Ch. 6: Chemical Equilibrium

Outline:

• 6-1 The Equilibrium Constant

• 6-2 Equilibrium and Thermodynamics

• 6-3 Solubility Product

• 6-4 Complex Formation

• 6-5 Protic Acids and Bases

• 6-6 pH

• 6-7 Strengths of Acids and Bases

Updated Oct. 5, 2011: minor fix on slide 11, new slides 31-42

The Equilibrium ConstantFor the reaction:

aA + bB cC + dD

the equilibrium constant K has the form

K =[C]c[D]d

[A]a[B]b

By definition, a reaction is favoured whenever K > 1.

Each concentration above is expressed as the ratio of the concentration of a species to its concentration in its standard state:Solutes: the standard state is 1 M. (e.g., [A] really means [A]/(1 M) if A is a solute)Gases: the standard state is 1 bar (≡ 105 Pa; 1 atm ≡ 1.013 25 bar)Solids and Liquids: the standard states are the pure solid or liquid. All of the terms above are dimensionless; hence, all equilibrium constants are dimensionless.

The Equilibrium Constant, 2For the various concentrations and pressures to be dimensionless:

Solutions: [A] must be in units of molarity (M or mol L-1)Gases: pD must be in barLiquids or Solids: The ratio [C]/[C]std state must be unity (1), since the standard state is the pure liquid or solid.Solvents: If B is a solvent, [B]/[B]std state is essentially one, since the concentrations are so close to one another.

Final summary: When one evaluates equilibrium constants:

1. Concentrations of solutes should be expressed as moles per liter.

2. Concentrations of gases should be expressed in bars.

3. Concentrations of pure solids, pure liquids, and solvents are omitted because they are unity.

The Equilibrium Constant, 3For the reaction:

HA H+ + A− ; K1 =

[H+ ][A− ][HA]

and the reverse reaction:

H+ + A− HA ; K1

−1 =[HA]

[H+ ][A− ]= 1 / K1

If two reactions are added, then K is the product of the two rate constants:

HA H+ + A− K1

H+ + C CH+ K2

HA + C A− + CH+ K3

K3 = K1K2 =[H+ ][A− ][HA]

•[CH+ ][H+ ][C]

=[A− ][CH+ ][HA][C]

If n reactions are added, the overall equilibrium constant is the product of n individual equilibrium constants.

Equilibrium and ThermodynamicsEquilibrium is controlled by the thermodynamics of a chemical reaction. The heat absorbed or released (enthalpy) and the degree of disorder of reactants and products (entropy) independently contribute to the degree to which the reaction is favoured or disfavoured.

The enthalpy change, ΔH, for a reaction is the heat absorbed or released when the reaction takes place under constant applied pressure. The standard enthalpy change, ΔH°, refers to the heat absorbed when all reactants and products are in their standard states. ΔH > 0 for endothermic processes, and ΔH < 0 for exothermic processes.

The entropy, S, of a substance is a measure of its “disorder.” ** The greater the disorder, the greater the entropy. In general, Sgas > Sliquid > Ssolid. Ions in aqueous solution are normally more disordered than in their solid salts. ΔS > 0 if the products are more ordered than the reactants, and ΔS < 0 if the products are less ordered than the reactants.

** We will not discuss entropy in a rigorous quantitative fashion as in intro thermodynamics courses (e.g., 59-240 and 59-241).

Gibbs EnergyWhen ΔH and ΔS are both positive or both negative, what decides whether a reaction will be favoured? The change in Gibbs energy, ΔG, is the arbiter between opposing tendencies of ΔH and ΔS. At constant temperature, T,

ΔG = ΔH − TΔS

A reaction is favoured (i.e., said to be spontaneous or allowed for a given set of conditions) if the change in Gibbs energy is negative, ΔG < 0. At 25 oC,

HCl(g) H+ (aq) + Cl− (aq); ΔH = −74.85 kJ mol−1

ΔG0 = ΔH 0 − TΔS0

= (−74.85 ×103 J mol−1) − (298.15 K)( −130.4 J K mol−1)= −35.97 kJ mol−1

ΔG° is negative, so the reaction is favoured when species are in their standard states. The favourable influence of ΔH° is greater than the unfavourable influence of ΔS° in this case.

Gibbs Energy, 2The equilibrium constant is dependent upon the Gibbs energy:

K = e−ΔG0 /RT

Hence, the more negative the value of ΔG°, the larger is the equilibrium constant. For the dissociation of HCl (g):

K = e−(−35.97×103 J mol−1 )/(8.1344 J K−1mol−1 )(298.15 K)

= 2.00 ×106

The large K indicates that HCl (g) is very soluble in water and is nearly completely ionized to H+ and Cl− when it dissolves.

To summarize, a chemical reaction is favoured by the liberation of heat (ΔH < 0) and by an increase in disorder (ΔS > 0). ΔG takes both effects into account to determine whether or not a reaction is favourable. We say that a reaction is spontaneous under standard conditions if ΔG° < 0, or equivalently, if K > 1. The reaction is not spontaneous (i.e., will not occur under a given set of conditions) if ΔG° is positive (K < 1).

LeChatelier’s PrincipleSuppose that a system at equilibrium is subjected to a change that disturbs the system.Le Châtelierʼs principle states that the direction in which the system proceeds back to equilibrium is such that the change is partially offset. For example:

BrO3− + 2Cr3+ + 4H2O Br− + Cr2O7

2− + 8H+

K =[Br− ][Cr2O7

2− ][H+ ]8

[BrO3− ][Cr3+ ]2 = 1×1011 at 25 oC

Starting conditions:[H+ ] = 5.0 M, [Cr2O7

2− ] = 0.10 M, [Cr3+ ] = 0.0030 M,[Br− ] = 1.0 M and [BrO3

− ] = 0.043 M

If the concentration of the dichromate is increased from 0.10 M to 0.20 M, in what direction will the reaction proceed to equilibrium?

The reaction should go back to the left to partially offset the increase in dichromate, which appears on the right side of the reaction equation. To confirm this, we normally calculate the reaction quotient, Q.

LeChatelier’s Principle, 2The form of Q is exactly that of K, except that Q is evaluated with whatever concentrations currently exist in the system (say after addition or removal of a reagent).

Q =[1.0][0.20][5.0]8

[0.043][0.0030]2= 2 ×1011 > K

Since Q > K, the reaction must go to the left in order to decrease the numerator and increase the denominator until Q = K.

• If a reaction is at equilibrium and products are added (or reactants are removed), the reaction goes to the left.

• If a reaction is at equilibrium and reactants are added (or products are removed), the reaction goes to the right.

If the temperature of the system is changed, then K also changes, as predicted by

K = e−ΔG0 /RT = e−(ΔH

0 −TΔS0 )/RT = e−ΔH0 /RT ieΔS

0 /R

The ΔS° term is independent of T; hence, the ΔH° term increases with increasing temperature if ΔH° is positive (endothermic, K increases with increase in T) and decreases if ΔH° is negative (exothermic, K decreases with increase in T).

LeChatelier’s Principle, 3These statements can be understood in terms of Le Châtelierʼs principle as follows. Consider an endothermic reaction:

heat + reactants products

If the temperature is raised, then heat is added to the system. The reaction proceeds to the right to partially offset this change.

Note: We are making thermodynamic predictions, not kinetic ones. In other words, we look at what it takes for a system to reach equilibrium, or to drive a reaction in a particular direction. We do not know how long the reaction will take! (i.e., a large K does not necessarily indicate a fast reaction).

Solubility ProductThe solubility product is the equilibrium constant for the reaction in which a solid salt dissolves to give its constituent ions in solution. Solid is omitted from the equilibrium constant because it is in its standard state.

Hg2Cl2 (s) Hg22+ + 2Cl−

Consider the dissolution of mercurous chloride in water:

The solubility product, Ksp, is

Ksp = [Hg22+ ][Cl− ]2 = 1.2 ×10−18

A solution containing excess, undissolved solid is said to be saturated with that solid. The solution contains all the solid capable of being dissolved under the prevailing conditions.

If an aqueous solution is left in contact with excess solid Hg2Cl2, the solid will dissolve until the condition above is satisfied. Thereafter, the amount of undissolved solid remains constant. Unless excess solid remains, there is no guarantee that [Hg22+][Cl-]2 = Ksp. On the other hand, if Hg2+ and Cl- are mixed such that [Hg22+][Cl-]2 > Ksp, then Hg2Cl2 will precipitate!

In chemical analysis, we encounter solubility in precipitation titrations, electrochemical reference cells, and gravimetric analysis

e.g., The effect of acid on the solubility of minerals and the effect of atmospheric CO2 on the solubility (and death) of coral reefs are important in environmental science.

Solubility Product, 2Most often, the solubility product is used to find the concentration of one ion when the concentration of the other is known or fixed by some means.

[Hg22+ ] =

Ksp

[Cl− ]2=1.2 ×10−18

0.102= 1.2 ×10−16M

e.g., What is the concentration of Hg22+ in equilibrium with 0.10 M Cl− in a solution of KCl containing excess, undissolved Hg2Cl2(s)?

Because Hg2Cl2 is so slightly soluble, additional Cl− obtained from Hg2Cl2 is negligible compared with 0.10 M Cl−.

Note: The solubility product does not tell the entire story of solubility. Many salts form soluble ion pairs to some extent, i.e., MX(s) can give MX(aq) as well as M+(aq) and X−(aq).

e.g., In a saturated solution of CaSO4, two-thirds of the dissolved calcium is Ca2+ and one third is CaSO4 (aq). The CaSO4 (aq) ion pair is a closely associated pair of ions that behaves as one species in solution (see Appendix J of the 8th edition for more information).

Common Ion EffectFor the ionic solubility reaction:

CaSO4 (s) Ca2+ + SO42− , Ksp = 2.4 ×10−5

The product [Ca2+][SO42-] is constant at equilibrium in the presence of excess solid CaSO4. If the concentration of Ca2+ were increased by adding another source of Ca2+, such as CaCl2, then [SO42-] must decrease so that [Ca2+] remains constant. i.e., less CaSO4 will dissolve if Ca2+ or SO42- is present from another source.

This application of Le Chatelierʼs principle is called the common ion effect: A salt will be less soluble if one of its constituent ions is already present in the solution.

Solubility of CaSO4 in solutions containing dissolved CaCl2. Solubility is expressed as total dissolved sulfate, which is present as free SO42- and as the ion pair, CaSO4 (aq).

Separation by PrecipitationPrecipitation can sometimes be used to separate ions from each other. For example, consider a solution containing lead(II) (Pb2+) and mercury(I) (Hg22+) ions, each at a concentration of 0.010 M. Each forms an insoluble iodide, but the mercury(I) iodide is considerably less soluble, as indicated by the smaller value of Ksp:

PbI2 (s) Pb2+ + 2I− , Ksp = 7.9 ×10−9

Hg2I2 (s) Hg22+ + 2I− , Ksp = 4.6 ×10−29

Is it possible to lower the concentration of Hg22+ by 99.990% by selective precipitation with I−, without precipitating Pb2+?

In other words, can we lower [Hg22+] to 0.010% of 0.010 M (1.0 × 10-6 M) without precipitating any Pb2+?

A yellow solid, lead(II) iodide (PbI2), precipitates when a colourless solution of lead nitrate (Pb(NO3)2) is added to a colourless solution of potassium iodide (KI).

The smaller Ksp implies a lower solubility for Hg2I2 because the stoichiometries of the two reactions are the same. If the stoichiometries were different, it does not follow that the smaller Ksp would imply lower solubility.

Complex FormationIf anion X− precipitates metal M+, it is often observed that a high concentration of X− causes solid MX to redissolve. The increased solubility arises from formation of complex ions, such as MX2, which consist of two or more simple ions bonded to one another.

A ligand is any atom or group of atoms attached to the species of interest.e.g., In complex ions such as PbI+, PbI3- and PbI42-, iodide, I-, is said to be a ligand of Pb2+.Pb2+ is said to act as a Lewis acid, and I- is said to act as a Lewis base.

The product of the reaction between a Lewis acid and a Lewis base is called an adduct, and the bond between them is called a dative or coordinate covalent bond.

Complex Formation, 2If Pb2+ and I− only reacted to form solid PbI2, then the solubility of Pb2+ would always be very low in the presence of excess I−:

High concentrations of I− cause solid PbI2 to dissolve. We explain this by the formation of a series of complex ions:

The species PbI2(aq) is dissolved PbI2, containing two iodine atoms bound to a lead atom.

Complex Formation, 3

Complex Formation, 4At low I− concentrations, the solubility of lead is governed by precipitation of PbI2(s). At high I− concentrations, all of the reactions are driven to the right (Le Châtelierʼs principle), and the total concentration of dissolved lead is considerably greater than that of Pb2+ alone.

All equilibria are satisfied simultaneously.If we know [I−], we can calculate [Pb2+] by substituting the value of [I−] into the equilibrium constant expression for the main reaction, regardless of whether there are other reactions involving Pb2+. The concentration of Pb2+ that satisfies any one equilibrium must satisfy all equilibria, i.e., there can be only one concentration of Pb2+ in the solution.

Total solubility of lead(II) (curve with circles) and solubilities of individual species (straight lines) as a function of the concentration of free iodide. To the left of the minimum, [Pb]total is governed by the solubility product for PbI2(s). As [I−] increases, [Pb]total decreases because of the common ion effect. At high values of [I−], PbI2(s) redissolves because it reacts with I− to form soluble complex ions, such as PbI42-. Note the logarithmic scales. The solution is made slightly acidic so that [PbOH+] is negligible.

Protic Acids and BasesAcids and bases are of paramount importance in analytical chemistry, since they influence:

- general chemical reactivity- complex formation- redox chemistry- molecular charge and shape- analytical separation processes

In aqueous chemistry, an acid is a substance that increases the concentration of H3O+ (hydronium ions) when added to water. Conversely, a base decreases the concentration of H3O+. A decrease in H3O+ concentration requires an increase in OH− concentration. (Therefore, a base increases the concentration of OH− in aqueous solution).

Protic refers to chemistry involving transfer of H+ from one molecule to another. The species H+ is also called a proton because it is what remains when a hydrogen atom loses its electron. The hydronium ion, H3O+, is a combination of H+ with H2O. Although H3O+ is a more accurate representation than H+ for the hydrogen ion in aqueous solution, H3O+ and H+ are used interchangeably.

Brønsted-Lowry Acids and BasesBrønsted and Lowry classified acids as proton donors and bases as proton acceptors.e.g., HCl is an acid (a proton donor), and it increases the concentration of H3O+ in water:

HCl + H2O H3O+ + Cl−

Brønsted and Lowry classifications do not require the formation of the hydronium cation, making these definitions useful for non-aqueous situations (e.g., gas phase, solvents, etc.).

HCl (g) + NH3(g) NH4+Cl−

Unless otherwise noted, these classifications are used for all acids and bases.

J. N. Brønsted (1879–1947) of the University of Copenhagen and T. M. Lowry (1874–1936) of Cambridge University independently published their definitions of acids and bases in 1923.

SaltsAny ionic solid is called a salt. In a formal sense, a salt can be thought of as the product of an acid-base reaction. When an acid and a base react, they are said to neutralize each other. Most salts containing cations and anions with single positive and negative charges are strong electrolytes—they dissociate nearly completely into ions in dilute aqueous solution.

NH4+Cl− (s)→ NH4

+ (aq) + Cl− (aq)

Conjugate Acids & BasesThe products of a reaction between an acid and a base may also be classified as acids and bases in some instances.e.g., Consider the reaction of acetic acid and methylamine (base). Acetate is a base because it can accept a proton to make acetic acid, whereas the methylammonium ion is an acid because it can donate a proton and become methylamine.

Acetic acid and the acetate ion are said to be a conjugate acid-base pair. Methylamine and methylammonium ion are likewise conjugate. Conjugate acids and bases are related to each other by the gain or loss of one H+, respectively.

The Nature of H+ and OH-

The proton does not exist by itself in water. The simplest formula found in some crystalline salts is H3O+. For example, crystals of perchloric acid monohydrate contain pyramidal hydronium (also called hydroxonium) ions:

Structure of hydronium ion, H3O+, proposed by M. Eigen and found in many crystals. The bond enthalpy (heat needed to break the OH bond) of H3O+ is 544 kJ/mol, about 84 kJ/mol greater than the bond enthalpy in H2O.

Other H3O+ structuresIn the gas phase, H3O+ can be surrounded by 20 molecules of H2O in a regular dodecahedron held together by 30 hydrogen bonds. There are numerous solid structures:

The Zundel structure of H3O+ ⋅ H2O.

Environment of aqueous H3O+. Three H2O molecules are bound to H3O+ by strong hydrogen bonds (dotted lines), and one H2O (at the top) is held by weaker ion-dipole attraction (dashed line). The OH...O hydrogen-bonded distance of 252 pm (picometers, 10−12 m) compares with an OH...O distance of 283 pm between hydrogen-bonded water molecules.

H3O+·3C6H6 cation found in the crystal structure of [(C6H6)3H3O+] [CHB11Cl11−]. [From E. S. Stoyanov, K.-C. Kim, and C. A. Reed, “The Nature of the H3O+ Hydronium Ion in Benzene and Chlorinated Hydrocarbon Solvents,”J. Am. Chem. Soc. 2006, 128, 1948.]

The Nature of H+ and OH-, 2We normally write H+ in most chemical equations, although we really mean H3O+. To emphasize the chemistry of water, we write H3O+. For example, water can be either an acid or a base. Water is an acid with respect to methoxide:

But with respect to hydrogen bromide, water is a base:

AutoprotolysisWater undergoes self-ionization, called autoprotolysis, in which it acts as both an acid and a base:

or equivalently:

Protic solvents have a reactive H+, and all protic solvents undergo autoprotolysis.e.g., acetic acid:

The extent of these reactions is very small. The autoprotolysis constants (equilibrium constants) for the reactions above are 1.0 × 10−14 and 3.5 × 10−15, respectively, at 25°C.

pHThe reason we discuss autoprotolysis is its relation to pH. The autoprotolysis constant for H2O has the special symbol Kw, where “w” stands for water:

Table 6-1 shows how Kw varies with temperature. Its value at 25.0 °C is 1.01 × 10−14.

pH, 2An approximate definition of pH is the negative logarithm of the H+ concentration.

(In chapter 7 we will look at a more accurate definition in terms of activities).

In pure water at 25°C with [H+] = 1.0 × 10−7 M, the pH is −log(1.0 × 10−7) = 7.00. If [OH−] = 1.0 × 10−3 M, then [H+] = 1.0 × 10−11 M and the pH is 11.00. A useful relation between [H+] and [OH−] is

This equation is equivalent to saying, for instance, that if pH = 3.58, then pOH = 14.00 – 3.58 = 10.42, or [OH−] = 10−10.42 = 3.8 × 10−11 M.

A solution is acidic if [H+] > [OH−]. A solution is basic if [H+] < [OH−]. At 25°C, an acidic solution has a pH below 7 and a basic solution has a pH above 7. Although pH generally falls in the range 0 to 14, these are not the limits of pH. A pH of −1, for example, means −log[H+] = −1 or [H+] = 10 M. This concentration is attained in a concentrated solution of a strong acid such as HCl.

pH, 3

pH of various substances. [From Chem. Eng. News, 14 September 1981.] The most acidic rainfall is a stronger acid than lemon juice. The most acidic natural waters known are mine waters, with total dissolved metal concentrations of 200 g/L and sulfate concentrations of 760 g/L. The pH of this water, –3.6, does not mean that [H+] = 103.6 M = 4 000 M! It means that the activity of H+ (discussed in Chapter 7) is 103.6. The surface of water or ice is ~2 pH units more acidic than the bulk because H3O+ is more stable on the surface. Surface acidity could be important to the chemistry of atmospheric clouds.

Pure water?Is there such a thing as pure water? (i.e., pH of 7.00 at 25 oC?) Of course! But in practice, in most daily situations (kitchen, lab, bathroom, etc.) water from the tap is acidic because it contains CO2 from the atmosphere, which is an acid by virtue of the reaction

CO2 can be largely removed by boiling water and then protecting it from the atmosphere. Again, the effects of increasing CO2 levels in our atmosphere, and their influence on ocean pH, fish populations, coral reefs, etc. must be stressed!

What about other constituents, such as commonly found metal and halogen ions?

More than a century ago, careful measurements of the conductivity of water were made by F. Kohlrausch and his students. To remove impurities, they found it necessary to distill water 42 consecutive times under vacuum to reduce conductivity to a limiting value!

Strengths of Acids and BasesAcids and bases are classified as strong or weak, depending upon whether they react “completely” or “partially” to produce H+ or OH-, respectively.

A strong acid or base is completely dissociated (or almost completely) in an aqueous solution (i.e., the values of K associated with such reactions are very large).

HCl(aq) H+ + Cl−

KOH(aq) K+ +OH−

You should be familiar with most of the strong acids and bases in this list (note the absence of HF, due to the formation of an H3O+⋄⋄⋄F- ion pair in solution).

In most cases, hydroxides of alkaline earth metals are considered to be strong bases.

Strengths of Acids and Bases, 2Weak acids and bases are only partially dissociated with water. For instance, a weak acid denoted as HA reacts with water:

HA + H2OKa

H3O+ + A− or equivalently HA

Ka

H+ + A−

Ka is the acid dissociation constant; for a weak acid, Ka must be “small.”

Ka =[H+ ][A− ][HA]

A weak base, B, abstracts a proton from water:

B+ H2OKb

BH+ + OH− Kb =[BH][OH− ]

[B]

Kb is the base hydrolysis constant, which is “small” for a weak base.

Classes of Acids and BasesAcetic acid (and most carboxylic acids) are weak acids; their anions (in this case the carboxylate anion) are weak bases.

Methylamine is a weak base, and the corresponding methylammonium ion is a weak acid (and also the conjugate acid of methylamine); this is the case for most amine and ammonium compounds.

Classes of Acids and Bases, 2Methylammonium chloride dissociates in aqueous solution to give methylammonium cation and chloride:

Methylammonium chloride is a weak acid because:1. It dissociates into CH3NH3+ and Cl−2. It is a weak acid, being conjugate to CH3NH2, a weak base.3. Cl− has no basic properties, and is conjugate to HCl, a strong acid (i.e., HCl dissociates completely). (i.e., in other words, Cl− has virtually no tendency to associate with H+, otherwise HCl would not be a strong acid).

Metal cations, Mn+, form weak acids by acid hydrolysis to form M(OH)(n−1)+. Monovalent metal ions form weak acids which are weaker than divalent cations, which in turn form weak acids that are weaker than those of trivalent cations (i.e., Kmonov < Kdiv < Ktriv). We also note that metal ions are sometimes hydrated by several H2O molecules, where the acid dissociation reaction is:

M(H2O)xn+

Kb

M(H2O)x-1(OH)n−1 + H+

Classes of Acids and Bases, 3Acid dissociation constants (−log Ka) for aqueous metal ions: e.g., for Li+, Ka = 10−13.64. Later, we will learn that the numbers in this table are called pKa. Darkest shades are strongest acids. [Data from R. M. Smith, A. E. Martell, and R. J. Motekaitis, NIST Critical Stability Constants of Metal Complexes Database 46 (Gaithersburg, MD: National Institute of Standards and Technology, 2001).]

Polyprotic Acids and BasesPolyprotic acids and bases are compounds that can donate or accept more than one proton. For example, oxalic acid is a diprotic acid:

Notation for acid and base equilibrium constants: Standard notation for successive acid dissociation constants of a polyprotic acid is K1, K2, K3, etc. Ka1 refers to the acidic species with the most protons and Kb1 (see next slide) refers to the basic species with the least protons. The subscript “a” in acid dissociation constants is usually omitted.

Polyprotic Acids and Bases, 2Phosphate is said to be tribasic:

Polyprotic Acids and Bases, 3The reaction of CO2 with water produces carbonic acid:

In comparing the Ka values for carbonic acid to other carboxylic acids, it may seem surprising that the acid is classified as diprotic (i.e., Ka1 is 102 to 104 times smaller).

Polyprotic Acids and Bases, 4The reason for this apparent anomaly is because the value of for Ka1 is calculated from:

Only about 0.2% of dissolved CO2 is in the form H2CO3. When the true value of [H2CO3] is used instead of the value [H2CO3 + CO2(aq)], the value of the equilibrium constant is:

Living cells utilize the enzyme carbonic anhydrase to speed the rate at which H2CO3 and CO2 equilibrate in order to process this key metabolite. The enzyme provides an environment just right for the reaction of CO2 with OH−, lowering the activation energy (the energy barrier for the reaction) from 50 to 26 kJ/mol and increasing the rate of reaction by more than a factor of 106.

Relation between Ka and KbA most important relation exists between Ka and Kb of a conjugate acid-base pair in aqueous solution.

If the reactions are added, their equilibrium constants can be multiplied to yield:

Ka iKb = Kw

where Kw is 1.0 × 10-14.

e.g., If the Ka for acetic acid is 1.75 × 10-5, what is Kb for the acetate ion?

Relation between Ka and Kb, 2For a diprotic acid:

Ka1iKb2 = Kw and Ka2 iKb1 = Kw

Since these sum up to yield the autoprotolysis equation for water, we get:

Relation between Ka and Kb, 2For a diprotic acid:

Ka1iKb2 = Kw and Ka2 iKb1 = Kw

Since these sum up to yield the autoprotolysis equation for water, we get: