Aqueous Equilibria

• Electrolytes• Acids and Bases (review)• The Equilibrium Constant• Equilibrium Expressions• “Special” Equilibrium Expressions• Solubility Products• Common-Ion Effects• Weak Acids and Bases• Introduction to Buffers• Henry’s Law

Electrolytes……• Strong electrolytes dissociate completely in

aqueous solutiono NaCl, KBr, Mg(NO3)2o Strong Acids, Strong Bases

• Weak electrolytes dissociate or only partially react in aqueous solutiono Most of these, for our examples, are weak acids

or baseso Ammonia, ammonium, phosphoric acid (all 3

protons are weak), acetic acid/acetate ion, etc.• Let’s write some example chemical

reactions for all of the above

Acids and Bases (review)

• Brønsted-Lowry Definition:o Acids are proton donorso Bases are proton acceptors

• Lewis Definitiono Acids are electron-pair acceptorso Bases are electron-pair donors

• Arrhenius Definitiono Acids react in water to release a protono Bases react in water to release hydroxide ion

• Acid + Base Salt + Water

• Acid + Base Conjugate Base + Conjugate Acid

• Some solvents are amphiprotico Water can act as an acid and a base!o Methanol can act as an acid and a base!

• Autoprotolysiso Some solvents can react with themselves to

produce an acid and a base• Water is a classical example

• Weak acids dissociate partially, weak bases undergo partial hydrolysis. Strong acids and bases are strong electrolytes.

The Equilibrium State•Consider a generic reaction

The concentrations of each reagent are constant at equilibrium, even though individual molecules are constantly reacting.

Concentrations are typically in molar (M) units, but gases can be expressed as their partial pressure (atm) and solids and pure liquids will have concentrations of unity (1).

Another way of saying this is that the reaction rate in one direction is equal to the reaction rate in the reverse direction.

Recall Le Châtelier’s Principle and how changing reaction components and conditions can alter equilibrium!

The Equilibrium Expression

•Consider a generic reaction

•Dissolved species are in molar (M) concentrations•Gaseous species partial pressures are in atmospheres•Pure liquids and pure solids have concentrations of 1.•Excess solvents, which do NOT participate in the reaction, also have concentrations of 1.•Equilibrium constants are reaction, phase, temperature and pressure dependent

Manipulating Equilibrium

Expressions• If you write a reaction in reverse, the new K is

the inverse of the original K

• If we add reactions, K values are multiplied

Special Equilibrium Constants and

Expressions

• Kw (dissociation of water)• Ksp (solubility of salts in saturated

solutions)• Ka (acid dissociation)• Kb (base hydrolysis)• x (complex ion formation)

• KH (Henry’s Law)

Kw (Dissociation of Water)

• Water is amphiprotic

• Kw = 1.0E-14 at about 25 ˚C• This is where the pH scale we commonly use

originates from!

• What is the concentration of hydronium and hydroxide ions in neutral solution? What is the pH? What is the pOH?

Solubility Products & Common Ion

Effect

• Ksp applies to salts in equilibrium in saturated solutions.

• The solution MUST be SATURATED!• The [solid] cancels out as it is 1.• You can calculate concentrations of the

salt, or the component ions.• This applies to dilute solutions in pure

water, and ignores activity (we’ll not worry about activity)

“I-C-E” Table

Initial Conc.(Molarity) 1 0 0

Change(Molarity) 1 +x +x

Equilibrium Conc.(Molarity)

1 0 + x 0 + x

• What is the ppb concentration sulfur in a saturated solution of of copper (I) thiocyanate?o Consider using an I-C-E “table”!o Write the reactiono Write the Ksp expressiono Look up Ksp in standardized tableo Substitute in for ion concentrations?o Solve algebraically!o Concentrations are in molar (M) units, you

may need to convert to ppm, ppb, etc.

• What is the concentration of the salt, and each ion, in a saturated solution of Calcium Phosphate?o Consider using an I-C-E “table”!o Write the reactiono Write the Ksp expressiono Look up Ksp in standardized tableo Substitute in for ion concentrations?o Solve algebraically!o Concentrations are in molar (M) units, you may

need to convert to ppm, ppb, etc.

Solubility Rules (General)

Common Ion Effect…• What if your now saturated solution

contained some ion before you added the salt?

• The pre-existing “common ion” influences the solubility of the salt!

• Use the previous steps, with an I-C-E table!

• What is the solubility of silver chloride in 1uM sodium chloride? Setup “I-C-E” table.

Weak Acid & Weak Base

Equilibria

• Weak acids produce weak conjugate bases, and weak bases produce weak conjugate acids

• Ka is a “special” equilibrium constant for the dissociation of a weak acid (found in standard tables)

• Kb is a “special” equilibrium constant for the hydrolysis of a weak base.

Calculations……..• What is the pH of a 1.0 M solution of

acetic acid (HAc)?

• What assumption can you make?o If [acid] is about 1000 times the Ka value,

it’s concentration in solution won’t change much!

o Use an “I-C-E” table to look at this.o There are more elaborate discussions of

approximations.

• What is the pH of a 4.0 M solution of phosphate ion?o Write reactiono Calculate Kbo Setup “I-C-E” tableo Make assumptionso Solve algebraically.

Buffers• Buffers resist the change in pH because they

have acid to neutralize bases and bases to neutralize acids.

• Made from a weak acid (HA) and the salt of its conjugate base (A-, where the counter ion is gone for example), or a weak base and the salt of its conjugate acid.

Features of Buffers• Buffers work best at maintaining pH near

the Ka of the acid component, usually about +/- 1 pH unit. This is their buffer capacity (see fig. 9-5)

• Buffers resist pH changes due to dilution.• All seen when we use the “Buffer Equation”

Henderson-Hasselbalch (Buffer)

Equation

• A modification of the equation for the dissociation of a weak acid.

• The pH is the pH of the buffered solution, pKa is the pKa of the weak acid.

• What is the pH of a buffer solution made from 1.0 M acetic acid and 0.9 M sodium acetate?

• You add .10 moles of sodium hydroxide to the above solution? What is the new pH?

H-H Equation & Buffers….

• If [A-] = [HA] pH = pKa!o This is what we see at half-way to the

equivalence point in the titration of a weak acid with a strong base!

• Dilution does not change the ratio of A- to HA, and thus the pH does not change significantly in most cases

• You want 1L of a buffer system that has a pH of 3.90?o What acid/conjugate base pair would you use?o How would you go about figuring out how much of

each reagent you might need?o How would you prepare and adjust the pH of this

solution?

Henry’s Law• At a given temperature (like any other equilibrium

situation), the amount of a gas that will dissolve in a liquid is proportional to the partial pressure of that gas over the liquid.

• A common form of Henry’s Law:

• What is the concentration of carbon dioxide in otherwise pure freshwater at the current partial pressure of CO2 in the atmosphere?

o Partial pressure of CO2= 39 Pa

o KH = 29.4 Latm/molo 1 Pa = 9.9E-6 atm

• Why worry about CO2 in the atmosphere in regards to water or other solutions?