Mole Concept

Concentration of Solutions

Solutions-An Overview

Large amount of salt is dissolved in seawater. This makes it unfit for drinking directly. Can we say that the amount of salt in the sea is the same everywhere?

The air contains gases like oxygen, carbon dioxide and ozone along with various small particles like pollen grains and dust. Are the gases and the particles present in equal amounts in air?

Soil contains a lot of substances, e.g., clay, organic matter, minerals, pebbles, etc.

Why do the amounts of clay, organic matter, minerals, etc. in soil vary from place to place?

All of the above substances (soil, air and seawater) are examples of mixtures. Let us go through the lesson to find out what mixtures are.

Mixtures

A mixture may be defined as a material having two or more types of pure forms of matter. For example, milk is a mixture as it contains a combination of water molecules, fat molecules and protein molecules. The constituents of a mixture can be separated by certain physical processes such as evaporation and boiling. Constituents of certain mixtures can also be separated manually. For example, a mixture of stones and sand can be separated manually. On the other hand, salt cannot be manually separated from saltwater. One needs to boil the mixture to separate the salt from water.

Mixtures

 

Solutions

Now that we know what mixtures are, let us study about solutions. Whenever we talk about solutions, we instantly think of liquids. But is it necessary for all solutions to be liquids?

No. A solution is simply a homogeneous mixture of two or more substances. Solutions can be solid, liquid and gaseous. Alloy is an example of a solid solution, while air is a gaseous solution.

A mixture is called solution when it has homogeneity at the particle level. A solution is formed when a solute is dissolved in a solvent.

Examples of solutions

Solutions	Solvents	Solutes
1. Saltwater 2. Solution of iodine in alcohol 3. Vinegar 4. Soda water 5. Air	Water Alcohol Water Water Nitrogen (present in the largest amount)	Salt Iodine Acetic acid Carbon dioxide Other gases (present in relatively smaller amounts)

Properties of Solutions

• They are homogeneous mixtures of solutes and solvents.
• The solute particles in a solution are extremely small in size. They are less than 1 nm (10⁻⁹ m) in diameter.
• The solute particles are not visible to the naked eye.
• As a result of the small size of the solute particles, a solution does not scatter a beam of light passing through it.
• Being small in size, the solute particles get dissolved in the solvent. Hence, the solute cannot be separated from the solvent by filtration.
• The solute particles do not settle down when left undisturbed.

Further Connect

Like a gas, a liquid exerts pressure of its own due to evaporation. This pressure is known as the vapour pressure of the liquid.

When a liquid solution is formed, it exerts its own vapour pressure. This results from the individual pressures of the solute and the solvent.

In 1882, a scientist named Francois-Marie Raoult established that for a solution containing volatile liquids, the partial vapour pressure of each component of the solution is proportional to its mole fraction present in solution.
                              
                                              p₁∝ x₁
                                              p₁=p₁^o x₁
 where p₁^o  is the vapour pressure of pure component at the same temperature.

1. The addition of solutes to solvents can lower the freezing point, elevate the boiling point and lower the vapour pressure of the solvents.

2. A solution is formed when two similar substances are mixed. For example, water and salt form a solution, but water and oil do not. This is because:

• Water and salt are polar substances (wherein the centres of positive charge and negative charge do not coincide), so they can mix with each other.
• Oil is a non-polar substance, so it does not mix with water to form a solution.

3. The solubility of a solute in a solvent is affected by temperature. Usually solubility increases with increase in temperature.

Concentration of a Solution

We come across many solutions in daily life, for example, saltwater, lime juice, squashes, coconut water, etc. How do we rate these solutions? We do so by classifying them as sweet, salty, etc., on the basis of our senses. 

In chemistry, however, such classification of solutions is not very informative or beneficial. So, chemists usually use words such as ‘saturated’, ‘unsaturated’, ‘supersaturated’, ‘dilute’ and ‘concentrated’ to define the concentration of a given solution.

Uses of Concentration in Real Life

• Maintenance of the ionic balance in our body
• Preparation of dyes
• Preparation of juices
• Labelling of alcoholic drinks
• Addition of antifreeze to vehicles

Let us learn more about concentration in this lesson.

Antifreeze

Antifreeze solutions are added to a liquid in a cooling system (such as the water in an automobile engine) to lower its freezing point and prevent ice build-up in the system at very low temperatures.

Functions of antifreeze

• It contains chemicals that prevent corrosion and scale formation in the engine and radiator of a vehicle.
• It provides protection against boiling during summers. At 1 atmosphere pressure, water boils at 100°C; but a 50-50 blend of water−ethylene glycol boils at 106°C.
• A mixture of antifreeze and distilled water (in the ratio, one part antifreeze to one part water) provides freeze protection down to −36.67°C and boil-over protection up to 129.4°C.

Precautions 

• Avoid using concentrated antifreeze in a cooling system. At least 40% of the mixture should be water.
• Do not increase the concentration of antifreeze above 60% as it damages the freezing and overheating protection of the engine. 
• Do not add too much water to the cooling system as it lowers the concentration of the corrosion inhibitor and antifreeze. This results in decreased protection against corrosion and freezing.

The coke or colas (aerated drinks) available in the market are actually super saturated solution of CO₂ in water.

Experiment to Demonstrate Solubility

Procedure: Take two beakers and label them A and B. Fill each with 50 mL of water. Dissolve sugar in beaker A and barium chloride in beaker B. Keep dissolving the solutes in the respective beakers till the solutions become saturated and no more solute can be further dissolved. After this, heat the solutions and dissolve one more spatula of the solutes in the respective beakers. Slowly cool down the solutions after the solutes added further get completely dissolved.

Result: 

• To saturate 50 mL of water, different amounts of sugar and barium chloride is added.
• Upon heating, the saturated sugar solution is able to dissolve more amount of sugar.
• When cooled, the sugar (dissolved after the saturated solution is heated) precipitates out from the solution.

Explanation: Upon heating, a saturated solution can accommodate more amount of solute. This is called a super-saturated solution. This solution is quite unstable as the molecules of the solute (dissolved after the saturated solution is heated) crystallise easily.

Conclusion: A particular amount of solute (here sugar or BaCl₂) can saturate a particular type of solvent (here water) at a particular temperature only. If temperature is changed, then the solubility of the solvent also changes. Solubility of a solute in a solvent is the maximum amount of solute that can be dissolved in 100 g of that solvent at a particular temperature. It is expressed in terms of concentration. For example, a maximum of 36 g sodium chloride can be dissolved in 100 g water at 20°C. Therefore, the solubility of sodium chloride in water is 36 g at 20°C.

Concentration and Its Classification

A solution is a homogeneous mixture of two or more substances. The substance that is dissolved in a solution is called the solute, and the substance that dissolves the solute is called the solvent. The amount of solute in a solution may vary. 

The amount of solute present in a given quantity of solution is called the concentration of that solution. The concentration of a solution helps us to determine the amount of solute present in the solution.

Depending on the amount of solute present, a solution can be classified as follows:

1.Dilute solution

2.Concentrated solution

3.Saturated solution

4.Unsaturated solution

5.Supersaturated solution

Concentration in terms of Mass by Mass Percentage 

 

Concentration in terms of Mass by Volume Percentage 

 

Brush Up

Summary

The following chart shows the types of solutions that can be formed by varying the concentration.

Mole Concept

The Mole Concept: A Brief Overview

Mole defines the quantity of a substance.

One mole of any substance will always contain 6.022 × 10²³ particles, no matter what that substance is. 

Therefore, we can say:

• 1 mole of sodium atoms (Na) contains 6.022 × 10²³ sodium atoms.

• 1 mole of sodium ions (Na⁺) contains 6.022 × 10²³ sodium ions.

• 1 mole of hydrogen atoms (H) contains 6.022 × 10²³ hydrogen atoms.

• 1 mole of hydrogen molecules (H₂) contains 6.022 × 10²³ hydrogen molecules.

The word ‘mole’ is derived from the Latin word ‘moles’ which means ‘heap’ or ‘pile’. It was first used by the German chemist Wilhelm Ostwald in 1896. It was accepted universally much later, in 1967, as a way of indicating the number of atoms or molecules in a sample.

Thus, mole can be defined as a unit of measurement used for determining the number of atoms or molecules or ions in a given sample. It is also used to express the amount of reactants and products in a chemical reaction.

The Mole Concept: A Brief Overview

Consider the formation of water by the combination of hydrogen and oxygen.

2H₂ + O₂ → 2H₂O

This reaction implies that 2 moles of hydrogen molecules combine with 1 mole oxygen molecules to form 2 moles of water molecules.

When carbon (C) reacts with oxygen (O), carbon dioxide is produced. Can you write the chemical equation for the same?

The chemical equation for the reaction is:

In this reaction, one atom of carbon combines with one molecule (or two atoms) of oxygen to form one molecule of carbon dioxide. We can also say that in this chemical reaction, 12 u of carbon combines with 32 u of oxygen to give 44 u of carbon dioxide. Clearly, we can represent the quantities of substances in terms of their masses. However, a chemical equation only indicates the numbers of atoms or molecules taking part in the chemical reaction. Therefore, it is easier to represent the quantities of substances involved in a chemical reaction by the numbers of their atoms or molecules rather than their masses. In order to do the same, the concept of mole is used.

Mole Concept 

In 1909, the French physicist Jean Perrin found that one gram atom of any element contains the same number of atoms and one gram molecule of any substance contains the same number of molecules, which is equal to 6.022 × 10²³.

He proposed naming this number in honour of the Italian physicist Amedeo Avogadro. Hence, 6.022 × 10²³ is known as Avogadro’s number (or Avogadro’s constant) and the amount of a substance containing 6.022 × 10²³ atoms/molecules/ions is called a mole.

Mole is a counting unit in chemistry as it is used to express large numbers of atoms or molecules.One mole of any substance can be defined as the amount of a substance that contains as many particles (atoms, molecules or ions) as there are atoms in 12 g of carbon-12 isotope. So, 

1 mole of oxygen atoms (O) = 6.022 × 10²³ oxygen atoms

1 mole of oxygen molecules (O₂) = 6.022 × 10²³ oxygen molecules

Jean Perrin (1870-1942) was a French physicist. He was awarded the Nobel Prize in Physics in 1962, for his contribution to the establishment of the atomic nature of matter, while conducting research on Brownian motion. In 1895, he showed that cathode rays are made up of negatively charged particles. He is also known for explaining the origin of solar energy through thermonuclear reaction of hydrogen (nuclear fusion) in the sun. In 1908, he studied Brownian motion using an ultramicroscope and gave experimental confirmation to the hypothesis that the random motion of suspended particles is due to the particulate nature of matter and the inter-particle interactions. He is also credited with estimating the size of a water molecule and the number of molecules of water present in a given amount of water.

 

Amedeo Avogadro (1776-1856) was an Italian lawyer; however, his interest in the natural sciences led him to study physics and mathematics privately. In 1809, while teaching the natural sciences in Vercelli, he hypothesized that under the same conditions of temperature and pressure, equal volumes of gases contain the same number of particles. This hypothesis later came to be known as Avogadro’s law.
 

 

Mole Concept 

The molar mass of a substance can be defined as the mass of one mole of a substance in grams. It is numerically equal to atomic/molecular/formula unit mass in u.

The mass of one atom is called atomic mass and its unit is unified mass (u), while the mass of one mole of atoms is called molar mass of atoms and its unit is gram (g). Molar mass of atoms is also called gram atomic mass.

For example, the atomic mass of nitrogen (N) is 14 u, while its gram atomic mass is 14 g. So, while 14 u of nitrogen contains only 1 atom of nitrogen, 14 g of nitrogen contains 1 mole of nitrogen atoms, i.e., 6.022 × 10²³ nitrogen atoms.

The mass of one molecule is called molecular mass and its unit is unified mass (u), while the mass of one mole of molecules is called molecular mass and its unit is gram (g). When molecular mass is expressed in grams, it is called gram molecular mass or gram molecule.

For example, the molecular mass of oxygen (O₂) is 32 u, while its gram molecular mass is 32 g. So, while 32 u of oxygen contains only 1 molecule of oxygen, 32 g of oxygen contains 1 mole of oxygen molecules, i.e., 6.022 × 10²³ oxygen molecules.

The volume of one mole of any substance is called its molar volume.

The molar volume of a gas at STP is numerically equal to 22.4 L.

Mole Concept 

 

Avogadro’s Law

In 1811, Avogadro hypothesized that under the same conditions of temperature and pressure, equal volumes of all gases contain equal number of moles. For example, at the same temperature and pressure, the two gases, oxygen and nitrogen possessing the same volume contain same number of molecules. This hypothesis is named Avogadro’s law. The mole concept provides the following information.

• If one mole of a substance (atoms, molecules or ions) is present, then the number of elementary particles present in that substance is equal to 6.022 × 10²³.

• The mass of one mole of a substance (atoms, molecules or ions) is equal to its molar mass.

• While carrying out reactions, scientists require the number of atoms and molecules. This requirement is fulfilled by the use of the mole concept as follows:

1 mole = 6.022 × 10²³ = Relative mass in grams.

Avogadro’s Law

Relationship between Mole, Avogadro’s Number and Mass

The relationship between mole, Avogadro’s number and mass is summarized in the given figure.

Gay-Lussac’s Law

This law gives the relationship between pressure and temperature. According to this law, at constant volume, the pressure of a fixed amount of a gas is directly proportional to the temperature. It can be represented mathematically as,

Mathematically,

p ∝T

= constant = k₃

If at constant volume,

p₁ = Pressure of a gas at T₁

p₂ = Pressure of the same gas at T₂

Then,

Gay-Lussac’s Law

 

Stoichiometric Calculations in Balanced Chemical Equations

• An example of a balanced chemical equation is given below.

From the above balanced chemical equation, the following information is obtained:

• One mole of C₃H₈(g) reacts with five moles of O₂(g) to give three moles of CO₂(g) and four moles of H₂O(l).

• One molecule of C₃H₈(g) reacts with five molecules of O₂(g) to give three molecules of CO₂(g) and four molecules of H₂O(l).

• 44 g of C₃H₈(g) reacts with (5 × 32 = 160) g of O₂(g) to give (3 × 44 = 132) g of CO₂(g) and (4 × 18 = 72) g of H₂O(l).

• 22.4 L of C₃H₈(g) reacts with (5 × 22.4 = 112) L of O₂(g) to give (3 × 22.4 = 67.2) L of CO₂(g) and (4 × 22.4 = 89.6) L of H₂O(l).

• Limiting reagent or limiting reactant:

• Reactant which gets completely consumed when a reaction goes to completion

• So called because its concentration limits the amount of the product formed

 

• Reactions in solutions:

Ways for expressing the concentration of a solution −

• Mass per cent or weight per cent (w/w%)

Mass per cent 

• Mole fraction:

If a substance ‘A’ dissolves in a substance ‘B’, then mole fraction of A 

Mole fraction of B 

n_A − Number of moles of A

n_B − Number of moles of B

• Molarity:

Number of moles of solute in 1 L of solution

Molarity (M) =

For a given solution, the molarity equation is as follows:

M₁V₁ = M₂V₂

M₁ = Molarity of a solution when its volume is V₁

M₂ = Molarity of the same solution when its volume is V₂

• Molality:

Number of moles of solute present in 1 kg of solvent

Molality (m) = 

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