Acid Base Equilibrium

How to Think Salt Problems Through

1. Look at the salt and ask yourself which acid and which base reacted to form it 2. Ask yourself "strong or weak?" for each 3. Embrace the fact that "strong wins" and predict whether the salt is acidic or basic based on that victory - If you predict acidic, write = H^+ - If you predict basic, write = OH^- 4. Relish in the fact that "strong is a spectator," which means that the remaining ion of the (weak) salt is the reactant along with water - If an acid solution, use the cation of the salt as a reactant - If a basic solution, use the anion of the salt as a reactant

pH Formula

14 = pH + pOH

Note on Formulas

14 = pH + pOH is applicable for any solution. Also note that you can use moles instead of molarity in the log ratio of either equation

When to use Henderson-Hasselbach Equation

A Ka or Kb problem requires a greater understanding of the factors involved and can always be used instead of the Henderson-Hasselbach equation. This equation is only valid for solutions that contain weak, monoprotic acids and their salts or weak bases and their salts. The buffered solution cannot be too dilute and the Ka/Kb cannot be too large.

Buffers

A buffer solution is one that resists changes in pH when either a small amount of acid or base is added to it. Usually a buffer solution is made from a weak acid and one of its salts (its conjugate base), or from a weak base and one of its salts (Its conjugate acid). These processes of "mopping up" of added base and acid allow the pH to remain relatively unchanged. Note that pure water has NO buffering capacity; acids and bases added to water directly affect the pH of the solution.

Note on the Strength of Acids and Bases

A large majority of all acids and bases are weak

Strengths of Acids and Bases

A strong acid or base undergoes complete ionization. For example, for a strong acid, HCl, and a strong base, B, the following reactions go to completion (completely to the right-hand side, RHS) to produce large numbers of H3O^* (aq) and OH^- (aq), respectively, in solution. HCl (aq) + H2O (l) = H3O^+ (aq) + Cl^- (aq) B (aq) + H2O (l) = BH^+ (aq) + OH^- (aq) If the first reaction is almost 100% to the RHS, then HCl is a very strong acid compared to H3O^+. It is also true to say that the CB of HCl (Cl^-), is a very weak base.

Base (Bronsted-Lowry definition)

A substance that accepts hydrogen ions (H^+) in an aqueous solution

Acid (Arrhenius definition)

A substance that dissolves in water to produce H3O^+ (Hydronium) ions

Base (Arrhenius definition)

A substance that dissolves in water to produce OH^- (hydroxide) ions

Acid (Bronsted-Lowry Definition)

A substance that donates hydrogen ions (H^+) in an aqueous solution

General Equation

Acid + Base = Salt + Water

Examples of Weak Bases

Ammonia (NH3), and organic bases such as amines and pyridines

In a Titration

As a base or an acid is added to an acid or base respectively, there is very little change in pH, and a pH change of less than approximately 1.5 is expected up to the point of 90% of the acid or base has been neutralized. When the moles of titrant (the solution that is added from the buret) are in the exact stoichiometric proportion with the titrate (the solution that the titrant is added to), i.e. 100% of the acid or base has been neutralized, then the equivalence point has been reached. At this point there is a rapid change in pH.

Note

At any temperature: If [H^+] = [OH^-], the solution is neutral If [H^+] > [OH^-], the solution is acidic If [H^+] < [OH^-], the solution is basic

Buffers and Titrations - Titrations with a Weak acid and Strong base

Buffer solutions are inadvertently produced during the titration of weak acids and weak bases Weak acid with a Strong base - as the base is gradually added to the weak acid, some of the weak acid is neutralized, and the result is the salt of the weak acid (its conjugate base) and water. Because not all of the weak acid has been neutralized, it is still present in solution alongside the salt. This combination in solution is a buffer acid and the new concentration of the salt. Then apply the Henderson-Hasselbach equation. OR [H^+] = Ka([Acid-base]/[Base+base])

Ka, the Equilibrium Constant for Weak Acids

Calculating the pH of weak acids involves setting up an equilibrium. It helps to start by writing the balanced equation, setting up the acid equilibrium expression (Ka), defining initial concentrations, changes, and final concentration in terms of x, substituting values and variables into the Ka expression, and solving for x. In other words, use the RICE table method.

Hydrolysis of Salts

Careful analysis of titration curves shows that the equivalence point is not necessarily at pH = 7. This is due to the fact that salts are not always neutral. Some salts due form neutral solutions, but others react with water to form acidic or basic solutions. The reaction is called Salt Hydrolysis.

Acid-Base Conjugate Pairs

Conjugate acid and base pairs are related by a difference of a hydrogen ion on either side of the equation.

Knowledge of Logarithms

Considering the acid version of the Henderson-Hasselbach equation, it can be seen that if the pH of a buffer solution is greater than the pKa of the acid, then the term, log([salt]/[acid]) must be a positive number. In order for the log of a number to be positive, then the number (in this case [salt]/[acid]), must be greater than 1, i.e. the salt concentration must be greater than the acid concentration. When the pH is less than the pKa, the opposite is true.

Strong Acid and Base pH

Dissociation is complete (100%), and therefore the concentration of the H3O^+ and OH^- ions can be determined directly from the stoichiometric ratio in the balanced equation and the concentration of acid or base.

Kb - The Equilibrium Constant for Weak Bases

For a weak base, dissociation is incomplete. For example, the following equilibrium is set up for NH3. NH3 + H2O = NH4^+ + OH^- Using the RICE table (reaction, initial, change, equilibrium) we can determine the dissociation in terms of x.

Examples of Strong Bases

Group 1 and group 2 hydroxides (Not Be or Mg)

In the following reaction, identify the acid, base, conjugate acid, and conjugate base. HBr + NH3 = NH4^+ + Br^-

HBr = Acid NH3 = Base NH4^+ = Conjugate Acid Br^- = Conjugate Base

Examples of Strong Acids

HCl, HBr, HI, HClO4 (strongest), HNO3, H2SO4, HCl3

What is the conjugate acid of NO3^-?

HNO3

What is the conjugate base of H2S?

HS^-

Significant Figures

If a logarithm is 7.45, the 7 is simply a placeholder. When using a "1.15 M solution," the pH should be recorded with 3 decimal places. A "1.2 M solution" should be reported to 2 decimal places.

Since the pKa or pKb is fixed for a weak acid or base

If the concentration of the components of the buffer are changing but remain the same ratio, the pH of the buffer will not change. However, changing the concentrations of the components does affect the capacity of the buffer. Optimum buffering occurs when [HA] = [A^-] and the pKa of the weak acid used should be as close as possible to the desired pH of the buffer system.

Acid Base Equilibria

It should be carefully noted that the concentration of H3O^+ and OH^- are dependent on two separate factors. Firstly, the strength of the acid or base (degree of ionization), and secondly, the amount of water present (concentration of solution). It is entirely possible to have a dilute but strong acid, and to have a concentrated but weak acid with the same hydronium concentration. Therefore, they could have the same pH value. Do not confuse concentration with strength.

Expressions

Ka = [H3O^+][A^-]/[HA] Ka = [H3O^+]^2/[HA] [H^+] = √Ka[HA] pKa = -log(Ka)

Example

Ka for acetic acid is 1.8*10^-5 R HC2H3O2 (aq) = H^+ (aq) + C2H3O2^- (aq) I 1.00*10^-4 0 0 C -x +x +x E (1.00*10^-4)-x x x Ka = 1.8*10^-5 = x^2/(1*10^-4 - x) x = 3.44*10^-5 -log (x) = 3.46 (2 SF)

Base Formulas

Kb = [OH^-][NH4^+]/[NH3] Kb = [OH^-]^2/[NH3] pKb = -log(Kb) = Kb = 10^-pKb

Manipulation of Kw Expression

Kw = 1.0*10^-14 = (Ka) (Kb) pKw = 14 = pH + pOH

Kw - The Ionic Product of Water

Kw = [H3O^+][OH^-] Like all equilibrium constants, Kw is temperature dependent. At 298 K (25 C), Kw = 1*10^-14. Only about 2 in a billion water molecules are ionized at any instant. Since pure H2O will have equal concentrations of H3O^+ and OH^-, then under these conditions [H3O^+] = [OH^-] = sqrt 1*10^-14 = 1.0*10^-7 M Applying pH = -log([H3O^+]), we find the the pH of pure water at 298 K is 7.

X term

Often, the -x term in a Ka expression can be neglected, which simplifies the math tremendously. To find out if x can be neglected, multiply the Ka by 100 and compare it to the original concentration. If the initial concentration is large in comparison, you can neglect the x term. If the Ka is large in comparison, the x term cannot be neglected.

Neutralization

One of the most important reactions of acids and bases is their ability to neutralize one another.l A neutralization reaction takes place when the hydrogen ions in an acidic solution react with the hydroxide ions from a basic solution to form water. This makes neutralization reactions a special type of double replacement reactions. The other product of a simple neutralization is a salt.

Examples of Weak Acids

Organic (carboxylic) acids e.g., butanoic, propanoic, ethanoic, methanoic, HF

Water

Sometimes water acts as a base, accepting a hydrogen ion, and also an acid by donating a hydrogen ion. [OH^-1] and [H3O^*]

Ka Value

Strong acid - Ka is large and far to the right. [H^-]≈[HA]o A^- is a much weaker base compared to H2O Weak acid - Ka is small and far to the left. [H^+]≪[HA]o A^- is a much stronger base than H2O

Possible Combinations of Salts and Bases and pH at Equivalence Point

Strong acid and Strong base ~ pH = 7 ~ neutral Strong base and Weak acid ~ pH > 7 ~ basic Strong acid and Weak base ~ pH < 7 ~ acidic Weak acid and Weak base ~ all pH's possible ~ various

Common Ion Effect pt. 2

The addition of a salt containing a common anion to a solution of a weak acid makes the solution less acidic. If we add NaC2H3O2 to the system (HC2H3O2 = H^+ + Cl^-), Q increases so the system must shift to the left, lowering H^+, which increases pH.

Common Ion Effect

The addition of an ion already present in a system causes the equilibrium to shift away from the common ion. For example: The addition of concentrated HCl to a saturated solution of NaCl will cause some solid NaCl to precipitate out of solution. The NaCl has become less soluble due to the additional Cl ions brought in by HCl. As the common ion is added to the reaction, the value of Q increases. When Q > K, the system must shift to the left to reach equilibrium.

Capacity of Buffers

The capacity of a buffer is defined as its ability to continue to react with any extra acid or base that is added to it without a significant change in pH. The higher the concentration of the components of a buffer, the more acid or base it can absorb, and the higher its capacity.

Note about SA CB pairs

The conjugate base being weak in the above reaction is true of all conjugate pairs in as much as a very strong component in a conjugate pair will always be accompanied by an equally weak partner.

Titration Indicators

The equivalence point is located in the middle of the vertical portion of the titration curves. The correct indicator is the one that changes color at a pH value closest to the equivalence point as possible. The observable color change of the indicator is called the "end point," and should correspond to the equivalence point as closely as possible.

Relative Strengths of Oxyacids

The more oxygen present in the polyatomic ion of an oxyacid the stronger its acid within that group. That's a trend, but not an explanation. So, why? First, notice that the H of the acid is bound to an oxygen and NOT any other nonmetal present. Oxygen is very electronegative and attracts the electrons of the O-H bond toward itself. If you add more oxygens, the effect is magnified and there is increasing electron density in the region of the molecule that is opposite the H. The bonds are easier to break and the compound dissociates more completely, which is described as 'strong.'

Relative Strengths of Weak, Carboxylic Acids

The relative strength of a carboxylic acid depends upon the stability of the anion that it forms, when it loses its labile. All carboxylic acids from this equilibrium, where 'R' varies. RCOOH =ROO^- + H^+ If the anion (RCOO^-) is relatively stable, then it will form in solution, and in the process the acid will tend to donate H^+ ions, making the acid relatively strong. Remember - the smaller pKa the stronger the acid

Titrations and Titration Curves

Titration is an experimental technique used to perform a neutralization reaction. Accurate measurement tools are used in a quantitative manner to determine the concentration of an unknown acid or base.

The pH Scale

Used to indicate the acidity or basicity of an aqueous solution. Usually measures from 0-14, with acids being < 7 and bases being > than 7. A solution with a pH of 7 is neutral. pH = -log[H3O^+] pOH = -log[OH^-]

Weak Acids and Weak Bases

Weak acids and weak bases have very little ionization and equilibria are set up with the equilibria laying heavily on the LHS i.e. the undissociated form.

Buffers and Titrations - Titrations with a Weak base and Strong acid

Weak base and Strong acid - as the acid is gradually added to the weak base, some of the weak base is neutralized, and the result is the salt of the weak base (its conjugate acid) and water. Because not all of the weak base has been neutralized, it is still present in solution alongside the salt. This combination in solution is a buffer solution, and its pOH can be calculated by using a RICE table to determine the remaining concentration of the weak base and the new concentration of the salt. Then apply the Henderson-Hasselbach equation. OR [H^+] = Ka([Acid+acid]/[Base-acid])

Half-Neutralization

When the titration is exactly halfway to the equivalence point. At this point the concentrations of salt and acid or salt and base are equal. This makes the ratios = 1, and the log(1) = 0. This simplifies the Henderson-Hasselbach equations to read pH = pKa and pOH = pKb, respectively.

pH of Buffers

While RICE tables are always and option, a shortcut way to calculate the pH of a buffer solution is with the Henderson-Hasselbach equation. This involves the pKa or pKb of the weak acid or base and the ratio of the concentrations of each component. To calculate the pH of an acidic buffer use this version of the Henderson-Hasselbach equation: pH = pKa + log([salt]/[acid]) For a basic buffer: pOH = pKb + log([salt]/[base])

Buffer Solution Formula (NMSI equation)

[H^+] = Ka [Acid]/[Base]

When Using RICE with Weak Bases

x represents [OH^-], not [H^+] as with weak acids. Taking the negative log of x will give you the pOH, not the pH! The major species in any solution of a weak acid or base will be the undissociated form.