can perform Is a state function G = H – TS ∆G = ∆H - T∆S (T, P = const) ∆G<0 corresponds to a spontaneous process Sometimes enthalpy “competes” with entropy Spontaneity or favorability of a process may change with temperature Gibbs free energy of reaction and standard Gibbs free energy of formation
0 0 0 ∆G rxn = ΣnG m(products) - ΣnG m(reactants)
Standard Gibbs free energy of formation for a compound is the standard Gibbs free energy of a reaction to produce 1 mole of said compound from elemental compounds in their standard state. Units of J/(mol).
0 0 0 ∆G rxn = ΣnG f(products) - ΣnG f(reactants)
Gibbs energy and non-expansion work
Gibbs energy of a closed system is the measure of the energy “free” to do non-expansion work (e.g., mechanical, electrical, etc.).
The change in free energy of a process (∆G) is the maximum non-expansion work this process can do. Effect of temperature on ∆G Physical Equilibria
∆G = 0 Vapor pressure Variation of vapor pressure with temperature
Clausius-Clapeyron equation
0 ln(P2/P1) = ∆H vap/R × (1/T1 –1/T2)
Vapor pressure increases with temperature The increase is greater for greater enthalpy of vaporization
Freezing and melting
For most substances (but not all! E.g., water) the density of the solid is higher than the density of the liquid. Because of this, melting points for most substances decrease with increasing pressure. For water, it is the opposite dependence. Phase diagrams
Phase diagram is a two- or multi- dimensional plot that shows the preference for phases as a function of conditions (temperature, pressure…)
Phase boundaries indicate equilibrium between two phases Triple points indicate equilibrium among three phases Phase diagrams for CO2 and sulfur
Critical point
Critical point – a point at which the liquid-vapor boundary disappears. Substance cannot be liquefied above its Tc Critical point data Solubility
The molar solubility of a substance in a solvent is the molar concentration of this substance at the point of dynamic equilibrium (saturated solution) “Like dissolves like”
Dissolution of A in B destroys the intermolecular interactions in A, but also diminishes them among the molecules (ions) of B. Something has to “pay” for the loss of these interactions if this is to be a spontaneous process. A-B interactions in solution therefore need to adequately compensate for the loss of A-A and the diminishment of B-B interactions. What different “likes” are out there?
Ambiphilic molecules
Solubility of gases: Henry’s Law
Solubility of gas in a liquid is proportional to the partial pressure of the gas:
s = kHP
Liquid breathing
Mice survived in liquid perfluoroalkane saturated with oxygen for hours.
Goldfish chilling in the water layer on top… Enthalpy of (dis)solution
Enthalpy of solution is the heat change upon dissolving a substance in a solvent In concentrated solutions, molecules or ions of solute may interact with each other differently at different concentrations and so the molar enthalpy of solution will be dependent on the final concentration. For that reason, it is easier to consider limiting enthalpies, which are enthalpies of solution at infinite dilution.
Ideal and non-ideal solutions
An ideal solution is one where intermolecular interactions between molecules of solvent and of the solute(s) are the same (in energy).
The enthalpy of formation of an ideal solution is zero.
Real solutions approach “ideality” if the solvent and the solute are very similar chemically or upon dilution.
Gibbs free energy of (dis)solution
∆G = ∆H - T∆S
Molality
Molarity is a measure of concentration expressed as moles of solute per liter of solution Molar fraction is a measure of concentration expressed as moles of solute per the total number of moles in the solution Molality is a measure of concentration expressed as moles of solute per kg of solvent Raoult’s law
The vapor pressure of the solvent is proportional to its molar fraction in solution
P = xsolventPpure
François-Marie Raoult Raoult’s law and ideal solutions
Solutions that obey Raoult’s law are ideal solutions
In reality A-A, A-B, and B-B interactions differ and solutions are then nonideal and do not obey Raoult’s law exactly
Solutions of ionic materials usually deviate to a greater extent
Solutions “approach ideality” at infinite dilution
bp Elevation and mp depression
The presence of non-volatile solute increases the boiling point of the solution
The presence of a solute decreases the freezing point of the solution Calculating ∆Ttransition
The increase of the boiling point of the solution (∆Tb) is proportional to the molality of the solute
∆Tb = Kb ×m
2 Kb = RTb × M / ∆Hb
The decrease of the freezing point of the solution (∆Tf) is proportional to the molality of the solute
∆Tf = Kf ×m
2 Kf = RTf × M / ∆Hf
Note on ionic compounds
Ionic compounds (aka electrolytes) may give more than one particle per formula unit upon dissolution. In dilute solutions, electrolytes are fully ionized. In more concentrated solutions, the “effective” number of particles is smaller.
∆Tf = i × Kf ×m
The coefficient “i” here is the empirical van’t Hoff coefficient. Its deviation from an ideal case is correlated with the degree of ionization. Osmosis Osmosis is a flow of the solvent through a membrane into a more concentrated solution
Semipermeable membrane permits only certain types of molecules or ions to pass through
Osmotic pressure (Π) is the pressure needed to counteract the flow of solvent Π = iRTc
Reverse Osmosis Osmosis in biology and industry Ebullioscopy, cryoscopy, and osmometry
Ebullioscopy allows determination of the concentration of the solute from the magnitude of the boiling point elevation.
Cryoscopy allows determination of the concentration of the solute from the magnitude of the freezing point depression.
Osmometry allows determination of the concentration of the solute from the osmotic pressure.
All three can be used to experimentally determine molecular weight or degree of dissociation. Binary Liquid Mixture: Vapor Pressure
PA = xA,liqPA,pure
PB = x B,liqPB,pure
P = PA + PB
xA,vapor = PA/P = PA/(PA + PB) xB,vapor = P B/P = PB/(PA + P B)
The vapor phase is richer in the more volatile component than the liquid phase Mixture boiling and distillation
The boiling point of a binary mixture is the temperature at which the total vapor pressure equals external pressure (e.g., 1 atm). Fully miscible liquid mixtures boil “together”. Individual components of the mixture do not boil “separately”. The bp of a binary mixture depends on the composition. Fractional distillation
Deviations from ideal behavior
If ∆Hmix for the solution is not zero, than the solution is not ideal and will deviate from Raoult’s law.
∆Hmix > 0 ∆Hmix < 0
Azeotropes
Azeotropes are mixtures for which the composition of the vapor phase is the same as the composition of the liquid phase Because of this, azeotropic mixtures cannot be separated by simple distillation Azeotropes can only form for non-ideal mixtures but deviation from ideal mixture does not automatically imply the existence of an azeotrope Azeotropes can be binary, tertiary, etc.
Minimum-boiling azeotrope
A minimum-boiling azeotrope has a boiling point that is below the boiling point of any other mixture of the components. In distillation, the distillate will approach the azeotrope but never cross past the azeotrope’s composition Maximum-boiling azeotrope
A maximum-boiling azeotrope has a boiling point that is above the boiling point of any other mixture of the components.
In distillation, the residue will approach the azeotrope but never cross past the azeotrope’s composition.
Some common azeotropes (by wt)
Water (2%) – ether (98%) +34.2 ºC Water (4%) – ethanol (96%) +78.1 ºC Water (9%) – benzene (91%) +69.3 ºC Water (80%) – hydrogen chloride (20%) +110 ºC Water (2%) – sulfuric acid (98%) +338 ºC Ethanol (32%) – benzene (68%) +68.2 ºC Water (7%) – ethanol (19%) – benzene (74%) +64.9 ºC
How do you “break” an azeotrope?
¾ Change the pressure ¾ Add a non-volatile material that dissolves differently in components (e.g., ionic salt for water mixtures) ¾ Chemically remove one component ¾ Add another component to form a new azeotrope Chemical Equilibrium
Chemical equilibrium is always dynamic The forward reaction and the reverse reaction are both taking place and the rates of the forward and the reverse reaction are the same At equilibrium, the system reaches minimal G Equilibrium constant
Activity of substance J or aJ is its “effective concentration” divided by standard concentration.
For ideal gases, activity is the partial pressure of the gas (in bars). For dilute solutions, activity is molar concentration. For non-ideal situations activity also reflects the deviations from ideal behavior. Equilibrium constant for a reaction is expressed as the product of activities of products over the product of activities of reactants where each activity is raised to the power of the coefficient in the chemical equation
Units
Equilibrium constant does not depend on pressure or concentrations but it does depend on temperature All equilibrium constants are unitless because we use unitless activities. However, because the activities are often replaces by pressures or concentrations, you might see K expressed in those units. NOT’s
Equilibrium constant is usually NOT simply the ratio of concentration of products to reactants! Equilibrium constant does NOT define the precise composition of an equilibrium mixture. Equilibrium constant CANNOT be negative (but can be less or greater than 1). Relationship of K with Gibbs energy
º ∆Gr = -RT × ln(K) º ∆Gr = ∆Gr + RT × ln(Q)
Q – reaction quotient; at equilibrium Q = K º ∆Gr - standard Gibbs free energy of reaction (difference in G between the products and reactants in their standard states)
∆Gr – Gibbs free energy difference between products and reactants at any point during the reaction. At equilibrium,
∆Gr = 0
Direction of Reaction
Q < K, ∆Gr < 0, reaction has a tendency to proceed towards products
Q > K, ∆Gr > 0, reaction has a tendency to proceed towards reactants
Q = K, ∆Gr = 0, reaction mixture is at equilibrium and has no tendency to go in either direction
Other expressions of Keq
If using concentrations of gases instead of pressures,
∆n K = (cºRT/Pº) Kc
The eq. constant corresponds to a reaction equation with specific coefficients The eq. const. for the forward reaction is the reciprocal of the eq. const. for the reverse reaction If a chemical reaction is a sum of two others, the eq. const. can be expressed as the product of the other two eq. constants.
Equilibria and change in conditions
Le Chatelier’s principle: When a stress is applied to a system in dynamic equilibrium, the equilibrium tends to adjust to minimize the effect of the stress
Henri Louis Le Chatelier Le Chatelier’s changes
Add reagents or remove products Æ favor forward reaction
Increase pressure Æ favor the direction reducing volume
Increase temperature Æ favor the endothermic direction
Ln(K2/K1) = ∆Hrº/R(1/T1 –1/T2)
Catalysis
Catalyst is a substance that increases the rate of a chemical reaction but is not itself consumed
A catalyst does not affect the equilibrium composition, the equilibrium constant, the standard free energy of the reaction
Kinetics has to do with rates of reactions (how & how fast) Thermodynamics has to do with functions of state Haber-Bosch process Nature Geoscience 1, 636 - 639 (2008)
Haber-Bosch process
Developed in 1909-1913 Originally used Os and U catalyst; then Fe (~500 ºC, 250 atm) Nobel prizes to Haber (1918) and Bosch (1931)
~100 million ton NH3 produced annually
~1% of world’s energy supply 80% used for fertilizer, the rest for chemicals and explosives Consumes 1% of the world’s energy (uses lots of natural gas for hydrogen production + the energy-intensive process) Important industrial processes Acid-Base concepts Svante August Arrhenius 1859 – 1927
Arrhenius concept
Arrhenius, 1880s:
+ Acids form hydrogen ions H (H2O)n in aqueous solution.
Bases form hydroxide ions in aqueous solution.
Examples of Arrhenius acids (in water): HCl, H2SO4, etc.
Examples of Arrhenius bases (in water): NaOH, NH3, etc.
Arrhenius definitions only apply to aqueous solutions.
A general Arrhenius acid-base reaction is the reaction between H+ and OH- to produce water.
Acid + Base Æ Salt + Water
H+ + NO3- + K+ + OH- Æ K+ + NO3- + H2O Johannes Nicolaus Brønsted Thomas Martin Lowry 1879 – 1947 1874 – 1936
Brønsted-Lowry concept
Brønsted and Lowry, 1923:
Acid – a species with a capability to lose H+.
Base – a species with a capability to gain H+.
[As often as not Lowry’s name is omitted and only Brønsted’s name is used.]
Brønsted’s acids and bases are by and large the same acids and bases as in the Arrhenius model but the model of Brønsted and Lowry is not restricted to aqueous solutions. Brønsted’s model introduces the notion of conjugate acid-base pairs. It is logical that if something (an acid) exists and may lose a proton, then the product of such a proton loss is by definition a base since it has the capability to add a proton. Conjugate acids and bases
Acid Base
+ H3 O H2 O
- H2 O OH OH- O2-
+ CH3 CH2
- CH4 CH3
- H2 NCH2 CO2 H H2 NCH2 CO2
+ [H3 NCH2 CO2 H] H2 NCH2 CO2 H
- H2 H Brønsted continued
¾ Theoretically, any compound that has a hydrogen atom in it may behave as a Brønsted acid. ¾ Likewise, any compound with a pair of electrons may behave as a Brønsted base. ¾ Not only the compounds with obvious lone pairs may behave as Brønsted bases. ¾ It is possible for the same compound to be able to behave as a Brønsted base and as a Brønsted acid. ¾ Usually a compound is called acid or base depending on the circumstances. Brønsted continued
Under the Brønsted-Lowry model, an acid-base reaction is always a reaction between an acid and a base giving their conjugate base and acid, respectively. - + - + EtOH + Me2N Li Æ EtO Li + Me2NH Acid1 + Base2 Æ Base1 + Acid2
+ - EtOH + H2SO 4 Æ EtOH2 + HSO4 Base1 + Acid2 Æ Acid1 + Base2
Generally, the reactions proceed to form weaker acids and bases. Solvent system concept
The solvent system concept is applicable to solvents that undergo autodissociation:
Acids are compounds that increase the concentration of the cation. Bases are compounds that increase the concentration of the anion.
The Arrhenius model can be viewed as a part of the solvent system model. Solvent system concept
The Arrhenius model can be viewed as a part of the solvent system model.
For instance, BrF3 undergoes autodissociation: + - 2BrF3 BrF2 + BrF4
In BrF3, KF will be classified as a base, and SbF5 – as an acid. + - KF + BrF3 K + BrF4 + - SbF5 + BrF3 BrF2 + SbF6 An acid-base reaction in water is the reaction between H+ and OH-; an + - acid-base reaction in BrF3 is the reaction between BrF2 and BrF4 . Gilbert Newton Lewis 1875 – 1946
Lewis Concept
Lewis, 1930s: Base is a donor of an electron pair. Acid is an acceptor of an electron pair. For a species to function as a Lewis acid, it needs to have an accessible empty orbital. For a species to function as a Lewis base it needs to have an accessible electron pair.
+ + 6+ Examples of Lewis acids: BF3, AlCl3, SbF5, Na , H , S , etc.
- Examples of Lewis bases: F , H2O, Me3N, C2H 4, Xe, etc. Lewis Continued
A more general view also classifies compounds that can generate a species with an empty orbital as Lewis acids.
Then we can include B2H 6, Al2Cl 6, HCl etc.
Since H+ and any cation from a solvent autodissociation is + a Lewis acid, and anything that can add H or a solvent- derived cation is a Lewis base, the Lewis acid concept effectively includes the ones discussed previously. Lewis Continued
Acid-base reactions under the Lewis model is the reactions of forming adducts between Lewis acids and bases.
BF3 + Me3N Æ F3B-NMe3 HF + F- Æ FHF- - 2- SiF4 + 2F Æ SiF6 - - CO2 + OH Æ HCO3
TiCl4 + 2Et2O Æ TiCl4(OEt2)2 In fact, any chemical compound can be mentally disassembled into Lewis acids and bases: 6+ - S + 6F Æ SF6 4+ - - + - C + 3H + NH2 Æ CH3 + NH2 Mikhail Ilyich Usanovich 1894 – 1981
Usanovich concept
Base – any material that forms salts with acids through neutralization, gives up anions, combines with cations, or gives up electrons. Acid – any material that forms salts with bases through neutralization, gives up cations, combines with anions, or accepts electrons. Hermann Lux Håkon Flood 1904 – 1999 1905 – 2001
Lux-Flood concept
Base – an oxide donor. Acid – an oxide acceptor.
Na2O + CO2 Æ Na2CO3 2- 2+ 2- ZnO + S2O 7 Æ Zn + 2SO4 Element oxides
Various element oxides can combine with water to produce acids or bases Basic oxides – upon reaction with water form materials that + are stronger Brønsted bases than water (decrease [H ]). Acidic oxides – upon reaction with water form materials that + are stronger Brønsted acids than water (increase [H ]) Amphoteric oxides – upon reaction with water form materials that can react with both bases and acids Element oxides
Basic oxides – typically metal oxides (oxides of the more electropositive elements) Acidic oxides – typically non-metal oxides (oxides of the more electronegative elements) Amphoteric oxides – typically oxides of the elements of intermediate electronegativity For the same element, the higher the oxidation state, the more acidic the oxide is.
Amphoteric is not to be confused with amphiprotic –a substance that can act as both a Brønsted acid and base
Proton exchange in water
Water undergoes rapid autodissociation or autoprotolysis:
The equilibrium constant at 25 ºC for this process is -14 Kw = 1.0 × 10
Proton and hydroxide concentrations
Concentrations of H+ and OH- in water are mutually dependent. When [H+] increases, [OH-] decreases pH, pOH and other pBeasts
In general, pX = -log10(X) pH = -log[H+] pOH = -log[OH-]pK= -logK In pure water, pH = pOH = 7 In acidic solution, pH <7; pOH > 7 In basic solutions, pH > 7, pOH < 7 Since pH + pOH = 14, either value is sufficient to describe + - both [H ] and [OH ]
Acidity constants
Acidity constants define the “strength” of an acid or its propensity to dissociate (which is a propensity to donate proton to the solvent) For dilute solutions of acid HA,
+ - Ka = [H ][A ] / [HA] pKa = -logKa
Ka is a constant at a given T for a given solvent; it is an intrinsic property of a compound
Basicity constants
Basicity constants define the “strength” of a base or its propensity to dissociate or accept protons (e.g., from water) For dilute aqueous solutions of base B,
+ - Kb = [HB ][OH ] / [B] pKb = -logKb
Kb is a constant at a given T for a given solvent; it is an intrinsic property of a compound
Conjugate acid-base pairs
The stronger the acid, the weaker its conjugate base The weaker the acid, the stronger its conjugate base
Ka ×Kb = Kw
The pKa value defines both acidity of the acid and the basicity of the conjugate base
Acidity and structure
Let us look at how the structure affects acidity of HA.
1) Which element is the hydrogen bound to? The acidity increases from left to right in the periodic table and from up to down (for main group elements). This is not the same trend as for electronegativities!
Thus HF > H2O > NH3 > CH4, but HI > HBr > HCl > HF, or H2Te > H2Se > H2S > H2O
For otherwise analogous compounds, the one with the heaviest element bound to H is the more acidic one. E.g., CH3SH is more acidic than CH3OH, PH3 is more acidic than NH3 etc.
2) Substituents on the atom that is directly bound to H in HA that stabilize the anion A- increase the acidity of HA. Generally, these are electron withdrawing substituents, however, both inductive and resonance effects must be taken into account. G-X-H system
For an acid G-X-H, where X is any relevant atom, and G – a substituent group:
Zero substituent effect: G = H
Very strongly e-withdrawing: RSO2 , NO2 , ClO3 , CN…
Strongly e-withdrawing: RCO, RSO, NO, CF3 , C6F 5 … Generally, the more oxo groups on the second atom from H, the stronger the effect. (HO-
ClO3 > HO-ClO2 > HO-ClO > HO-Cl)
Weakly e-withdrawing: Aryl, vinyl, halogen, R3 Si, RS, RO…
Anything with a low-lying empty orbital on the 2nd atom from H makes acid stronger.
E-donating: Alkyl, (amino), anionic element of modest e-negativity, such as carbon. The structure of G matters, too. E.g., acetone is more acidic than its imines, but less acidic than 1,1,1-trifluoroacetone: R O O N > > H F C H C C H 3 C H H2 2 H2
Obviously, the farther the change, the smaller the impact.
http://www.chem.wisc.edu/areas/reich/pkatable/ http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf Compound Approx. pKa Compound Approx. pKa
CH4 44 PhCH3 40
NH3 33 Ph3CH 29
H2O 15 CH3 COCH3 22
H2 S 9 O2N-CH 3 10
HF 3.5 C5H 6 15 HCl -7 Indene 19
HI -11 Ph-NH2 31
HOCl 7.2 Ph2NH 25
HOClO 2 (Me3 Si)2 NH 26
HOClO3 -10 Me2 NH 35
H2 SO4 -3 iPr2 NH 38 - HSO4 2 MeOH 16
CF3 SO3H -13 t-BuOH 19 + NH4 9 Me3 SiOH 16 - HS 19 CH3 COOH 4
H3 PO4 2.1 PhCOOH 3
H3AsO 4 2.3 F3 CCOOH 0 pH of solutions of weak acids
Toolbox 10.1 pH of solutions of weak bases
Toolbox 10.2 pH of salt solutions
Salts of weak acids make basic solutions Salts of weak bases make acidic solutions
In other words, salts can be acids or bases, too
Acid rain Solvent Limitations
Solution acidities often differ greatly from the gas phase acidities. This stems from the interaction of solvent with the bases and acids involved.
Solvent itself may also function as a base or an acid.
+ - - + H2O + HCl H3O + Cl H2O + CH3Li OH + Li + CH4 Water as a base Water as an acid
+ - HNO3 + H2SO4 H2NO3 + HSO4
HNO3 as a base - + HNO3 + Me3N NO3 + HNMe3
HNO3 as an acid
+ - Me2SO + HClO4 Me2SOH + ClO4
DMSO as a base - Me2SO + Ph-K MeSOCH2 + Ph-H DMSO as an acid Solvent leveling effect
Solvent leveling effect: in any solvent, the strongest Brønsted acid that can exist is the protonated solvent species; the strongest Brønsted base that can exist is the deprotonated solvent species.
The nature of the solvent defines the window of possible acidities of solutions. The weaker the solvent is as an acid, the greater basicity can be achieved in such a solution. The weaker the solvent is as a base, the greater acidity can be achieved in such a solution. Weak acid solvent permits solutions of stronger bases.
Weak base solvent permits solutions of stronger acids.
+ Solvents for which the difference in pKa’s of [Solv] and [Solv]H is small (e.g., H SO ) have narrow “acidity windows”. 2 4
Solvents for which the difference in pK ’s of [Solv] and [Solv]H+ is large (e.g., a hydrocarbons) have wide “acidity windows”.
pH of polyprotic acid solutions
Name Formula pKa1 pKa2
Oxalic HO2C-CO2H 1.29 4.28
Malonic HO2C-CH2-CO2H 2.85 5.70
Succinic HO2C-(CH2)2-CO2H4.255.64
Glutaric HO2C-(CH2)3-CO2H4.345.42
Adipic HO2C-(CH2)4-CO2H4.435.42
Solutions of salts of polyprotic acids
We can estimate the pH of a solution of an amphiprotic salt of a polyprotic acid: pH = ½(pK + pK ) a1 a2 Provided that for the input concentration of the salt S,
S >> Kw/Ka2 and S >> Ka1
For a solution of a salt containing an anion of the polyprotic acid from which all the protons responsible for acidity in water are removed we simply use the techniques for calculating pH for a solution of a weak base. Examples: Na2S, K3PO4, K2HPO 3, CH3PO3K2
Concentrations of solute species
Example 10.13 Very dilute solutions of strong acids and bases
Example 10.14 Very dilute solutions of weak acids
Example 10.15 Composition and pH Phosphoric acid and pH Buffers
Buffer is usually a mixture of either a weak acid with its salt by a strong base (e.g., AcOH + NaOAc)
or a mixture of weak base with its salt by a strong acid
In other words, buffers contain comparable concentrations of conjugate acid and base and both are weak pH of a buffer solution
- - [HA] ≈ [HA]init and [A ] ≈ [A ]init
The pH of a buffer is usually close to the pKa
Lewis Acids and Bases
The empty orbital of a more classical Lewis acid is usually an essentially non- bonding unoccupied orbital. It is usually predominantly a single atomic orbital of an appropriate symmetry to form a sigma bond.
The pair of electrons of a more classical Lewis base is usually a lone pair of electrons which occupy a non-bonding or an antibonding orbital.
Two very common classes of Lewis acids based on main group elements are trivalent boron and aluminum compounds such as BCl3 or AlCl3 and pentahalides of group 15 elements (e.g., SbF5).
+ Carbocations R3C are isoelectronic with R3B and are also Lewis acids.
The lower the empty orbital of a compound is in energy, the stronger it is a Lewis acid.
The higher the empty orbital of a compound is in energy, the stronger it is a Lewis base. The strength of a Lewis acid or base may also be defined by the equilibrium constant of:
A + :B A-B Keq = [AB]/([A][B])
Problem: by this definition, the strength of an acid will vary depending on the base, and vice versa. In fact, there is no scale of Lewis acid (or base) strength precisely for this reason. We can define such scale for Lewis acids (bases) only with respect to the same and only Lewis base (acid). It would be slightly impractical to have a 60 volume “Handbook of Tables of Lewis Acid and Bases Strengths”
In addition, it is not the only problem… SIZE MATTERS!
We had a good reason to ignore steric effects in our discussion of Brønsted acid-base properties. H is the smallest atom and the steric component to the equilibrium below is usually negligible. No te also that the Brønsted system is the Lewis system with a single acid – H+. That’s why we could have a scale of Brønsted acidities. + - HA H + A sterics are not important That is not true for the Lewis concept. It is tempting to think that Lewis basicities will parallel Brønsted basicities. That holds, and only approximately, when we compare Lewis bases (acids) of similar steric influence. CH3
N N N CH3 N CMe3
CH3 H3C B CH3
Comparative Lewis acid/base data
Amine -PA, gas pKb in Order, ΔH, Order, t phase H2O BF3 BMe3 BBu 3
NH3 -202 4.75 3 -13.8 2
MeNH2 -211 3.38 2 -17.6 1
Me2NH -218 3.23 1 -19.3 3
Me3N -222 4.20 4 -17.6 4
Et2NH -16.9
Et3N -229 -10 Quinuclidine -231 -20 Pyridine -218 -17.9 N Quinuclidine
PA – proton affinity (-∆H of proton addition), in kcal/mol;
t With BF3 and BBu 3 the order only given (1 – strongest adduct), with BMe3 ΔH of formation of a complex of amine with BMe3 is given in kcal/mol.
Table taken from Brown, H. C. J. Chem. Soc. 1956, 1248.
Heats of reactions of pyridine bases with Lewis acids
Lewis Acid Pyridine base, R = ΔHreaction, kcal/mol
PCl5 H -25.5
PCl4F H -30.1 Numbering of positions PCl3F2 H -37.3 about the pyridine ring SbCl5 H -38.7 4 BF3 H -31.7 5 3
BCl3 H -39.5 6 2 BBr3 H -44.5 N
SbCl5 2-Methyl -36.6
SbCl5 4-Methyl -41.4
SbCl5 4-Ethyl -41.1
SbCl5 4-Isopropyl -40.5
Source: Holmes, R. R.; Gallagher, W. P.; Carter, R. P. Inorg. Chem. 1963, 2, 437. Adducts of Me3Al with N, P, S, and O donors
# Base ΔHf, # Base ΔHf,
1 NH3 -27.6 10 THF -22.9 Values are for monomeric AlMe . ∆H for the 2 MeNH -30.0 11 2-Methyl-THF -22.9 3 2 reaction 3 Me2NH -30.8 12 2,5-DimethylTHF -23.0 AlMe3 Æ ½Al2Me6 4 Me N -30.0 13 Et O -20.2 3 2 is –10.2 kcal/mol 5 Pyridine -27.6 14 Me O -20.3 2 References: 6 2-Picoline -26.1 15 Ph P -17.6 3 (a) Henrickson, C. H.; Duffy, 7 2,6-Lutidine -19.9 16 Me3P -21.0 D.; Eyman, D. P. Inorg. Chem . 1968, 7, 1047. 8 Et3N -26.5 17 Et3P -22.1 (b) (b) Henrickson, C. H.; 9 Et2NH -27.3 18 Et2S -16.8 Eyman, D. P. Inorg. 19 Me2S -16.7 Chem . 1968, 7, 1047.
Numbering of positions picoline = methylpyridine about the THF ring lutidine = dimethylpyridine THF = tetrahydrofuran 4 3 5 2 O Donor (Acceptor) Atom Size Influence
Acid Base ΔHf
BMe3 Me3N -17.6
BMe3 Et3N -10
BMe3 Et2NH -16.9
AlMe3 Me3N -30.0
AlMe3 Et3N -26.5
AlMe3 Et2NH -27.3
AlMe3 Me3P -21.0
AlMe3 Et3P -22.1
Steric effects diminish in importance with the increasing size of the donor and/or acceptor atom in a Lewis acid/base pair.
In other words, heavier analogs (R3 Al vs. R3 B; R3 P: vs. R3 N:) are less sensitive to varying the sterics of the counterpart. Titration of strong acid by strong base and vice versa
Stoichiometric point always at pH = 7
Titration of weak acid by strong base
The stoichiometric point is at pH > 7. At that point, the solution contains water and a salt of a weak acid (i.e., a weak base) To calculate the pH at any point, consider the chemical reaction taking place and use the product concentrations to find the pH. Before the stoichiometric point: buffer conditions (B, C, D on graph) After the stoichiometric point: pH of a solution of a strong base Titration of weak base by strong acid
The stoichiometric point is at pH < 7. At that point, the solution contains water and a salt of a weak base (i.e., a weak acid) To calculate the pH at any point, consider the chemical reaction taking place and use the product concentrations to find the pH. Before the stoichiometric point: buffer conditions (top part of graph) After the stoichiometric point: pH of a solution of a strong acid pKa Determination
At the point halfway to the stoichiometric point, the pH of the solution in a titration of (1) a weak acid by strong base or
(2) weak base by strong acid
corresponds to the pKa of the weak acid (1) or the pKa of the conjugate acid of the weak base (2) Indicators
Indicators (in this context) are compounds that dramatically change color in response to changes in pH. Typically, indicator molecules are weak acids and the color change corresponds to the difference in color between the acid and its conjugate base. An indicator changes color near the pH that equals to the pKa of the indicator. Color change occurs mostly within the range of ±1 unit of pH within pKa.
Various indicators Me2N Me2N CO2Na N N N N
SO3Na Basic form of Methyl orange Basic form of Methyl red pKa =3.4 pKa =5.0
HO OH HO OH
O O SO2 C O
Acid form of Phenol red Acid form of Phenolphthalein pKa =7.9 pKa =9.4 Indicator selection
The best indicator has the pKa close to the pH of the equivalence point of the solution under study Polyprotic acid titrations
With polyprotic acids, tritration by a strong base results in more than one stoichiometric point.
The stoichiometry of the reaction tells us which species are present in solution and that knowledge allows us to calculate pH. On the graph, points B and D are the two stoichiometric points (solution of - 2- HC2O4 or C2O4 , resp.).
Points A and C correspond to equal
- concentrations of either H2C2O4/HC2O4 or HC O -/C O 2- and so pH(A) = pK 2 4 2 4 a1 and pH(C) = pK a2
Solubility equilibria
The equilibrium constant for the reaction of dissolution is denoted Ksp (solubility product).
Ksp is NOT the solubility. Solubility of the material in water can be calculated from K . We will denote sp the molar solubility as s.
Ksp is calculated for complete dissociation in water. Because of various approximations, K and the associated calculations sp should be thought of as estimates.
Common ion effect
The common ion effect is one of the manifestations of the Le Chatelier principle.
The molar solubility of the material will be smaller if the aqueous solution already contains one of the ions this material would produce upon dissolution. For example, the solubility of AgCl will be decreased if chloride ions are added to the solution.
Again, this is mostly an estimate – the behavior of ions is often not ideal.
Predicting precipitation
Precipitation will be thermodynamically favorable if
Qsp > Ksp