Module 7.5: Advanced Topics

7.5.1 Hard-soft Acid-base (HSAB) Theory

I HSAB is one of the most useful qualitative theories in chemistry, can be used to predict a wide variety of reactions such as:

1. Qualitative Analysis
2. Solubility reactions
3. Organic reactions

II Note that HSAB is only a rough estimate and other factors may be dominant.

III hard acids or bases: nonpolarizable acids or bases

1. small, charged, and have high LUMOs (for acids) and low HOMOs (for bases).

2. a strong interaction between hard acids and bases are dominated by charge attraction.

   1. interaction between hard acids and bases tend to have a large gap between the HOMO and LUMO

   2. very similar to ionic bonding. (Ref. Figure 81)

IV soft acids or bases: polarizable acids or bases

1. large, uncharged, and have low LUMOs (for acids) and high HOMOs (for bases).

2. a strong interaction between soft acids and bases are dominated by orbital interaction.

   1. interaction between soft acids and bases tend to have a small gap between the HOMO and LUMO

   2. very similar to covalent bonding. (Ref. Figure 81)

V Soft acids prefer soft bases, and hard acids prefer hard bases.

VI Qualitative analysis tests for what ions are present in a given solution

1. Group 1 are cations that precipitate out in the presence of acid or chloride anion

   1. soft acids such as $\textrm{Ag}^{+}$, $\textrm{Pb}^{2+}$, and $\textrm{Hg}_{2}^{2+}$ will precipitate out, although $\textrm{Cl}^{-}$ is a marginally hard base. This is due to the sizes of the cations that lead to strong bonding within the crystal lattice (water is a hard base, and therefore these cations prefer to interact with chloride anion instead of water)

2. Group 2 are cations that precipitate out in the presence of $\textrm{H}_{2}\textrm{S}$ in acidic conditions

   1. borderline and (less) soft acids such as $\textrm{HgS}$, $\textrm{CdS}$, $\textrm{CuS}$, $\textrm{SnS}$, $\textrm{As}_{2}\textrm{S}_{3}$, $\textrm{Sb}_{2}\textrm{S}_{3}$, $\textrm{Bi}_{2}\textrm{S}_{3}$ will precipitate out ($\textrm{S}^{2-}$).

3. Group 3 are cations that precipitate out in the presence of $\textrm{H}_{2}\textrm{S}$ in basic conditions

   1. borderline acids such as $\textrm{MnS}$, $\textrm{FeS}$, $\textrm{CoS}$, $\textrm{NiS}$, $\textrm{ZnS}$, precipitate out. The basic conditions (forming hydroxide) will cause $\textrm{Al}(\textrm{OH})_{3}$ and $\textrm{Cr}(\textrm{OH})_{3}$ to also precipitate out.

4. Group 4 are cations that precipitate out in the presence of carbonate anion (hard).

   1. hard acids such as Group 2 metal cations ($\textrm{Ca}^{2+}$, $\textrm{Sr}^{2+}$, $\textrm{Ba}^{2+}$) precipitate out.

5. Group 5 are cations that do not precipitate at all. They are the hardest acids.

6. In order to conduct quantitative analysis, you follow the order below to test for groups:

   1. Group 1 - add $\textrm{HCl}$ (aq)

   2. Group 2 - add $\textrm{H}_{2}\textrm{S}$ (aq)

   3. Group 3 - add $\textrm{NaOH}$ (aq)

   4. Group 4 - add $(\textrm{NH}_{4})_{2}\textrm{CO}_{3}$ (aq), or $\textrm{Na}_{2}\textrm{CO}_{3}$ (aq)

VII Solubility of certain species can also be roughly predicted through HSAB. For example, $\textrm{AgCl}$, $\textrm{AgBr}$, $\textrm{AgI}$ are all extremely insoluble, but $\textrm{AgF}$ is soluble.

1. As the Lewis base (halides) become softer as you go down the group, the interaction with the Lewis acid becomes stronger, and the compound therefore more insoluble.

2. $\textrm{AgF}$ and $\textrm{AgCl}$ are white, but the silver halides become more yellow as you go down the group. This is because color depends on HOMO-LUMO differences; as the gap between the HOMO and LUMO become larger, it results in shorter wavelengths of light being absorbed.

VIII Many organic reactions can also be predicted with HSAB.

1. A hard Lewis base such as $\textrm{OH}^{-}$ or butyllithium reagents will tend to react with hard Lewis acids

   1. these reactions will be dominated by significant charge attraction

2. A soft Lewis base such as $\textrm{SH}^{-}$ or organocopper reagents will tend to react with soft Lewis acids

   1. these reactions will be dominated by significant orbital interaction

3. reactions involving conjugate addition can be predicted through HSAB

   1. For more detail, refer to my organic chemistry notes.

7.5.2 Titrations

IX Titration is an analytical method to determine the concentration of a certain species.

1. An acid-base titration involves the determination of concentration of an acid using a known concentration of base, or the reverse.

2. A redox reaction involves the determination of concentration of a reducing agent using a known concentration of an oxidizing agent, or the reverse.

X Here are words that are commonly used throughout titrations:

1. titrant: what is being added, or the reagent of the known concentration.

2. analyte: what is being tested, or the reagent of the unknown concentration.

3. analyte: what is being tested, or the reagent of the unknown concentration.

   1. for bases such as sodium hydroxide that slowly react with carbon dioxide, it must be standardized regularly to ensure the known concentration is accurate.

   2. Standardization is done by using primary standards. These are compounds with high purity, high stability, high molecular mass, and high solubility.

      1. $\textrm{KHP}$ (for $\textrm{NaOH}$), $\textrm{Na}_{2}\textrm{CO}_{3}$ (for $\textrm{HCl}$), $\textrm{Na}_{2}\textrm{C}_{2}\textrm{O}_{4}$ (for $\textrm{KMnO}_{4}$)

   3. Secondary standards are the chemicals that has been standardized against a primary standard.

4. equivalence point: when the quantity of added titrant is the exact amount necessary for stoichiometric reaction with the analyte

   1. also known as the stoichiometric point

   2. equivalence points are a property of the chemical reaction taking place

5. end point: the abrupt change in the physical property of a solution

   1. end points are a property of indicators

   2. indicators are weak acids that change color when they are deprotonated

   3. it requires slightly more titrant to reach the end point compared to the equivalence point, when $\textrm{pH} = \textrm{pK}_{a}$ (indicator)

   4. it is wise to choose an indicator that is $\pm 1 \, \textrm{pH}$ of the $\textrm{pH}$ at the stoichiometric point.



6. direct titration: the addition of titrant to analyte until the reaction is complete

7. back titration: addition of a known excess of one standard reagent to the analyte, and then titrate the excess reagent with a second standard reagent

   1. used when the end point is clear than the end point of the direct titration

XI Some tips for acid-base titrations:

1. Utilize the Henderson-Hasselbalch equation for titrations as well.

2. When possible, avoid using molarity in titrations and use number of moles instead.

   1. make sure to keep track of changes in volume throughout the reaction!

   2. In the Henderson-Hasselbalch equation, the volumes in concentrations for the acid and conjugate base can be cancelled out.

3. Make sure to keep track of units. Keep in mind that dividing millimoles with millimoles results in the same answer as dividing moles with moles. Same for milliliters.

4. for the titration of a weak acid, at half the volume of its equivalence point, this is the maximum buffer region, where $[\textrm{A}^{-}] = [\textrm{HA}]$ and $\textrm{pH} = \textrm{pK}_{a}$

   1. very useful to determine the $\textrm{pK}_{a}$ of a weak unknown acid

   2. for polyprotic acids, you will observe multiple stoichiometric points and multiple buffer regions.