solutions (chem )

Introduction to Solutions

• Definition: A solution is defined as a homogeneous mixture of two or more components that can be classified as solute and solvent.

• Solvent: The component of the solution which is present in a large amount.

• Solute: The component of the solution which is present in the smallest amount.

• Binary Solution: A type of solution containing only two components. An example is a sugar solution. Binary solutions are classified based on the physical state of the solute and the solvent.

Types of Binary Solutions

Solutions are classified according to the physical states of the solute and solvent into three main categories, each with three sub-types:

1. Solid Solutions:

   • Solid in Solid: Example: Copper dissolved in Gold.

   • Liquid in Solid: Example: Amalgam of Mercury with Sodium ($Hg$ in $Na$).

   • Gas in Solid: Example: Solution of Hydrogen in Palladium ($H_2$ in $Pd$).

2. Liquid Solutions:

   • Solid in Liquid: Example: Glucose dissolved in water.

   • Liquid in Liquid: Example: Ethanol dissolved in water.

   • Gas in Liquid: Example: Oxygen dissolved in water.

3. Gas Solutions:

   • Solid in Gas: Example: Camphor in Nitrogen gas.

   • Liquid in Gas: Example: Chloroform mixed with Nitrogen gas ($\text{CHCl}_3$ in $N_2$).

   • Gas in Gas: Example: Mixture of Oxygen and Nitrogen gases.

Expressing Concentration of Solutions

• Concentration: It can be defined as the amount of solute present in a given quantity of solution or solvent.

Concentration Terms

• Molarity ($M$): Defined as the number of moles of solute dissolved in $1$ liter ($dm^3$) of solution.

  • Formula: $\text{Molarity} = \frac{\text{No. of moles of solute}}{\text{Volume in liters}}$

  • $M = \frac{n_2}{V_{(L)}}$, where $n_2 = \frac{w_2}{M_2}$ (given mass of solute / molar mass of solute).

  • Unit: $\text{mol/L}$ or $\text{mol/dm}^3$ or $M$.

  • Note: Molarity depends on temperature because volume changes with temperature. As temperature increases, volume increases, thus molarity decreases ($M \propto \frac{1}{V}$).

• Molality ($m$): Defined as the number of moles of solute dissolved in $1\text{ kg}$ of solvent.

  • Formula: $\text{Molality} = \frac{\text{No. of moles of solute}}{\text{Mass of solvent in kg}}$

  • $m = \frac{n_2}{w_1 \text{ (in kg)}}$ or $m = \frac{w_2 \times 1000}{M_2 \times w_1 \text{ (in g)}}$.

  • Unit: $\text{mol/kg}$.

  • Note: Molality is independent of temperature because it is based on mass, not volume.

• Mole Fraction ($x$): It is defined as the ratio of the moles of a particular component to the sum of the moles of all components present in the solution.

  • For a binary solution with components $1$ and $2$:

    • $x_1 = \frac{n_1}{n_1 + n_2}$

    • $x_2 = \frac{n_2}{n_1 + n_2}$

  • The sum of mole fractions is always unity: $x_1 + x_2 = 1$.

• Mass Percentage (w/w): Mass of solute present in $100\text{ g}$ of solution.

  • Formula: $\frac{\text{Mass of solute}}{\text{Total mass of solution}} \times 100$

• Volume Percentage (v/v): Volume of solute in $ml$ present in $100\text{ ml}$ of solution.

  • Formula: $\frac{\text{Volume of solute}}{\text{Total volume of solution}} \times 100$

• Mass by Volume Percentage (w/v): Mass of solute in grams present in $100\text{ ml}$ of solution.

  • Formula: $\frac{\text{Mass of solute}}{\text{Total volume of solution}} \times 100$

• Parts Per Million (ppm): Useful for expressing concentrations when a solute is present in trace quantities.

  • Formula: $\text{ppm} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 1000000 \text{ (or } 10^6)$

Solubility

• Definition: The maximum amount of solute that can be dissolved in a specific quantity of solvent at a specified temperature.

Solubility of a Solid in a Liquid

1. Nature of Solute and Solvent: "Like dissolves like." Polar solutes are soluble in polar solvents (e.g., NaCl in water), and non-polar solutes are soluble in non-polar solvents.

2. Temperature: Usually, as temperature increases, the solubility of solids in liquids increases.

3. Pressure: Pressure has no significant effect on the solubility of solids in liquids because solids and liquids are incompressible.

4. Volume of Solvent: As the volume of solvent increases, the solubility of the solute also increases.

Key Processes

• Dissolution: The process of adding a solute to a solvent to form a solution.

• Crystallization: When solute particles in a solution collide with solid solute particles and get precipitated out.

• Saturated Solution: A solution in which no more solute can be added at a given temperature.

• Unsaturated Solution: A solution in which more solute can be added.

Solubility of Gas in Liquid and Henry's Law

• Temperature: Temperature is inversely proportional to the solubility of gas in liquid. Solubility decreases as temperature increases.

• Pressure: Pressure is directly proportional to the solubility of gas in liquid.

Henry's Law

• Statement: The partial pressure of the gas in the vapour phase ($p$) is directly proportional to the mole fraction of the gas ($x$) in the solution.

• Formula: $p = K_H \times x$

  • $p$ = partial pressure of gas

  • $x$ = mole fraction of gas in solution

  • $K_H$ = Henry's Law constant

Significance of $K_H$

1. Different gases have different $K_H$ values at the same temperature, meaning it depends on the nature of the gas.

2. Higher the value of $K_H$, the lower the solubility of the gas in the liquid.

3. $K_H$ increases with an increase in temperature, which is why solubility of gases decreases at higher temperatures. This explains why aquatic species are more comfortable in cold water than in warm water.

Applications of Henry's Law

1. Cold Drinks: Soft drink and soda bottles are sealed under high pressure to increase the solubility of $\text{CO}_2$.

2. Scuba Diving (Bends): Scuba divers breathe air at high pressure underwater, increasing the solubility of atmospheric gases in the blood. When divers come to the surface, the pressure decreases and dissolved Nitrogen ($N_2$) bubbles out of the blood, blocking capillaries and creating a painful medical condition called "Bends." To avoid this, tanks are filled with air diluted with Helium ($11.7\%\text{ He}$, $56.2\%\text{ N}_2$, $32.1\%\text{ O}_2$).

3. High Altitudes (Anoxia): At high altitudes, the partial pressure of Oxygen is less than at ground level. This leads to low concentrations of Oxygen in the blood and tissues of climbers, causing them to become weak and unable to think clearly—a condition known as Anoxia.

Vapour Pressure and Raoult's Law

• Vapour Pressure: The pressure exerted by the molecules of vapour on the surface of the liquid when it is in equilibrium with the liquid at a given temperature.

Factors Affecting Vapour Pressure

1. Temperature: Directly proportional ($T \uparrow, VP \uparrow$).

2. Nature of Liquid: Liquids with weak intermolecular forces are more volatile and have higher $VP$ (e.g., Ethers > Alcohols > $H_2O$).

3. Surface Area: Larger surface area allows more molecules to escape into the vapour phase, increasing $VP$.

4. Presence of Solute: When a non-volatile solute is added to a solvent, the vapour pressure of the solution is lower than that of the pure solvent because the solute particles occupy space on the surface, hindering the escape of solvent molecules.

Colligative Properties

Colligative properties are properties of dilute solutions that depend only on the total number of solute particles (moles/concentration) and not on the nature of the solute.

1. Relative Lowering of Vapour Pressure (RLVP)

• Let $p^\circ$ be the vapour pressure of the pure solvent and $p$ be the vapour pressure of the solution.

• Lowering of vapour pressure = $p^\circ - p$.

• RLVP Definition: It is the ratio of the lowering of vapour pressure to the vapour pressure of the pure solvent ($\frac{p^\circ - p}{p^\circ}$).

• Raoult's Law (for non-volatile solutes): $\frac{p^\circ - p}{p^\circ} = x_2$ (mole fraction of solute).

• Relationship with Molar Mass: For dilute solutions where $n_2$ is negligible compared to $n_1$:

  • $\frac{p^\circ - p}{p^\circ} = \frac{w_2 / M_2}{w_1 / M_1}$

  • $M_2 = \frac{w_2 \times M_1 \times p^\circ}{(p^\circ - p) \times w_1}$

2. Osmotic Pressure ($\pi$)

• Osmosis: The spontaneous flow of solvent molecules from a region of low solute concentration (pure solvent) to a region of