CHSE Odisha Class 12 Chemistry Notes Chapter 2 Solutions

Chapter 2: Solutions

Introduction to Solutions

A solution is a homogeneous mixture of two or more substances. In a solution, the substance present in a smaller amount is called the solute, while the one in a larger amount is called the solvent. Solutions are widely used in various chemical processes.

Types of Solutions

Solutions can be classified based on the physical states of the solute and solvent. Some common examples are:

Gaseous Solutions:

Solute: Gas, Solvent: Gas (e.g., Air)

Liquid Solutions:

Solute: Gas, Solvent: Liquid (e.g., Carbonated water)

Solute: Liquid, Solvent: Liquid (e.g., Alcohol in water)

Solute: Solid, Solvent: Liquid (e.g., Sugar in water)

Solid Solutions:

Solute: Gas, Solvent: Solid (e.g., Hydrogen in palladium)

Solute: Liquid, Solvent: Solid (e.g., Amalgams)

Solute: Solid, Solvent: Solid (e.g., All

Definition and Explanation of Solutions

A solution is a homogeneous mixture of two or more components, in which the solute is uniformly distributed within the solvent at the molecular level. This means that the properties of the solution are identical throughout the mixture. Solutions can exist in all three states of matter: solid, liquid, and gas.

Key Terminology:

• Solute: The substance that is dissolved in the solvent. Usually, it is present in a smaller quantity.
• Solvent: The substance in which the solute dissolves. Usually, it is present in a larger quantity.
• Homogeneous: The composition of the solution is uniform throughout.
• Concentration: The amount of solute present in a given quantity of solvent or solution.

Properties of Solutions:

1. Homogeneous nature: Solutions are uniform throughout, meaning that no part of the solution is different from another part.
2. Particle size: The solute particles are of molecular size (less than 1 nm in diameter), which makes them invisible to the naked eye.
3. No settling of solute: Solute particles do not settle out of the solution when it is left standing.
4. Cannot be filtered: Solute particles in a solution cannot be separated by filtration.
5. Clear and transparent: Solutions are typically clear and do not scatter light unless the solution is colloidal.

Types of Solutions

Solutions are classified based on the physical states of the solute and solvent:

Solvent State	Solute State	Example
Gas	Gas	Air (Oxygen dissolved in Nitrogen)
Gas	Liquid	Water vapor in air (humidity)
Gas	Solid	Smoke (solid particles in air)
Liquid	Gas	Carbonated water (CO₂ in water)
Liquid	Liquid	Alcohol in water
Liquid	Solid	Sugar solution (sugar in water)
Solid	Gas	Hydrogen in palladium
Solid	Liquid	Amalgams (mercury in silver)
Solid	Solid	Alloys (copper in gold)

Concentration of Solutions

1. Mass Percentage (%w/w)

Definition: Mass percentage is the mass of a solute in 100 g of a solution. It expresses the concentration of the solute in the entire solution.

 

$$\text{Mass \% of component}=\frac{\text{Mass of component in solution}}{\text{Total mass of solution}}\times 100$$

 

Example: If 5 g of NaCl is dissolved in 95 g of water, the total mass of the solution is 100 g. The mass percentage of NaCl will be:

 

$$\text{Mass \% of NaCl} = \frac{5}{100} \times 100 = 5\%$$ 

2. Volume Percentage (%v/v)

Definition: Volume percentage represents the volume of a solute in 100 mL of solution. This is commonly used when both the solute and solvent are liquids.

 

$$\text{Volume \% of component} = \frac{\text{Volume of component}}{\text{Total volume of solution}} \times 100$$ 

Example: If 30 mL of ethanol is mixed with 70 mL of water to make 100 mL of solution, the volume percentage of ethanol is:

 

$$\text{Volume \% of ethanol}=\frac{30}{100}\times 100=30\mathrm{\%}$$3. Mass by Volume Percentage (%w/v)

Definition: Mass by volume percentage expresses the mass of solute in grams in 100 mL of solution. It is frequently used for solutions in which a solid is dissolved in a liquid.

 

$$\text{Mass by Volume \%} = \frac{\text{Mass of solute in grams}}{\text{Volume of solution in mL}} \times 100$$ 

Example: If 2 g of sugar is dissolved in 100 mL of water, the mass by volume percentage is:

 

$$\text{Mass by Volume \% of sugar} = \frac{2}{100} \times 100 = 2\%$$4. Parts Per Million (ppm)

Definition: Parts per million (ppm) is used to express very dilute concentrations. It is the number of parts of a solute per million parts of the solution. This unit is often used in environmental science for pollutants and chemicals in air or water.

 

$$\text{ppm} = \frac{\text{No. of parts of component}}{\text{Total no. of parts of solution}} \times 10^6$$ 

Example: If 0.002 g of chlorine is present in 1,000,000 g of water, the concentration in ppm is:

 

$$\text{ppm of chlorine}=\frac{0.002}{1,000,000}\times 10^6=2\text{ppm}$$5. Mole Fraction (x)

Definition: The mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in a solution. It is a unitless quantity.

 

$$\text{Mole Fraction of A}, x_A = \frac{n_A}{n_A + n_B}$$​​Where:

${}_{}$$n_A$ = moles of component A

 

$n_B$$n_B$= moles of component B

Example: In a binary solution where 2 moles of A are mixed with 3 moles of B, the mole fraction of A will be:

 

$$x_A = \frac{2}{2 + 3} = 0.4$$ 

6. Molarity (M)

Definition: Molarity is the number of moles of solute per liter of solution. It is expressed as moles per liter (mol/L).

 

$$\text{Molarity}, M = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}$$​

Example: If 1 mole of NaCl is dissolved in 1 L of water, the molarity of the solution is:

 

$$M = \frac{1}{1} = 1 \, \text{M}$$ 

Important: Molarity is temperature-dependent because the volume of a solution can change with temperature.

7. Molality (m)

Definition: Molality is the number of moles of solute per kilogram of solvent. Unlike molarity, molality is independent of temperature because it is based on mass.

 

$$\text{Molality}, m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kilograms}}$$​

Example: If 0.5 moles of sugar are dissolved in 1 kg of water, the molality of the solution is:

 

$$m = \frac{0.5}{1} = 0.5 \, \text{mol/kg}$$ 

8. Normality (N)

Definition: Normality is the number of equivalents of solute per liter of solution. It is used for reactions where the solute reacts in a specific ratio, such as acid-base or redox reactions.

 

$$\text{Normality}, N = \frac{\text{Number of equivalents of solute}}{\text{Volume of solution in liters}}$$Normality,N=Volume of solution in litersNumber of equivalents of solute​Where the number of equivalents of solute (eq) is:

 

$$\text{eq} = \frac{\text{Weight of solute}}{\text{Equivalent weight (E)}}$$eq=Equivalent weight (E)Weight of solute​And:

 

$$E = \frac{M}{z}$$ 

 

$M$ = Molar mass of solute

$z$ = Valency factor

Example: If 0.1 equivalents of HCl are dissolved in 1 liter of water, the normality is:

 

$$N = \frac{0.1}{1} = 0.1 \, \text{N}$$ 

Dilution Law (Important Relationship)

Definition: The dilution law states that when a solution is diluted by adding more solvent, the amount of solute remains constant, but the concentration changes.

 

$$M_1{V}_1=M_2{V}_2$$V1​ = initial molarity and volume

V2​ = final molarity and volume

Normality also follows a similar relationship:

 

$$N_1{V}_1=N_2{V}_{\mathrm{2<span\; style="font-size:\; inherit;\; font-family:\; -apple-system,\; system-ui,\; BlinkMacSystemFont,\; \text{'}Segoe\; UI\text{'},\; Helvetica,\; Arial,\; sans-serif,\; \text{'}Apple\; Color\; Emoji\text{'},\; \text{'}Segoe\; UI\; Emoji\text{'},\; \text{'}Segoe\; UI\; Symbol\text{'};"></span>}}$$Molarity and Normality Relationship

Definition: Normality and molarity are related by the valency factor, $z$. The formula to relate the two is:

 

$$N = z \times M$$Where:

$N$ = Normality

$M$ = Molarity

$z$ = Valency factor (number of equivalents per mole)

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Effect of Temperature on Concentration Units

Temperature-independent units: Mass percentage, parts per million (ppm), mole fraction, and molality are not affected by temperature because they depend on mass, which remains constant with temperature changes.

Temperature-dependent units: Molarity and normality are affected by temperature because they depend on the volume of the solution, which expands or contracts with temperature.

• The concentration of a solution represents the amount of solute present in a given quantity of solvent or solution. It can be expressed in several ways:
• Mass Percentage (w/w%):
• $$\text{Mass \% of solute} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100$$
• Mass % of solute=(Mass of solutionMass of solute​)×100
• Volume Percentage (v/v%):
• $$\text{Volume \% of solute} = \left( \frac{\text{Volume of solute}}{\text{Volume of solution}} \right) \times 100$$
• Volume % of solute=(Volume of solutionVolume of solute​)×100
• Mass by Volume Percentage (w/v%):
• $$\text{Mass/Volume \%} = \left( \frac{\text{Mass of solute}}{\text{Volume of solution}} \right) \times 100$$
• Mass/Volume %=(Volume of solutionMass of solute​)×100
• Molarity (M):
• $$M = \frac{\text{Number of moles of solute}}{\text{Volume of solution in Liters}}$$
• M=Volume of solution in LitersNumber of moles of solute​Molarity is temperature-dependent because volume changes with temperature.
• Molality (m):
• $$m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}}$$
• m=Mass of solvent in kgNumber of moles of solute​Molality is independent of temperature since it is based on the mass of the solvent.
• Normality (N):
• $$N = \frac{\text{Number of gram equivalents of solute}}{\text{Volume of solution in Liters}}$$
• N=Volume of solution in LitersNumber of gram equivalents of solute​Normality depends on the reaction being studied and the equivalent weight of the solute.
• Mole Fraction (X):
• $$X_A = \frac{\text{Number of moles of component A}}{\text{Total number of moles of all components in solution}}$$
• XA​=Total number of moles of all components in solutionNumber of moles of component A​The sum of mole fractions of all components of a solution is always 1.

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• Ideal and Non-Ideal Solutions

1. Ideal Solutions:
   • Ideal solutions obey Raoult’s law, which states that the partial vapor pressure of each volatile component in the solution is directly proportional to its mole fraction.
   • There is no change in volume or enthalpy when the components are mixed.
   • Example: Benzene and Toluene mixture.
2. Non-Ideal Solutions:
   • Non-ideal solutions deviate from Raoult’s law, either showing positive or negative deviations.
     • Positive deviation: The vapor pressure of the solution is higher than predicted by Raoult’s law. Example: Ethanol and Acetone.
     • Negative deviation: The vapor pressure of the solution is lower than predicted by Raoult’s law. Example: Water and Nitric Acid.
   • There is a change in volume and enthalpy upon mixing.

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• Vapor Pressure of Liquid Solutions
• The vapor pressure of a liquid is the pressure exerted by the vapor in equilibrium with its liquid at a given temperature.

1. For a pure solvent: The vapor pressure depends on the nature of the solvent and temperature.
2. For a solution: According to Raoult’s law, the vapor pressure of the solution decreases as solute is added because the number of solvent molecules escaping to the vapor phase decreases.

• Colligative Properties
• Colligative properties are properties of solutions that depend only on the number of solute particles, not their identity. These include:

1. Relative lowering of vapor pressure
2. Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure

• Relative Lowering of Vapor Pressure:
• $$\frac{P^0 – P}{P^0} = X_{\text{solute}}$$
• P0P0−P​=Xsolute​Where
• $P^0$
• P0 is the vapor pressure of the pure solvent and
• $P$
• P is the vapor pressure of the solution.
• Elevation of Boiling Point:
• $$\Delta T_b = K_b \cdot m$$
• ΔTb​=Kb​⋅mWhere
• $K_b$
• Kb​ is the ebullioscopic constant, and
• $m$
• m is the molality of the solution.
• Depression of Freezing Point:
• $$\Delta T_f = K_f \cdot m$$
• ΔTf​=Kf​⋅mWhere
• $K_f$
• Kf​ is the cryoscopic constant, and
• $m$
• m is the molality of the solution.
• Osmotic Pressure:
• $$\pi = iCRT$$
• π=iCRTWhere
• $i$
• i is the van’t Hoff factor,
• $C$
• C is the concentration,
• $R$
• R is the gas constant, and
• $T$
• T is the temperature.

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• Van’t Hoff Factor (i)
• The van’t Hoff factor accounts for the degree of dissociation or association of solute particles in a solution. For example:
• For a solute that fully dissociates into 2 particles (like NaCl),
  $i = 2$ 

  $i=2$.

• For solutes that do not dissociate,
  $i = 1$ 

  $i=1$.