Normality, morality, molality & mole fraction

Analytical Techniques

Admin | First year, Semester2

Syllabus Notes Assignments

These are important concentration terms used in chemistry to describe the amount of a substance in a given volume or mass of a solution. Each has its specific applications and units.

Normality (N)

Definition: Normality is the number of equivalents of solute per liter of solution. It is often used in acid-base chemistry and in redox reactions where the number of reactive units (equivalents) is important.

Equivalents: An equivalent is the amount of substance that reacts with or supplies one mole of hydrogen ions (H⁺) in acid-base reactions or one mole of electrons in redox reactions.

Example:

For HCl (hydrochloric acid), which has one equivalent per mole: $Normality = Molarity$
For H₂SO₄ (sulfuric acid), which has two equivalents per mole (since each mole of H₂SO₄ provides two H⁺ ions): $Normality = 2 \times Molarity$

Molarity (M)

Definition: Molarity is the number of moles of solute per liter of solution. It is the most commonly used concentration unit in chemistry.

Example:

A 1 M solution of NaCl contains 1 mole of NaCl in 1 liter of solution.

Molality (m)

Definition: Molality is the number of moles of solute per kilogram of solvent. Unlike molarity, it is not affected by temperature changes because it is based on the mass of the solvent.

Example:

A 1 m solution of NaCl contains 1 mole of NaCl in 1 kilogram of water.

Mole Fraction (χ)

Definition: Mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in the mixture.

Example:

In a solution with 2 moles of ethanol (C₂H₅OH) and 8 moles of water (H₂O), the mole fraction of ethanol is:
Summary
1. Normality (N):
  - Used in acid-base and redox reactions.
  - Depends on the number of equivalents.
  - Units: equivalents per liter (eq/L).
2. Molarity (M):
  - Most common concentration unit.
  - Depends on the volume of the solution.
  - Units: moles per liter (mol/L).
3. Molality (m):
  - Independent of temperature.
  - Depends on the mass of the solvent.
  - Units: moles per kilogram (mol/kg).
4. Mole Fraction (χ):
  - Ratio of moles of a component to the total moles in the mixture.
  - Unitless.

Buffer solution

Buffer solutions play a crucial role in quantitative analytical chemistry by maintaining a stable pH environment, which is essential for many analytical procedures. They are solutions that resist changes in pH when small amounts of acids or bases are added, or when the solution is diluted.

Basic Concepts

Definition and Components

A buffer solution consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. The components of a buffer solution are:

Weak Acid and Conjugate Base:
- Example: Acetic acid (CH₃COOH) and sodium acetate (CH₃COONa).
Weak Base and Conjugate Acid:
- Example: Ammonia (NH₃) and ammonium chloride (NH₄Cl).

Buffer Capacity

Buffer capacity is a measure of the ability of a buffer solution to resist changes in pH. It depends on the concentration of the buffer components and their ratio. Higher concentrations of the buffering agents result in greater buffer capacity.

Importance in Quantitative Analytical Chemistry

pH Control

Many analytical methods, such as titrations, enzymatic reactions, and electrochemical measurements, require a specific pH to ensure accurate results. Buffer solutions maintain the required pH, thereby ensuring the stability and reproducibility of the analysis.

Stability of Reagents and Samples

Some chemical reagents and samples are sensitive to pH changes. Buffers help in stabilizing the pH, which prevents the degradation of these reagents and samples, leading to more reliable analytical results.

Enhanced Reaction Rates and Specificity

Certain reactions are highly pH-dependent. Buffer solutions can optimize the pH to enhance reaction rates and specificity, improving the efficiency and accuracy of the analytical procedure.

Preparation of Buffer Solutions

Selection of Components

The choice of the weak acid/base and its conjugate base/acid depends on the desired pH range. The selected buffer system should have a $p K_{a}$ or $p K_{b}$ value close to the target pH.

Calculation of Buffer Composition

Using the Henderson-Hasselbalch equation, the ratio of the concentrations of the buffer components can be calculated to achieve the desired pH.

Practical Preparation Steps

Dissolve the Weak Acid/Base:
- Weigh and dissolve the appropriate amount of the weak acid/base in distilled water.
Add the Conjugate Base/Acid:
- Add the calculated amount of the conjugate base/acid to the solution.
Adjust the pH:
- Use a pH meter to monitor the pH and adjust it if necessary by adding small amounts of strong acid (e.g., HCl) or strong base (e.g., NaOH).
Dilute to Volume:
- Transfer the solution to a volumetric flask and dilute to the desired final volume with distilled water.

Examples of Common Buffers

Acetate Buffer:
- Acetic acid (CH₃COOH) and sodium acetate (CH₃COONa).
- Effective pH range: 3.6 - 5.6.
Phosphate Buffer:
- Sodium dihydrogen phosphate (NaH₂PO₄) and disodium hydrogen phosphate (Na₂HPO₄).
- Effective pH range: 6.0 - 8.0.
Tris Buffer:
- Tris(hydroxymethyl)aminomethane (Tris) and Tris hydrochloride (Tris-HCl).
- Effective pH range: 7.0 - 9.0.
Ammonium Buffer:
- Ammonium chloride (NH₄Cl) and ammonia (NH₃).
- Effective pH range: 8.0 - 10.0.

Applications

Titrations: In acid-base titrations, buffers are used to maintain a stable pH near the equivalence point.
Biochemical Assays: Enzymatic reactions often require specific pH conditions, maintained by buffers.
Chromatography: In liquid chromatography, buffers are used in the mobile phase to control the pH and improve separation.
Electrophoresis: Buffers are essential in gel electrophoresis to maintain the pH and ionic strength for protein and nucleic acid separation.
Calibration of pH Meters: Standard buffer solutions with known pH values are used to calibrate pH meters.

Common ion effect

The common ion effect is a principle in chemistry that describes the decrease in solubility of an ionic compound when a common ion is added to a solution already containing one of the ions in the compound. This phenomenon is a direct consequence of Le Chatelier's Principle, which states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

Principle

The common ion effect can be explained through the dissociation of a weak electrolyte in the presence of a strong electrolyte that shares a common ion. When the concentration of one of the ions in the solution is increased, the equilibrium shifts to reduce this change, often resulting in the precipitation of the weak electrolyte.

For example, consider the dissolution of silver chloride (AgCl) in water:

$AgCl (s) ⇌ {Ag}^{+} (a q) + {Cl}^{-} (a q)$

When sodium chloride (NaCl), which is a strong electrolyte, is added to this solution, it dissociates completely to give Na $^{+}$ and Cl $^{-}$ ions. The increase in the concentration of Cl $^{-}$ ions due to the addition of NaCl will shift the equilibrium of the dissolution of AgCl to the left, reducing the solubility of AgCl.

Example 1: Solubility of Silver Chloride (AgCl)

Initial Equilibrium:
- When AgCl is dissolved in water, it dissociates into Ag $^{+}$ and Cl $^{-}$ .
- The solubility product constant (Ksp) for AgCl is given by: $K_{s p} = [{Ag}^{+}] [{Cl}^{-}]$
Addition of a Common Ion:
- Adding NaCl to the solution increases the concentration of Cl $^{-}$ .
- As a result, the product of the ion concentrations $[{Ag}^{+}] [{Cl}^{-}]$ exceeds the Ksp value.
- To re-establish equilibrium, the reaction shifts to the left, leading to the precipitation of AgCl.

Example 2: Acetic Acid (CH₃COOH) and Sodium Acetate (CH₃COONa)

Initial Equilibrium:
- Acetic acid partially dissociates in water: ${CH}_{3} COOH ⇌ {CH}_{3} {COO}^{-} + H^{+}$
Addition of Sodium Acetate:
- Adding sodium acetate, which dissociates completely, increases the concentration of ${CH}_{3} {COO}^{-}$ .
- According to Le Chatelier's Principle, the increased concentration of ${CH}_{3} {COO}^{-}$ shifts the equilibrium to the left, reducing the ionization of acetic acid.
- As a result, the pH of the solution increases (becomes less acidic).

Applications of Common Ion Effect

Buffer Solutions:
- The common ion effect is fundamental in the preparation of buffer solutions, which are used to maintain a stable pH in chemical and biological systems.
- Example: A buffer solution made of acetic acid and sodium acetate.
Analytical Chemistry:
- Used in qualitative analysis to control the solubility of different compounds.
- Example: Selective precipitation of ions in a mixture to identify specific components.
Industrial Processes:
- In various industrial processes, the common ion effect is used to control the solubility of salts and manage the concentration of ions in solution.
- Example: Water treatment processes to remove unwanted ions.

Mathematical Treatment

To quantitatively describe the common ion effect, one must consider the equilibrium expressions and apply the principles of equilibrium constants (Ksp and Ka).

For a sparingly soluble salt $AB$ dissolving in water:

$AB (s) ⇌ A^{+} (a q) + B^{-} (a q)$

The solubility product (Ksp) is:

$K_{s p} = [A^{+}] [B^{-}]$

If an additional source of $B^{-}$ is introduced, the concentration of $B^{-}$ increases, and to maintain the Ksp constant, the concentration of $A^{+}$ must decrease, leading to the precipitation of $AB$ .

Oxidation reduction reactions

Oxidation-reduction reactions, often referred to as redox reactions, are chemical reactions that involve the transfer of electrons between two species. These reactions are essential for numerous biological, chemical, and industrial processes.

Key Concepts

Oxidation: The process in which an atom, ion, or molecule loses electrons.
- Oxidizing Agent: The substance that gains electrons and is reduced in a chemical reaction.
- Oxidation State: An indicator of the degree of oxidation of an atom in a chemical compound.
Reduction: The process in which an atom, ion, or molecule gains electrons.
- Reducing Agent: The substance that loses electrons and is oxidized in a chemical reaction.

Oxidation and Reduction

Oxidation: $A \to A^{+} + e^{-}$ For example, in the reaction $Zn \to {Zn}^{2 +} + 2 e^{-}$ , zinc is oxidized.
Reduction: $B^{+} + e^{-} \to B$ For example, in the reaction ${Cu}^{2 +} + 2 e^{-} \to Cu$ , copper ion is reduced.

Redox Reaction Examples

Combustion of Hydrocarbons: ${CH}_{4} + 2 O_{2} \to {CO}_{2} + 2 H_{2} O$
- Here, carbon in methane (CH₄) is oxidized to carbon dioxide (CO₂), and oxygen is reduced to water (H₂O).
Displacement Reaction: $Zn + {CuSO}_{4} \to {ZnSO}_{4} + Cu$
- Zinc is oxidized (Zn to Zn²⁺), and copper is reduced (Cu²⁺ to Cu).
Electrochemical Cells:
- In galvanic cells, spontaneous redox reactions produce electrical energy.
- In electrolytic cells, electrical energy drives non-spontaneous redox reactions.

Balancing Redox Reactions

Balancing redox reactions involves ensuring that the number of electrons lost in oxidation equals the number of electrons gained in reduction. This can be done using the half-reaction method:

Separate the reaction into two half-reactions.
Balance all elements except hydrogen and oxygen.
Balance oxygen atoms by adding H₂O.
Balance hydrogen atoms by adding H⁺ (in acidic solutions) or OH⁻ (in basic solutions).
Balance the charge by adding electrons.
Combine the half-reactions, ensuring electrons are canceled out.

Redox Reactions in Everyday Life

Photosynthesis: $6 {CO}_{2} + 6 H_{2} O + light energy \to C_{6} H_{1} 2 O_{6} + 6 O_{2}$
- Carbon dioxide is reduced to glucose, and water is oxidized to oxygen.
Cellular Respiration: $C_{6} H_{1} 2 O_{6} + 6 O_{2} \to 6 {CO}_{2} + 6 H_{2} O + energy$
- Glucose is oxidized to carbon dioxide, and oxygen is reduced to water.
Corrosion:
- Iron oxidizes to form rust (iron oxide) when exposed to moisture and oxygen: $4 Fe + 3 O_{2} + 6 H_{2} O \to 4 {Fe(OH)}_{3}$

Applications of Redox Reactions

Industrial Processes:
- Extraction of metals from ores (e.g., aluminum production).
- Synthesis of chemicals (e.g., ammonia synthesis in the Haber process).
Energy Production: Batteries and fuel cells rely on redox reactions to produce electrical energy.
Environmental Applications: Redox reactions are used in water treatment and waste management to remove contaminants.

Preparation of standard solution, primary standard and secondary standard

Standard solutions are solutions of known concentration used in chemical analysis. They are crucial for quantitative analyses, such as titrations, where they serve as the reference to determine the unknown concentration of an analyte. There are two types of standards: primary and secondary standards.

Preparation of Standard Solutions

Steps for Preparing a Standard Solution

Choosing the Solute:
- Select the appropriate substance (solute) to prepare the standard solution. This can be a primary standard or a solute that can be standardized against a primary standard.
Weighing the Solute:
- Accurately weigh the required amount of solute using an analytical balance.
Dissolving the Solute:
- Dissolve the weighed solute in a small amount of solvent (usually distilled or deionized water) in a beaker.
Transferring to a Volumetric Flask:
- Transfer the solution to a volumetric flask using a funnel. Rinse the beaker and funnel with the solvent and add these rinsings to the flask to ensure all the solute is transferred.
Diluting to the Mark:
- Add solvent to the volumetric flask until the bottom of the meniscus is at the calibration mark on the neck of the flask. Ensure thorough mixing by inverting the flask several times.
Labeling:
- Label the flask with the concentration and the date of preparation.

Primary Standards

Characteristics of Primary Standards

A primary standard is a highly pure, stable, non-hygroscopic compound with a high molar mass, which allows for precise weighing. It should react completely and predictably with the analyte. Examples include sodium carbonate (Na₂CO₃) for acid-base titrations and potassium dichromate (K₂Cr₂O₇) for redox titrations.

Preparation of Primary Standards

Selection:
- Choose a suitable primary standard compound based on the type of analysis.
Purity Verification:
- Verify the purity of the primary standard, usually 99.9% or higher.
Weighing:
- Accurately weigh the primary standard on an analytical balance.
Dissolution:
- Dissolve the weighed primary standard in a small amount of solvent in a beaker.
Transfer and Dilution:
- Transfer the solution to a volumetric flask, rinse the beaker and funnel, and dilute to the mark with solvent.
Labeling:
- Label the flask appropriately.

Secondary Standards

Characteristics of Secondary Standards

A secondary standard is a solution whose concentration is determined by titration against a primary standard. Secondary standards are less pure and stable than primary standards but are used because the primary standard might not be suitable for direct use in all titrations.

Preparation of Secondary Standards

Preparation:
- Prepare a solution of approximate concentration by weighing the solute and dissolving it in the solvent, similar to the preparation of a standard solution.
Standardization:
- Standardize the prepared solution by titrating it against a primary standard solution.
- Calculate the exact concentration of the secondary standard using the titration data.
Labeling:
- Label the flask with the exact concentration and date of standardization.

Example Procedures

Preparation of a Sodium Carbonate (Na₂CO₃) Primary Standard Solution

Weighing: Weigh accurately 1.325 g of anhydrous sodium carbonate (Na₂CO₃).
Dissolution: Dissolve the Na₂CO₃ in a small amount of distilled water in a beaker.
Transfer and Dilution: Transfer the solution to a 250 mL volumetric flask, rinse the beaker and funnel, and dilute to the mark with distilled water.
Mixing: Mix thoroughly by inverting the flask several times.
Labeling: Label the flask with the concentration and date.

Preparation of a Hydrochloric Acid (HCl) Secondary Standard Solution

Preparation: Prepare approximately 0.1 M HCl by diluting concentrated HCl with distilled water in a volumetric flask.
Standardization: Standardize the HCl solution by titrating it against the primary standard Na₂CO₃ solution.
- Use the reaction: ${Na}_{2} {CO}_{3} + 2 HCl \to 2 NaCl + H_{2} O + {CO}_{2}$
Calculation: Calculate the exact concentration of the HCl solution using the titration data.
Labeling: Label the flask with the exact concentration and date of standardization.

The preparation of standard solutions, primary standards, and secondary standards is fundamental in quantitative chemical analysis. Primary standards provide the basis for accurate and precise measurements due to their high purity and stability. Secondary standards, standardized against primary standards, offer practical solutions for routine analysis. Proper preparation, standardization, and labeling ensure the reliability and accuracy of analytical results.