week. 4 electrolytes vs non electrolytes

Pharmaceutics I: Physical Pharmacy Study Notes

Learning Objectives

• Calculate solution concentrations using:

  • Molarity

  • Molality

• Differentiate between:

  • Non-electrolytes and electrolytes

  • Strong and weak electrolytes

• Understand and apply the Van’t Hoff factor

• Calculate ionic strength

Definition of Solution

• A solution is a mixture in which the minor component (solute) is uniformly distributed (dissolved) in the major component (solvent).

• Characteristics of a solution:

  • It is one phase (homogeneous).

  • Can be in the form of a:

  • Gas

  • Liquid

  • Solid

Focus on Liquid Solutions

• Our discussion is limited to liquid solutions.

• Common dosage forms of solutions include:

  • Oral solutions

  • Parenteral solutions

  • Total parenteral nutrition

Non-Electrolytes vs. Electrolytes

• Non-electrolytes:

• Do not ionize when dissolved in water.

• Conduct electrical current poorly in solution.

• Examples: Sugars, urea, carbamezepine.

• Electrolytes:

  • Completely or partially ionize when dissolved in water.

  • Conduct electrical current in solution.

  • Examples: Salts (e.g., NaCl, KCl), acids (e.g., HCl), bases (e.g., NaOH), and most drugs.

Strong vs. Weak Electrolytes

• Strong electrolytes:

  • Completely ionized in water and exist in the form of ions in solution.

  • Note: Dissociated ions can form clusters, which thus reduces the total number of ions in the solution.

• Weak electrolytes:

  • Partially ionized in water.

  • Some compounds exist in the ionic form and some in the molecular (un-ionized) form.

  • Most drug compounds are weak electrolytes.

Ionic Behavior of Electrolytes in Solution

• When electrolytes are dissolved in water:

  • The solute exists in the form of ions in solution.

  • Ions can form clusters, reducing the number of free ions in solution.

  • Ion clusters decrease the number of effective particles present in the solution.

Van’t Hoff Factor

• Theoretical number of free ions in solution based on molecular formula $( u)$:

  • For NaCl, v= 2

  • For ZnCl2, v= 3

• Van’t Hoff factor (i):

  • The actual number of ions generated in solution is less than the theoretical number due to ion clustering.

  • Van’t Hoff factor (i) is always less than v due to ion clustering formation.

  • Examples:

  • NaCl, I= 1.8

  • ZnCl2, I= 2.6

• Question: What is the Van’t Hoff factor for non-electrolytes? The Van’t Hoff factor for non-electrolytes is 1, as they do not dissociate into ions.

Degree of Dissociation

• Understanding of the Degree of Dissociation ($ ext{α}$):

  • Defined as the ratio of conductance of a dilute solution (Λo)to the conductance of an infinitely dilute solution (Λc):
    α= Λc/Λo

• Relationship between degree of dissociation and Van’t Hoff factor:

  • i=1+{α}(v-1)

• The degree of dissociation can be calculated if the Van’t Hoff factor is known:

  α= i - 1/ v- 1

Ionic Strength Calculation

• Ionic Strength (μ):

  • Related to the molar concentration (ci) and charges (zi) of ions in the solution.

• Steps to calculate ionic strength:

  1. Find all ions (positive and negative) in the solution.

  2. Calculate the molar concentration of each ion.

• Use the equation for ionic strength:
  \mu=\frac12\Sigma CiZi^2

Example Calculations

• Example 1: Calculate the ionic strength of a 0.9% NaCl solution.

  • μ = rac{1}{2}(0.2m imes (+1)^2 + 0.2m imes (-1)^2)

• Example 2: Ionic strength of a buffer solution prepared with 0.3 moles of K$2$HPO$4$ and 0.1 mole of KH$2$PO$4$ in 0.5 L water.

• Activity (a) and Activity Coefficient (γ):

  • When a solute (especially an electrolyte) is dissolved in another electrolyte solution (e.g., a strong electrolyte such as salt or buffer solutions), the solute ions are surrounded by other ions. This affects the properties of the solute electrolyte.

  • Activity describes the "effective concentration" of electrolytes, which is less than the molar or molal concentration.

  • Activity coefficient (γ < 1) links activity and molar (c) or molal (m) concentration:

  • a = γ imes m

  • a = γ imes c

Debye-Huckel Theory

• Activity coefficient (γi) for an ion of charge $z_i$ is related to the ionic strength $(μ)$:

  • Factor A is a constant related to temperature.

  • The higher the ionic strength, the lower the activity coefficient.

• Mean Ionic Activity Coefficient:

  • For a binary electrolyte consisting of ions with charges of $z^+$ and $z^-$ in diluted solutions $(μ < 0.01)$:
    ext{log } γ^{ ext{±}} = -A z^+ z^- μ

• For aqueous solutions at 25°C:

  • ext{log } γ^{ ext{±}} = -0.05091(z^+ z^{-}) μ

• These equations are for informational purposes only.

Concentration Expressions

• Many concentration expressions exist. Percent concentration and milliequivalence are covered in the calculation class.

• Focus on Molarity and Molality:

  • Molarity (M): The number of moles of solute in 1 L of solution (moles/L).

  • ext{Molarity (M)} = rac{ ext{Weight of solute (g)}}{ ext{MW (g/mol)} imes ext{Volume (L)}}

  • 1 mole/L = 1 M = 1000 mmol/mL

  • Molality (m): The number of moles of solute in 1000 g of solvent.

  • Unit: Moles/kg, not moles/L.

  • ext{Molality (m)} = rac{ ext{Weight of solute (g)}}{MW (g/mol) imes ext{Weight of solvent (kg)}}

Example Calculations (continued)

• Example 3: A pharmacist needs to prepare 200 mL of phenobarbital solution at a concentration of 0.02 M.

  • MW (phenobarbital) = 232.3 g/mol.

• Example 4: What is the molar and molal concentration of a 0.9% NaCl solution?

  • Specific gravity = 1.0053, MW = 58.5 g/mol.

  • What is the molal concentration of 0.9% NaCl if 10g of KCl is added? Will molar concentration change?

Summary of Molarity and Molality Relations

• Molarity (M):

  • The number of moles of solute in 1 L of solution.

  • Formula:
    ext{Molarity (M)} = rac{ ext{Weight of solute (g)}}{ ext{MW (g/mol)} imes ext{Volume (L)}}

• Molality (m):

  • The number of moles of solute in 1000 g of solvent.

  • Formula:
    ext{Molality (m)} = rac{ ext{Weight of solute (g)}}{ ext{MW (g/mol)} imes 1000 ext{ (g/kg)}}

Assignments and Reading Material

• Assignment: Refer to Chapters 3 and 4 for detailed readings.

  • Chap 3, pages 41 - 45

  • Chap 4, page 61

Learning Objectives

• Calculate solution concentrations using:

  • Molarity

  • Molality

• Differentiate between:

  • Non-electrolytes and electrolytes

  • Strong and weak electrolytes

• Understand and apply the Van’t Hoff factor

• Calculate ionic strength

Definition of Solution

• A solution is a mixture in which the minor component (solute) is uniformly distributed (dissolved) in the major component (solvent).

• Characteristics of a solution:

  • It is one phase (homogeneous).

  • Can be in the form of a:

  • Gas

  • Liquid

  • Solid

Focus on Liquid Solutions

• Our discussion is limited to liquid solutions.

• Common dosage forms of solutions include:

  • Oral solutions

  • Parenteral solutions

  • Total parenteral nutrition

Non-Electrolytes vs. Electrolytes

• Non-electrolytes:

  • Do not ionize when dissolved in water.

  • Conduct electrical current poorly in solution.

  • Examples: Sugars, urea, carbamazepine.

• Electrolytes:

  • Completely or partially ionize when dissolved in water.

  • Conduct electrical current in solution.

  • Examples: Salts (e.g., NaCl, KCl), acids (e.g., HCl), bases (e.g., NaOH), and most drugs.

Strong vs. Weak Electrolytes

• Strong electrolytes:

  • Completely ionized in water and exist in the form of ions in solution.

  • Note: Dissociated ions can form clusters, which thus reduces the total number of ions in the solution. Ion clustering affects colligative properties and the effective concentration of ions.

• Weak electrolytes:

  • Partially ionized in water.

  • Some compounds exist in the ionic form and some in the molecular (un-ionized) form.

  • Most drug compounds are weak electrolytes.

Ionic Behavior of Electrolytes in Solution

• When electrolytes are dissolved in water:

  • The solute exists in the form of ions in solution.

  • Ions can form clusters, reducing the number of free ions in solution.

  • Ion clusters decrease the number of effective particles present in the solution.

Van’t Hoff Factor

• Theoretical number of free ions in solution based on molecular formula (v):

  • For NaCl, v= 2

  • For ZnCl2, v= 3

• Van’t Hoff factor (i):

  • The actual number of ions generated in solution is less than the theoretical number due to ion clustering.

  • Van’t Hoff factor (i) is always less than v due to ion clustering formation.

  • Examples:

  • NaCl, i= 1.8

  • ZnCl2, i= 2.6

• Question: What is the Van’t Hoff factor for non-electrolytes? The Van’t Hoff factor for non-electrolytes is 1, as they do not dissociate into ions.

Degree of Dissociation

• Understanding of the Degree of Dissociation (\alpha):

  • Defined as the ratio of conductance of a dilute solution (\Lambdao) to the conductance of an infinitely dilute solution (\Lambdac):
    \alpha = \frac{\Lambdac}{\Lambdao}

  • Relationship between degree of dissociation and Van’t Hoff factor:
    i = 1 + \alpha(v-1)

  • The degree of dissociation can be calculated if the Van’t Hoff factor is known:
    \alpha = \frac{i - 1}{v - 1}

Ionic Strength Calculation

• Ionic Strength (µ):

  • Ionic strength is a measure of the total concentration of ions in a solution. It is crucial for predicting the behavior of ions and molecules in solution, especially regarding activity coefficients and deviations from ideal behavior.

  • Related to the molar concentration (ci) and charges (zi) of ions in the solution.

• Steps to calculate ionic strength:

  1. Find all ions (positive and negative) in the solution.

  2. Calculate the molar concentration of each ion.

  • Use the equation for ionic strength:
    \mu = \frac{1}{2}\Sigma ci zi^2

Example Calculations

• Example 1: Calculate the ionic strength of a 0.9% NaCl solution.

  • \mu = \frac{1}{2}(0.2m \times (+1)^2 + 0.2m \times (-1)^2)

• Example 2: Ionic strength of a buffer solution prepared with 0.3 moles of K_2HPO_4 and 0.1 mole of KH_2PO_4 in 0.5 L water.

Activity (a) and Activity Coefficient (γ)

• When a solute (especially an electrolyte) is dissolved in another electrolyte solution (e.g., a strong electrolyte such as salt or buffer solutions), this ionic interaction affects the behavior and properties of the solute electrolyte, making its "effective concentration" different from its nominal analytical concentration.

• Activity describes the "effective concentration" of electrolytes, which accounts for these interionic interactions and is generally less than the molar or molal concentration.

• Activity coefficient (γ) is a factor that relates the activity to the molar or molal concentration. It quantifies how much a real solution deviates from ideal behavior.

  • For ideal solutions, \gamma = 1 (activity equals concentration).

  • For real electrolyte solutions, \gamma < 1 due to interionic attraction reducing the effective concentration of ions.

  • The relationship is given by: a = \gamma \times c (where c is molar or molal concentration).

Debye-Huckel Theory

• The Debye-Huckel theory provides a theoretical basis for calculating activity coefficients in dilute electrolyte solutions.

• Activity coefficient (γi) for a single ion of charge z_i is related to the ionic strength (µ) by the Debye-Hückel Limiting Law:

  • \log \gammai = -A zi^2 \sqrt{\mu}

  • Where:

  • A is a constant related to the dielectric constant of the solvent and temperature (e.g., for water at 25^\circ \text{C} , A \approx 0.509 ).

  • z_i is the charge of the ion.

  • \mu is the ionic strength of the solution.

  • This equation implies that the higher the ionic strength, and the higher the charge of the ion, the lower the activity coefficient (i.e., greater deviation from ideal behavior).

• Mean Ionic Activity Coefficient ( \gamma_\pm ):

  • Since absolute activity coefficients of single ions cannot be experimentally determined, the concept of a mean ionic activity coefficient is used for electrolytes.

  • For a binary electrolyte (e.g., M{v^+} X{v^-} ) consisting of ions with charges of z^+ and z^- in diluted solutions (µ < 0.1 \text{ M}), the mean ionic activity coefficient is given by:

  • \log \gamma_\pm = -A |z^+ z^-| \sqrt{\mu}

  • This coefficient represents the effective activity of the electrolyte as a whole.

• Extended Debye-Hückel Equation: For less dilute solutions, a term accounting for the finite size of ions is added:

  • \log \gammai = \frac{-A zi^2 \sqrt{\mu}}{1 + Ba\sqrt{\mu}}

  • Where B is a constant and a is the effective diameter of the hydrated ion.

Concentration Expressions

• Many concentration expressions exist. Percent concentration and milliequivalence are covered in the calculation class.

• Focus on Molarity and Molality:

  • Molarity (M): The number of moles of solute in 1 L of solution (moles/L).

  • \text{Molarity (M)} = \frac{\text{Weight of solute (g)}}{\text{MW (g/mol)} \times \text{Volume (L)}}

  • 1 mole/L = 1 M = 1000 mmol/mL

  • Molality (m): The number of moles of solute in 1000 g of solvent.

  • Unit: Moles/kg, not moles/L.

  • \text{Molality (m)} = \frac{\text{Weight of solute (g)}}{\text{MW (g/mol)} \times \text{Weight of solvent (kg)}}

Example Calculations (continued)

• Example 3: A pharmacist needs to prepare 200 mL of phenobarbital solution at a concentration of 0.02 M.

  • MW (phenobarbital) = 232.3 g/mol.

• Example 4: What is the molar and molal concentration of a 0.9% NaCl solution?

  • Specific gravity = 1.0053, MW = 58.5 g/mol.

  • What is the molal concentration of 0.9% NaCl if 10g of KCl is added? Will molar concentration change?

Summary of Molarity and Molality Relations

• Molarity (M):

  • The number of moles of solute in 1 L of solution.

  • Formula:
    \text{Molarity (M)} = \frac{\text{Weight of solute (g)}}{\text{MW (g/mol)} \times \text{Volume (L)}}

• Molality (m):

  • The number of moles of solute in 1000 g of solvent.

  • Formula:
    \text{Molality (m)} = \frac{\text{Weight of solute (g)}}{\text{MW (g/mol)} \times 1000 \text{ (g/kg)}}

Assignments and Reading Material

• Assignment: Refer to Chapters 3 and 4 for detailed readings.

  • Chap 3, pages 41 - 45

  • Chap 4, page 61