Chemical Theory

Chemical Theory

Acids and Bases

In this section we will base our discussion on the Brönsted-Lowry theory of acids and bases, which defines an acid as a proton donor and a base as a proton acceptor. A proton, for the purposes of this manual, is an ionized hydrogen atom (H+). Examples of Brönsted-Lowry acids and bases are illustrated below.

Hydrochloric acid

Equ 1: Proton donor

Proton donor

Ammonia

Equ 2: Proton acceptor

Proton acceptor

Water

Equ 3: Proton donor
Equ 4: Proton acceptor

Proton donor or acceptor

In aqueous solution, protons complex with water to form hydronium ions (H3O+); however, we will use H+ as shorthand for H3O+. [1]

Acids and bases can be classified as strong or weak. Strong acids or bases dissociate completely when dissolved in water. Examples include hydrochloric acid (HCl), sulfuric acid (H2SO4), nitric acid (HNO3), sodium hydroxide (NaOH), calcium hydroxide (Ca(OH)2) and magnesium hydroxide (Mg(OH)2).

Weak acids or bases dissociate incompletely when dissolved in water and establish equilibrium between the acid or base and conjugate species. Examples include acetic acid (CH3COOH), phosphoric acid (H3PO4) and ammonia (NH3). The conjugate species for these examples are CH3COO-, H2PO4- and NH4+. The acid dissociation constant (Ka), which describes the equilibrium, is defined as:

Equ 5: Acid Dissociation   Equ 6: Equilibrium   Equ 7: pKa

where [H+] is the hydronium ion concentration, [A-] is the conjugate base concentration and [HA] is the weak acid concentration. The base dissociation constant (Kb) can be derived in a similar manner. [2]

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Units of Concentration

Solute concentrations are generally reported either per unit mass of solvent or per unit volume of solvent.

A common mass solute : mass solvent unit is percent by mass (w/w%). Calculating concentration in this percentage is convenient since information about the solute’s chemical nature is not required. One liter (L) of water has a mass of one kilogram (kg). To create a 10% salt solution, add 100g salt to 900mL water:

Equ 8: Sample Calculation

Two common mass solute : volume solvent units are molarity (M) and normality (N). These units describe the concentration of solute molecules in a solution. The Periodic Table lists the average atomic weight (g/mol) for every element. [3]

Molarity is defined as moles solute per liter solvent. To create a 1M salt solution (sodium chloride, MWNaCl = 23g/mol (Na) + 35.5g/mol (Cl) = 58.5 g/mol), add 1 mol salt (58.4g) to 1L water:

Equ 9: Sample Calculation

Diluting a concentrated stock can also create a desired solution. To create 1L of a 0.25M sulfuric acid (H2SO4) solution from a 1M stock, add 250mL stock to 750mL water:

Equ 10: Sample Calculation

Equ 11: Sample Calculation

Normality is closely related to molarity and is defined as mole equivalents solute per liter solvent. In the case of strong acid or bases, normality can be calculated by:

Equ 12: Normality

where n is the number of protons or hydroxyl groups exchanged in a reaction. A 1.0M hydrochloric acid solution (HCl) has a normality of 1.0N, since 1 proton dissociates in an aqueous solution. A 1.0M sulfuric acid solution has a normality of 2.0N, since 2 protons dissociate in an aqueous solution.

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pH

pH is a logarithmic scale that describes the hydronium ion concentration in a solution. It is defined as:

Equ 13: pH

The traditional pH scale ranges from 0 --> 14, where values less than 7 are acidic, values greater than 7 are basic and values equivalent to 7 are neutral. The scale’s range is based on the dissociation constant of pure water and neutral pH is defined as the hydronium concentration of pure water.

Equ 14: Dissociation of Water

Equ 15: Dissociation Constant

Equ 16: Neutral pH

Similarly, pOH is a logarithmic scale that describes the hydroxyl ion concentration in a solution. It is defined as:

Equ 17: pOH, where Equ 18: pH Sum

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Neutralization

Neutralization is defined as a chemical reaction where an acid and a base react to form water and a neutral salt. Common neutralizations in industrial settings involve strong acids and strong bases, as illustrated below. The subscript (aq) indicates that the species are aqueous (soluble in water) and (l) indicates that the species exist in the liquid state.

Sulfuric acid and Sodium hydroxide

Equ 19: Neutralization sample

Hydrochloric acid and Calcium hydroxide

Equ 20: Neutralization sample

Hydrofluoric acid and Magnesium hydroxide

Equ 21: Neutralization sample

Neutralization is an exothermic reaction, thus it releases energy in the form of heat, causing neutralization process systems to heat up during use. The heat energy released by a general neutralization reaction at standard temperature and pressure (STP, 25oC/1atm) is: [4]

Equ 22: Formation of Water   Equ 23: Free energy of water

where Equ 24: Calorie definition. [5] Uncontrolled neutralization reactions with concentrated reactants are potentially dangerous. The heat released could raise the system’s temperature past the solvent’s boiling point or cause some plastics and temperature sensitive materials to soften, distort or fail.

One can quickly estimate the vessel’s temperature after neutralization if the solvent’s specific heat, initial temperature, volume and the extent of the neutralization reaction are known. The specific heat for an aqueous solution is:

Equ 25:  Specific heat of water

For example if one adds 750mL 1M HCl to 500mL 1M NaOH in a 25oC vessel, the final temperature will be 33oC.

Equ 26: Sample calculation   Equ 27: Sample calculation

Equ 28: Sample calculation

Equ 29: Sample calculation

Equ 30: Sample calculation

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Titration Curves

A titration curve illustrates how pH changes as a titrating agent is added during a neutralization reaction. In the titration of any strong acid with any strong base, there are three regions of the titration curve that represent different kinds of calculations.

  1. Before the neutralization point, the pH is determined by excess H+ in solution
  2. At the neutralization point, the H+ and OH- concentration in solution are equal. pH is determined by the dissociation of water.
  3. After the neutralization point, the pH is determined by excess OH- in solution.

The following table and figure illustrates the calculation of the titration curve for 1L of 1M HCl treated with 1M NaOH.

 

Vtotal (L)

NaOH (L)

[H+]

[OH-]

pH

 

1.00

0.00

1.000

 

0.00

 

1.20

0.20

0.667

 

0.18

 

1.40

0.40

0.429

 

0.37

 

1.60

0.60

0.250

 

0.60

Region 1

1.80

0.80

0.111

 

0.95

 

1.90

0.90

0.053

 

1.28

 

1.95

0.95

0.026

 

1.59

 

1.99

0.99

0.005

 

2.30

 

1.999

0.999

0.0005

 

3.30

Region 2

2.00

1.00

--

--

7.00

 

2.001

1.001

 

0.0005

10.70

 

2.01

1.01

 

0.005

11.70

 

2.05

1.05

 

0.024

12.39

 

2.10

1.10

 

0.048

12.68

Region 3

2.20

1.20

 

0.091

12.96

 

2.40

1.40

 

0.167

13.22

 

2.60

1.60

 

0.231

13.36

 

2.80

1.80

 

0.286

13.46

 

3.00

2.00

 

0.333

13.52

Table 1: Titration curve
Figure 1: Titration curve for 1L of 1M HCl treated with 1M NaOH Titrant [6]

Characteristic of all titrations is a sudden change in pH near the neutralization point. Notice that a 2mL addition of 1M NaOH near the neutralization point produces a pH change of 7.4 units. The solution’s pH is more stable in Regions 1 and 3, which are further away from the neutralization point. A 20mL addition of NaOH at pH 13 only produces a pH change of 0.26 units.

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Processes

Neutralization Processes

The objective of most industrial neutralizing operations is to maintain a process’s pH within a specified range, not to hold the process at its neutralization point. For example, wastewater pH might have to be maintained between pH 6 and 9 before it can be pumped into a municipal sewer system. Treatment must be sensitive near the neutralization point since small volumes of titrating agent can cause dramatic pH shifts.

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Other pH Control Processes

Sometimes the objective is to hold a process’s pH at a value other than neutral. For example, processes used for the precipitation of heavy metals as hydroxides must remain alkaline and processes used for the dissolution of materials from electronic etching processes must remain acidic. Treatment must be more aggressive further away from the neutralization point since larger volumes of titrating agent have less effect on the system’s pH.

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Buffers

A buffer consists of a mixture of an acid and its conjugate base or a base and its conjugate acid. A buffered solution resists changes in pH when acids or bases are added because the buffer consumes the added acid or base. As the buffer is consumed, it becomes less resistant to changes in pH.

The Henderson-Hasselbalch Equation defines the pH of a solution, provided the acid’s dissociation constant and the ratio of the conjugate acid and base concentrations are known.

Equ 31: Henderson-Hasselbalch

Adding 0.25mol of KH2PO4 (34g) and K2HPO4 (43.5g) to 1L H2O can create a 0.5M phosphate buffered solution with pH 7.2.

Equ 32: Sample calculation

Equ 33: Sample calculation

Equ 34: Phosphate dissociation

Equ 35: Sample Calculation   Equ 36: Sample calculation

Equ 37: Sample calculation

A buffered solution is most effective when its pH is within one pH unit of its pKa. If 2mL of 1M NaOH is added to this solution, H2PO4- is consumed by excess hydroxide to produce HPO4-2. The resulting pH would be 7.21.

Equ 38: Phosphate buffer

Equ 39: Sample calculation

The addition of 2mL of 1M NaOH to the buffered solution resulted in a pH change of 0.01 units while the addition to an unbuffered solution resulted in a pH change of 7.4 units. Buffers can add a tremendous amount of pH stability to a solution.

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Solubility

Neutralizing agents do not have to be aqueous; insoluble reagents may be used. These reagents are typically salts, such as limestone (CaCO3), and are partially soluble in water. The solubility product defines the concentration of an insoluble reagent in water as

Equ 40: Dissociation   Equ 41: Solubility constant   Equ 42: pKsp

where Ksp is the solubility product, [X+] is the cation concentration and [A-] is the anion concentration. [7]

Limestone neutralizes hydronium ions by forming carbon dioxide and water using the following pathway:

Equ 43: Limestone neutralization   Equ 44: Limestone neutralization

Equ 45: Sample calculation   Equ 46: Sample calculation

The limestone neutralization system is limited by the concentration and the rate of dissolution of carbonate. The solubility product defines that the carbonate dissolution cannot exceed 4.9x10-9 N. Increasing the surface area of limestone can optimize the rate of dissolution; however, it must be ground to a particle size of approximately -200 mesh to be effective. As Shinskey notes, "limestone cannot be recommended for complete neutralization of wastes whose acid content exceeds 0.001 N." [8]

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[1] Another theory, the Lewis theory, defines acids and bases in terms of electron transfer. The Lewis theory is beyond the scope of this manual.

[2] In actuality, strong acids and bases do not completely dissociate. Their dissociation constants are large and the concentration of the associated acid or base species is negligible.

[3] One mole (mol) is equivalent to approximately 6.022 x 1023 molecules (Avogadro’s number).

[4] Spectator ions omitted.

[5] Calculated by two methods: Free energy difference analysis from thermodynamic data in Atkins, Peter. (1998) Physical Chemistry 6th Ed. W.H. Freeman and Co: New York. Electrochemical analysis from electrical potential data in CRC. (2001) Handbook of Chemistry and Physics 81st Ed. CRC Press: New York.

[6] A titration where base is neutralized by acid would yield a mirror image of the curve shown above.

[7] A list of solubility product constants is found in CRC. (2001) Handbook of Chemistry and Physics 81st Ed. CRC Press: New York.

[8] Shinskey, F.G. (1973) pH and pION Control in Process and Waste Streams. Wiley-Interscience Publication: New York.

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