Stoichiometry & Raoult’s Law: Principles and Applications

Posted on Dec 24, 2024 in Chemistry

Determination of Stoichiometric Ratio in a Complex

The distribution method is a widely used technique to determine the stoichiometric ratio of a complex formed between a metal ion and a ligand. This method is based on the principle of partitioning a substance between two immiscible phases, usually an organic solvent and an aqueous solution.

Principle

When a metal ion forms a complex with a ligand, the distribution of the metal ion between the aqueous and organic phases changes. The stoichiometric ratio of the complex can be determined by studying the relationship between the concentration of the metal ion in one phase and the concentration of the ligand in the other phase.

Procedure

  1. Preparation of Solutions:
    • A known concentration of the metal ion solution (aqueous phase).
    • A solution of the ligand in an organic solvent immiscible with water.
  2. Mixing: The two phases are mixed and allowed to reach equilibrium.
  3. Measurement: The concentration of the metal ion in one phase (typically the aqueous phase) is determined before and after equilibrium, using techniques like UV-Vis spectrophotometry, atomic absorption spectroscopy, or other analytical methods.
  4. Plotting: A plot is made between the concentration of the metal ion in the organic phase (or ligand concentration) and the ligand-to-metal ratio.

Determination of Stoichiometric Ratio

The stoichiometric ratio is determined by analyzing the data using one of the following methods:

1. Slope Analysis

From the plot of log (distribution ratio) vs. log (ligand concentration), the slope gives the stoichiometric ratio (n) of the complex, where:

n = slope of the line.

2. Job’s Method (Continuous Variation)

A series of solutions with varying ratios of metal to ligand are prepared, maintaining a constant total concentration.

The absorbance or distribution ratio is plotted against the molar fraction of the ligand.

The maximum value indicates the stoichiometric ratio.

3. Limiting Distribution Ratio

At high ligand concentrations, the distribution ratio becomes constant, indicating the predominant stoichiometry of the complex.

Applications

  • Used in coordination chemistry to determine the composition of metal-ligand complexes.
  • Helps in understanding the stability and formation constants of complexes.
  • Useful in designing extraction systems in analytical chemistry.

This method is particularly useful because it requires no isolation of the complex and works well with systems in dynamic equilibrium.


Raoult’s Law

Raoult’s Law is a principle in vapor pressure and solution chemistry that describes the relationship between the vapor pressure of a solvent in a solution and the concentration of that solvent. It applies to ideal solutions, where the intermolecular forces between the components (solvent and solute) are similar.

Statement of Raoult’s Law:

Raoult’s Law states that:

The partial vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution.

Mathematically, it is expressed as:

PA = XA .PA0

Where:

  • PA = Partial vapor pressure of component A in the solution
  • XA = Mole fraction of component A (the solvent) in the solution
  • PA0 = Vapor pressure of pure component A (the solvent) at the given temperature

Similarly, for component B (if it is a solute in a binary solution):

PB = XB . PB0

Where:

  • PB = Partial vapor pressure of component B (the solute) in the solution
  • XB = Mole fraction of component B in the solution
  • PB0 = Vapor pressure of pure component B

For a two-component solution, the total vapor pressure is the sum of the partial pressures of the solvent and the solute:

Ptotal= PA + PB = XA . PA0 + XB .PB0

Assumptions for Raoult’s Law:

  1. Ideal solution: The law assumes that the solution is ideal, meaning that the interactions between molecules of the solvent and solute are similar to the interactions between molecules of the same substance. There is no change in volume or heat when the solute is added to the solvent.
  2. Non-volatile solute: Raoult’s Law is mainly applied to solutions where the solute is non-volatile. If the solute is volatile, the vapor pressure of the solute should also be considered in the law.
  3. Low concentrations: Raoult’s Law is more applicable when the solute concentration is relatively low, as deviations become more significant at higher concentrations.

Applications of Raoult’s Law:

1. Vapor Pressure Depression:

According to Raoult’s Law, the addition of a non-volatile solute to a solvent lowers the vapor pressure of the solvent. This is because the mole fraction of the solvent decreases, thus reducing its contribution to the total vapor pressure.

Example: When salt (a non-volatile solute) is added to water, the vapor pressure of water decreases, which is the principle behind freezing point depression and boiling point elevation.

2. Boiling Point Elevation:

The decrease in vapor pressure caused by the addition of a non-volatile solute leads to an increase in the boiling point of the solution (known as boiling point elevation). This occurs because a solution with a lower vapor pressure requires a higher temperature to reach the point where its vapor pressure equals the external pressure.

3. Freezing Point Depression:

Similarly, the vapor pressure lowering leads to freezing point depression, where the freezing point of a solution is lower than that of the pure solvent. The more solute that is added, the more the freezing point is depressed.

4. Determination of Molecular Weight:

Raoult’s Law is used in colligative property measurements to determine the molecular weight of solutes. By measuring the change in vapor pressure (or other properties like boiling point elevation or freezing point depression), the molar mass of a solute can be calculated.

Limitations of Raoult’s Law:

1. Non-ideal solutions:

Raoult’s Law assumes ideal behavior, but many real solutions do not follow Raoult’s Law perfectly. In non-ideal solutions, the intermolecular forces between solvent and solute molecules differ from those within the pure solvent or solute, leading to deviations.

If the solute-solvent interaction is stronger than solvent-solvent and solute-solute interactions, the solution’s vapor pressure is lower than predicted (positive deviation).

If the solute-solvent interaction is weaker than solvent-solvent and solute-solute interactions, the solution’s vapor pressure is higher than predicted (negative deviation).

2. High Concentrations:

At high concentrations of solute, Raoult’s Law does not hold well because the solution behavior departs from ideality.

Example of Raoult’s Law:

Consider a solution of water and ethanol:

If you add a small amount of ethanol to water, the vapor pressure of water will decrease according to Raoult’s Law because the mole fraction of water decreases.

The vapor pressure of ethanol will also be proportional to its mole fraction, and the total vapor pressure will be the sum of the vapor pressures of both components.

At a specific temperature, the total vapor pressure is the sum of the individual partial vapor pressures:

Ptotal= Pwater + Pethanol = Xwater . Pethanol

This relationship can help in understanding the behavior of the solution and in designing mixtures with desired vapor pressures.

Conclusion:

Raoult’s Law is a fundamental principle in solution chemistry, particularly important in understanding how the addition of solutes affects the vapor pressure, freezing point, and boiling point of a solvent. Though it applies most accurately to ideal solutions, it still offers valuable insights into the properties of many solutions, particularly in areas such as thermodynamics, colligative properties, and chemical engineering.