Solutions (Basic Properties)

Solutions (Basic Properties)

In our previous discussion, we learned that many substances around us are mixtures, and among them, solutions are particularly important. A solution is defined as a homogeneous mixture of two or more chemically non-reacting substances whose composition can be varied within certain limits.

When we dissolve sugar in water, we get a sugar solution. Sugar is the substance that is dissolved, called the solute, and water is the medium in which the solute is dissolved, called the solvent. The solvent is typically the component present in the larger amount, and the solute is the component present in the smaller amount.

Solutions are not limited to solids dissolved in liquids. They can exist in various physical states, depending on the physical state of the solvent.

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Types Of Solutions

Solutions can be classified based on the physical state of the solvent. Since the solvent determines the physical state of the solution, we have solid, liquid, and gaseous solutions. The solute can be in any of the three states (solid, liquid, or gas).

Here's a table summarising the different types of solutions:

State of Solvent	State of Solute	Example
Gas	Gas	Mixture of oxygen and nitrogen gases (Air)
Gas	Liquid	Chloroform mixed with nitrogen gas
Gas	Solid	Camphor in nitrogen gas
Liquid	Gas	Oxygen dissolved in water, Soda water (CO$_2$ in water)
Liquid	Liquid	Ethanol dissolved in water, Petrol and diesel mixture
Liquid	Solid	Glucose dissolved in water, Salt dissolved in water, Sugar dissolved in water
Solid	Gas	Solution of hydrogen in palladium
Solid	Liquid	Amalgam of mercury with sodium
Solid	Solid	Copper dissolved in gold (Alloys like brass, bronze)

Most of our discussions in this section will focus on solutions where the solvent is a liquid.

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Expressing Concentration Of Solutions

The composition of a solution can be described by expressing its concentration, which refers to the amount of solute present in a given amount of solvent or solution. Concentration can be expressed in various ways, both qualitative (dilute, concentrated, saturated) and quantitative.

Quantitative methods for expressing the concentration of a solution include:

1. Mass Percentage ($ \% \text{ w/w}$):

   Defined as the mass of solute in grams present in 100 grams of the solution.

   $ \text{Mass percentage of solute} = \frac{\text{Mass of solute (g)}}{\text{Mass of solution (g)}} \times 100 $

   Mass of solution = Mass of solute + Mass of solvent.

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2. Volume Percentage ($ \% \text{ v/v}$):

   Defined as the volume of solute in mL present in 100 mL of the solution. Used when both solute and solvent are liquids.

   $ \text{Volume percentage of solute} = \frac{\text{Volume of solute (mL)}}{\text{Volume of solution (mL)}} \times 100 $

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3. Mass by Volume Percentage ($ \% \text{ w/v}$):

   Defined as the mass of solute in grams present in 100 mL of the solution. Commonly used in pharmacy and medicine.

   $ \text{Mass by volume percentage of solute} = \frac{\text{Mass of solute (g)}}{\text{Volume of solution (mL)}} \times 100 $

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4. Parts per Million (ppm):

   Used for very dilute solutions. Defined as the mass or volume of solute present in one million parts by mass or volume of the solution.

   $ \text{ppm of solute} = \frac{\text{Mass/Volume of solute}}{\text{Mass/Volume of solution}} \times 10^6 $

   For example, if 1 gram of a substance is dissolved in $10^6$ grams of solution, the concentration is 1 ppm.

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5. Mole Fraction ($\chi$):

   Defined as the ratio of the number of moles of one component to the total number of moles of all components present in the solution. It is unitless.

   For a binary solution containing component A (solute) and component B (solvent), if $n_A$ is the number of moles of A and $n_B$ is the number of moles of B, then:

   $ \text{Mole fraction of A}, \chi_A = \frac{n_A}{n_A + n_B} $

   $ \text{Mole fraction of B}, \chi_B = \frac{n_B}{n_A + n_B} $

   The sum of mole fractions of all components in a solution is always equal to 1: $\chi_A + \chi_B = 1$.

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6. Molarity (M):

   Defined as the number of moles of solute dissolved in one litre (1 L) of the solution. Unit: mol/L or M.

   $ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution (L)}} $

   Molarity is temperature-dependent because the volume of the solution changes with temperature.

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7. Molality (m):

   Defined as the number of moles of solute dissolved in one kilogram (1 kg) of the solvent. Unit: mol/kg or m.

   $ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} $

   Molality is temperature-independent because mass does not change with temperature.

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Solubility

Solubility is a measure of how much solute can dissolve in a given amount of solvent at a specific temperature to form a saturated solution. A saturated solution is a solution in which no more solute can be dissolved at a given temperature and pressure. An unsaturated solution is one in which more solute can be dissolved.

Solubility depends on several factors, including the nature of the solute and solvent, temperature, and pressure.

The general rule of thumb for solubility is "like dissolves like". This means that polar solutes tend to dissolve in polar solvents (e.g., salt in water), and non-polar solutes tend to dissolve in non-polar solvents (e.g., oil in petrol). This is because the intermolecular forces between the solute and solvent particles are similar.

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Solubility Of A Solid In A Liquid

When a solid solute is added to a liquid solvent, two processes occur simultaneously: the solid dissolves (dissolution), and dissolved solute particles return to the solid phase (crystallisation). At saturation, the rate of dissolution equals the rate of crystallisation, forming a dynamic equilibrium.

Solubility of a solid in a liquid is affected by:

1. Nature of Solute and Solvent: As mentioned, 'like dissolves like'. Polar ionic or polar covalent solutes (e.g., NaCl, sugar) dissolve well in polar solvents (e.g., water). Non-polar covalent solutes (e.g., naphthalene, iodine) dissolve well in non-polar solvents (e.g., benzene, carbon tetrachloride).
2. Effect of Temperature: The effect of temperature on the solubility of solids in liquids depends on whether the dissolution process is exothermic or endothermic.
   • If dissolution is endothermic ($\Delta H_{solution} > 0$), solubility increases with increasing temperature (as per Le Chatelier's principle). Example: Dissolving potassium nitrate (KNO$_3$) in water.
   • If dissolution is exothermic ($\Delta H_{solution} < 0$), solubility decreases with increasing temperature. Example: Dissolving calcium chloride (CaCl$_2$) or calcium sulphate (CaSO$_4$) in water at certain concentrations.
   • If there is negligible heat change, temperature has little effect.

   Generally, for most solids, dissolving in liquid is an endothermic process, so their solubility increases with temperature.

3. Effect of Pressure: Pressure has no significant effect on the solubility of solids in liquids because solids and liquids are highly incompressible, and their volumes are not significantly affected by pressure changes.

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Solubility Of A Gas In A Liquid

Gases also dissolve in liquids (e.g., oxygen in water, carbon dioxide in soft drinks). The solubility of a gas in a liquid is affected by:

1. Nature of Gas and Liquid: Some gases are more soluble in certain liquids due to specific interactions (e.g., polar gases like HCl are highly soluble in polar solvents like water due to dipole-dipole interactions and chemical reaction). Non-polar gases like N$_2$, O$_2$, He are less soluble in water but may be more soluble in non-polar solvents.
2. Effect of Temperature: The dissolution of a gas in a liquid is generally an exothermic process ($\Delta H_{solution} < 0$) because energy is released when intermolecular forces form between gas and liquid particles, while the energy required to separate gas particles is minimal. Therefore, according to Le Chatelier's principle, the solubility of gases in liquids decreases with increasing temperature. This is why aquatic life is more comfortable in colder water, as it contains more dissolved oxygen. Heating water also drives out dissolved gases.
3. Effect of Pressure: Pressure has a significant effect on the solubility of gases in liquids. The solubility of a gas in a liquid increases with increasing pressure. This relationship is described by Henry's Law.

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Henry's Law

Henry's Law states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the surface of the liquid.

Alternatively, it can be stated that the partial pressure of the gas in the vapour phase ($p$) is proportional to the mole fraction of the gas ($\chi$) in the solution.

$ p = K_H \chi_{gas} $

Where:

• $p$ is the partial pressure of the gas in the vapour phase above the solution.
• $\chi_{gas}$ is the mole fraction of the gas in the solution.
• $K_H$ is Henry's Law constant, which is specific for a given gas-solvent pair and temperature.

The value of $K_H$ depends on the nature of the gas, the nature of the solvent, and the temperature. A higher value of $K_H$ at a given temperature indicates that the gas has lower solubility in the liquid.

Applications of Henry's Law:

• Carbonated drinks: Carbon dioxide gas is dissolved in soft drinks under high pressure. When the bottle is opened, the pressure above the liquid decreases, and the solubility of CO$_2$ decreases, causing it to bubble out rapidly.
• Deep-sea diving: When divers breathe compressed air at high pressure underwater, nitrogen and oxygen dissolve in their blood and tissues. As they ascend, the pressure decreases, and the dissolved gases come out of solution, forming bubbles in the blood capillaries. These bubbles can cause a painful condition called 'the bends' (decompression sickness). To avoid this, divers use tanks filled with air diluted with helium (instead of nitrogen) because helium is less soluble in blood under pressure.
• Functioning of lungs at high altitudes: At high altitudes, the partial pressure of oxygen is lower than at sea level. This causes a decrease in the concentration of oxygen dissolved in the blood of people living at high altitudes. This can lead to a condition called 'anoxia', which results in weakness and inability to think clearly.

Limitations of Henry's Law: Henry's Law is applicable only under certain conditions:

• The pressure of the gas is not too high.
• The temperature is not too low.
• The gas does not undergo chemical reaction with the solvent (e.g., HCl reacts with water).
• The gas does not associate or dissociate in the solvent.

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Vapour Pressure Of Liquid Solutions

When a non-volatile solid is dissolved in a volatile liquid, the vapour pressure of the solution is lower than that of the pure solvent. Similarly, when two volatile liquids are mixed, the vapour pressure of the resulting solution depends on the vapour pressures of the pure components and their relative amounts in the solution. This relationship is described by Raoult's Law.

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Vapour Pressure Of Liquid-Liquid Solutions

For a solution containing two volatile liquid components, A and B, Raoult's Law describes the partial vapour pressure of each component and the total vapour pressure of the solution.

Raoult's Law: For a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction in the solution.

Let $p_A$ and $p_B$ be the partial vapour pressures of components A and B in the solution, respectively.

Let $\chi_A$ and $\chi_B$ be their respective mole fractions in the solution.

Let $p_A^0$ and $p_B^0$ be the vapour pressures of pure component A and pure component B, respectively, at the same temperature.

According to Raoult's Law:

$ p_A = p_A^0 \chi_A $

$ p_B = p_B^0 \chi_B $

The total vapour pressure of the solution ($P_{total}$) is given by Dalton's Law of Partial Pressures:

$ P_{total} = p_A + p_B $

Substituting the expressions for $p_A$ and $p_B$ from Raoult's Law:

$ P_{total} = p_A^0 \chi_A + p_B^0 \chi_B $

Since $\chi_B = 1 - \chi_A$, we can also write:

$ P_{total} = p_A^0 \chi_A + p_B^0 (1 - \chi_A) = p_A^0 \chi_A + p_B^0 - p_B^0 \chi_A $

$ P_{total} = (p_A^0 - p_B^0) \chi_A + p_B^0 $

This equation shows that the total vapour pressure over the solution varies linearly with the mole fraction of component A (or B) in the solution.

The composition of the vapour phase in equilibrium with the solution is different from the composition of the liquid phase. The mole fraction of component A in the vapour phase ($y_A$) can be calculated using Dalton's Law of Partial Pressures:

$ y_A = \frac{p_A}{P_{total}} $

$ y_B = \frac{p_B}{P_{total}} $

Since the component with the higher vapour pressure in the pure state will contribute more to the vapour phase, the vapour phase is richer in the more volatile component compared to the liquid phase.

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Raoult’S Law As A Special Case Of Henry’S Law

Henry's Law relates the partial pressure of a gas above a liquid to its mole fraction in the liquid solution ($p = K_H \chi$). Raoult's Law relates the partial vapour pressure of a volatile component in a liquid solution to its mole fraction ($p_A = p_A^0 \chi_A$).

If we consider a volatile component (like A) in a solution, it is essentially a gas (vapour of A) in equilibrium with the liquid solution where A is a component.

Comparing the two laws:

Henry's Law: $p_A = K_H \chi_A$

Raoult's Law: $p_A = p_A^0 \chi_A$

If we consider the component A as a "gas" dissolved in component B, then according to Henry's Law, $p_A$ is proportional to $\chi_A$. According to Raoult's Law, the proportionality constant is $p_A^0$.

Thus, Raoult's Law is a special case of Henry's Law where the proportionality constant $K_H$ is equal to the vapour pressure of the pure component ($p_A^0$). This applies when the gas (component A in vapour form) is a component of the solution itself, i.e., component A behaves as a "solute" in the context of Henry's Law application to its own partial pressure, with the "solvent" being the entire solution and the "Henry's constant" being its pure vapour pressure.

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Vapour Pressure Of Solutions Of Solids In Liquids

When a non-volatile solid solute (like sugar, salt, urea, glucose) is dissolved in a volatile liquid solvent (like water), the vapour pressure of the solution is always found to be lower than the vapour pressure of the pure solvent at the same temperature.

Explanation: In pure solvent, the entire surface is occupied by solvent molecules, and the rate of evaporation depends on the number of solvent molecules on the surface having sufficient kinetic energy to escape. When a non-volatile solute is added, some of the surface area is occupied by solute particles, which are non-volatile and do not evaporate. This reduces the number of solvent molecules on the surface available for vaporisation. Consequently, the rate of evaporation of the solvent from the solution is lower than that from the pure solvent, resulting in a lower vapour pressure above the solution.

Raoult's Law can also be applied to such solutions: The vapour pressure of the solution ($p_{solution}$) is proportional to the mole fraction of the solvent ($\chi_{solvent}$) in the solution.

$ p_{solution} = p_{solvent}^0 \chi_{solvent} $

Where $p_{solvent}^0$ is the vapour pressure of the pure solvent.

The lowering of vapour pressure ($\Delta p$) is the difference between the vapour pressure of the pure solvent and the solution:

$ \Delta p = p_{solvent}^0 - p_{solution} $

Substituting from Raoult's Law:

$ \Delta p = p_{solvent}^0 - p_{solvent}^0 \chi_{solvent} = p_{solvent}^0 (1 - \chi_{solvent}) $

Since $\chi_{solvent} + \chi_{solute} = 1$, $(1 - \chi_{solvent}) = \chi_{solute}$.

$ \Delta p = p_{solvent}^0 \chi_{solute} $

This shows that the lowering of vapour pressure depends on the mole fraction of the solute, not its nature. This phenomenon, the lowering of vapour pressure, is one of the colligative properties, which depend only on the number of solute particles in the solution, not on their identity.

The relative lowering of vapour pressure is $\frac{\Delta p}{p_{solvent}^0} = \frac{p_{solvent}^0 - p_{solution}}{p_{solvent}^0}$.

$ \frac{p_{solvent}^0 - p_{solution}}{p_{solvent}^0} = \chi_{solute} $

This is Raoult's Law in its original form, stating that the relative lowering of vapour pressure of a solution is equal to the mole fraction of the solute.

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Ideal And Nonideal Solutions

Based on their adherence to Raoult's Law, liquid solutions can be classified as ideal solutions or non-ideal solutions.

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Ideal Solutions

An ideal solution is a solution that obeys Raoult's Law over the entire range of concentration and at all temperatures.

For an ideal binary solution of A and B:

• $p_A = p_A^0 \chi_A$ and $p_B = p_B^0 \chi_B$ for all $\chi_A$ and $\chi_B$.
• $P_{total} = p_A^0 \chi_A + p_B^0 \chi_B$.

Characteristics of Ideal Solutions:

1. Obeys Raoult's Law: The partial pressure of each component is directly proportional to its mole fraction.
2. Enthalpy of mixing is zero ($\Delta H_{mix} = 0$): No heat is evolved or absorbed when the components are mixed to form the solution.
3. Volume of mixing is zero ($\Delta V_{mix} = 0$): The total volume of the solution is the sum of the volumes of the individual components before mixing. There is neither expansion nor contraction on mixing.
4. Intermolecular Interactions: The intermolecular forces of attraction between A-B molecules are of similar strength to the A-A interactions and B-B interactions in the pure components. ($A-B \approx A-A \approx B-B$).

In reality, perfectly ideal solutions are rare. However, solutions formed by mixing compounds that are structurally very similar and have very similar intermolecular forces behave approximately as ideal solutions.

Examples: Mixture of Benzene (C$_6$H$_6$) and Toluene (C$_6$H$_5$CH$_3$), n-Hexane and n-Heptane, Chloroethane and Bromoethane.

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Non-Ideal Solutions

Non-ideal solutions are solutions that do not obey Raoult's Law over the entire range of concentration and temperature. Most real solutions are non-ideal.

For non-ideal solutions, $\Delta H_{mix} \neq 0$, $\Delta V_{mix} \neq 0$, and the intermolecular interactions between A-B molecules are different from the A-A and B-B interactions.

Non-ideal solutions are of two types:

1. Non-Ideal Solutions Showing Positive Deviation from Raoult's Law:
   • Deviation: The partial vapour pressure of each component and the total vapour pressure of the solution are higher than predicted by Raoult's Law ($p_A > p_A^0 \chi_A$, $p_B > p_B^0 \chi_B$, $P_{total} > P_{ideal}$).
   • Interactions: A-B intermolecular forces of attraction are weaker than the A-A and B-B interactions. This makes it easier for molecules to escape into the vapour phase, leading to higher vapour pressure.
   • Enthalpy of mixing: Endothermic ($\Delta H_{mix} > 0$). Energy is required to overcome the stronger A-A and B-B forces to form weaker A-B forces.
   • Volume of mixing: Positive ($\Delta V_{mix} > 0$). The total volume of the solution is greater than the sum of the volumes of the components before mixing, as particles move slightly further apart due to weaker attractions.
   • Examples: Mixture of Ethanol and Acetone, Carbon disulphide and Acetone, Benzene and Acetone. In Ethanol and Acetone, ethanol has hydrogen bonds (strong A-A interaction), and acetone has dipole-dipole forces. Mixing them breaks some hydrogen bonds in ethanol, and the A-B interaction (dipole-dipole between ethanol and acetone) is weaker than the original hydrogen bonding in ethanol, leading to positive deviation.

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2. Non-Ideal Solutions Showing Negative Deviation from Raoult's Law:
   • Deviation: The partial vapour pressure of each component and the total vapour pressure of the solution are lower than predicted by Raoult's Law ($p_A < p_A^0 \chi_A$, $p_B < p_B^0 \chi_B$, $P_{total} < P_{ideal}$).
   • Interactions: A-B intermolecular forces of attraction are stronger than the A-A and B-B interactions. This makes it harder for molecules to escape into the vapour phase, leading to lower vapour pressure.
   • Enthalpy of mixing: Exothermic ($\Delta H_{mix} < 0$). Energy is released as stronger A-B forces are formed.
   • Volume of mixing: Negative ($\Delta V_{mix} < 0$). The total volume of the solution is less than the sum of the volumes of the components before mixing, as particles pack closer together due to stronger attractions.
   • Examples: Mixture of Phenol and Aniline, Chloroform and Acetone, Nitric Acid and Water. In Chloroform and Acetone, a new hydrogen bond forms between chloroform's acidic hydrogen and acetone's oxygen, making the A-B interaction stronger than the original A-A and B-B interactions, leading to negative deviation.

Non-ideal solutions that show significant deviations from Raoult's Law can form azeotropes, which are binary mixtures that boil at a constant temperature and have the same composition in both liquid and vapour phases. Azeotropes cannot be separated by simple distillation.

• Solutions showing positive deviation form minimum boiling azeotropes (boiling point lower than either pure component). Example: Ethanol (95.6%) and Water (4.4%).
• Solutions showing negative deviation form maximum boiling azeotropes (boiling point higher than either pure component). Example: Nitric Acid (68%) and Water (32%).

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