Atoms Molecules and Chemical Arithmetic Nios Chapter- 1st

 Chemistry is the study of matter and the changes it undergoes. Chemistry is often called the central science, because a basic knowledge of chemistry is essential for the study of biology, physics, geology, ecology, and many other subjects.   

Although chemistry is an ancient science, its modern foundation was laid in the nineteenth century, when intellectual and technological advances enabled scientists to break down substances into ever smaller components and consequently to explain many of their physical and chemical characteristics.

Chemistry plays a pivotal role in many areas of science and technology e.g. in health, medicine, energy and environment, food, agriculture and new materails.

As you are aware, atoms and molecules are so small that we cannot see them with our naked eyes or even with the help of a microscope. Any sample of matter which can be studied consists of extremely large number of atoms or molecules. In chemical reactions, atoms or molecules combine with one another in a definite number ratio. Therefore, it would be pertinent if we could specify the total number of atoms or molecules in a given sample of a substance. We use many number units in our daily life. For example, we express the number of bananas or eggs in terms of ‘dozen’. In chemistry we use a number unit called mole which is very large.

With the help of mole concept it is possible to take a desired number of atoms/ molecules by weighing. Now, in order to study chemical compounds and reactions in the laboratory, it is necessary to have adequate knowledge of the quantitative relationship among the amounts of the reacting substances that take part and

products formed in the chemical reaction. This relationship is knows as stoichiometry. Stoichiometry (derived from the Greek Stoicheion = element and metron = measure) is the term we use to refer to all the quntatitative aspects of chemical compounds and reactions. In the present lesson, you will see how chemical formulae are determined and how chemical equations prove useful in predicting the proper amounts of the reactants that must be mixed to carry out a complete reaction. In other words we can take reactants for a reaction in such a way that none of the reacting substances is in excess. This aspect is very vital in chemistry and has wide application in industries.


After seeing this video you will be able to:

  •  Explain the scope of chemistry;
  •  Explain the atomic theory of matter;
  • State the laws of chemical combinaton;
  •  Explain Dalton’s atomic theory;
  • Define the terms element, atoms and molecules.
  • State the need of SI units;
  •  list base SI units;
  •  Explain the relationship between mass and number of particles;
  • Define Avogadro’s constant and state its significance;
  • Calculate the molar mass of different elements and compounds;
  • Define molar volume of gases at STP.
  •  Define empirical and molecular formulae;
  • Differentiate between empirical and molecular formulae;
  • Calculate precentage by mass of an element in a compound and also work out empirical formula from the percentage composition;
  • Establish relationship between mole, mass and volume;
  •  Calculate the amount of substances consumed or formed in a chemical reaction using a balanced equation and mole concept, and z explain the role of limiting reagent in limiting the amount of the products formed.

Atoms Molecules and Chemical Arithmetic Nios Chapter- 1st ( Part- 1st )


Chemistry plays an important role in all aspects of our life. Let us discuss role of chemistry in some such areas.

Health and Medicine

Three major advances in this century have enabled us to prevent and treat diseases. Public health measures establishing sanitation systems to protect vast numbers of people from infectious diseases; surgery with anesthesia, enabling physicians to cure potentially fatal conditions, such as an inflamed appendix; and the introduction of vaccines and antibiotics that made it possible to prevent diseases spread by microbes. Gene therapy promises to be the fourth revolution in medicine. (A gene is the basic unit of inheritance.) Several thousand known conditions, including cystic fibrosis and hemophilia, are carried by inborn damage to a single gene. Many other ailments, such as cancer, heart disease, AIDS, and arthritis, result to an extent from impairment of one or more genes involved in the body’s defenses. In gene therapy, a selected healthy gene is delivered to a patient’s cell to cure or ease such disorders. To carry out such a procedure, a doctor must have a sound knowledge of the chemical properties of the molecular components involved.

Chemists in the pharmaceutical industry are researching potent drugs with few or no side effects to treat cancer, AIDS, and many other diseases as well as drugs to increase the number of successful organ transplants. On a broader scale, improved understanding of the mechanism of ageing will lead to a longer and healthier lifespan for the world’s population.

(Part 2nd)


There was tremendous progress in Chemical Sciences after 18th century. It arose out of an interest in the nature of heat and the way things burn. Major progress was made through the careful use of chemical balance to determine the change in mass that occurs in chemical reactions. The great French Chemist Antoine Lavoisier used the balance to study chemical reactions. He heated mercury in a sealed flask that contained air. After several days, a red substance mercury (II) oxide was produced. The gas remaining in the flask was reduced in mass. The remaining gas was neither able to support combustion nor life. The remaining gas in the flask was identified as nitrogen. The gas which combined with mercury was oxygen. Further he carefully performed the experiment by

taking a weighed quantity of mercury (II) oxide. After strong heating, he found that mercury (II) oxide, red in colour, was decomposed into mercury and oxygen. He weighed both mercury and oxygen and found that their combined mass was equal to that of the mercury (II) oxide taken. Lavoisier finally came to the conclusion that in every chemical reaction, total masses of all the reactants is equal to the masses of all the products. This law is known as the law of conservation of mass.

There was rapid progress in science after chemists began accurate determination of masses of reactants and products. French chemist Claude Berthollet and Joseph Proust worked on the ratio (by mass) of two elements which combine to form a compound. Through a careful work, Proust demonstrated the fundamental law of definite or constant proportions in 1808. In a given chemical compound, the proportions by mass of the elements that compose it are fixed, independent of the origin of the compound or its mode of preparation.

In pure water, for instance, the ratio of mass of hydrogen to the mass of oxygen is always 1:8 irrespective of the source of water. In other words, pure water contains 11.11% of hydrogen and 88.89% of oxygen by mass whether water is obtained from well, river or from a pond. Thus, if 9.0 g of water are decomposed, 1.0 g of hydrogen and 8.0 g of oxygen are always obtained. Furthermore, if 3.0 g of hydrogen are mixed with 8.0 g of oxygen and the mixture is ignited, 9.0 g of water are formed and 2.0 g of hydrogen remains unreacted. Similarly sodium chloride contains 60.66% of chlorine and 39.34% of sodium by mass whether we obtained it from salt mines or by crytallising it from water of ocean or inland salt seas or synthesizing it from its elements sodium and chlorine. Of course, the key word in this sentence is ‘pure’. Reproducible experimental results are highlights of scientific thoughts. In fact modern science is based on experimental findings. Reproducible results indirectly hint for a truth which is hidden. Scientists always worked for findings this truth and in this manner many theories and laws were discovered. This search for truth plays an important role in the development of science.

The Dalton’s atomic theory not only explained the laws of conservations of mass and law of constant proportions but also predicted the new ones. He deduced the law of multiple proportions on the basis of his theory. The law states that when two elements form more than one compound, the masses of one element in these compound for a fixed mass of the other element are in the ratio of small whole numbers. For example, carbon and oxygen form two compounds: carbon monoxide and carbon dioxide. Carbon monoxide contains 1.3321 g of oxygen for each 1.0000 g of carbon, whereas carbon dioxide contains 2.6642 g of oxygen for 1.0000 g of carbon. In other words, carbon dioxide contains twice the mass of oxygen as is contained in carbon monoxide.

(2.6642 g = 2 × 1.3321 g) for a given mass of carbon. Atomic theory explains this by saying that carbon dioxide contains twice as many oxygen atoms for a given number of carbon atoms as does carbon monoxide. The deduction of law of multiple proportions from atomic theory was important in convincing chemists of the validity of the theory.

(Part 3rd)


As we learnt earlier, Lavosier laid the experimental foundation of modern chemistry. But the British chemist John Dalton (1766–1844) provided the basic theory; all matter – whether element, compound, or mixture –is composed of small particles called atoms. The postulates, or basic assumptions of Dalton’s theory are presented below in this section.

Postulates of Dalton’s Atomic Theory

In 1803, Dalton published a new system of chemical philosophy in which the following statements comprise the atomic theory of matter:

  • Matter consists of indivisible atoms.
  •   All the atoms of a given chemical element are identical in mass and in all other properties.
  •  Different chemical elements have different kinds of atoms and in particular such atoms have different masses.
  •  Atoms are indestructible and retain their identity in chemical reactions.
  • The formation of a compound from its elements occurs through the combination of atoms of unlike elements in small whole number ratio.

Dalton’s fourth postulate is clearly related to the law of conservation of mass. Every atom of an element has a definite mass. Also in a chemical reaction there is rearrangement of atoms.Therefore after the reaction, mass of the product should remain the same. The fifth postulate is an attempt to explain the law of definite proportions. A compound is a type of matter containing the atoms of two or more elements in small whole number ratio. Because the atoms have definite mass, the compound must have the elements in definite proportions by mass.

The Dalton’s atomic theory not only explained the laws of conservations of mass and law of constant proportions but also predicted the new ones. He deduced the law of multiple proportions on the basis of his theory. The law states that when two elements form more than one compound, the masses of one element in these compound for a fixed mass of the other element are in the ratio of small whole numbers. For example, carbon and oxygen form two compounds: Carbon monoxide and carbon dioxide. Carbon monoxide contains 1.3321 g of oxygen for each 1.000g of carbon, whereas carbon dioxide contains 2.6642 g of oxygen for 1.0000 g of carbon. In other words, carbon dioxide contains twice the mass of oxygen as is contained in carbon monoxide (2.6642 g = 2 × 1.3321 g) for a given mass of carbon. Atomic theory explains this by saying that carbon dioxide contains twice as many oxygen atoms for a given number of carbon atoms as does carbon monoxide. The deduction of law of multiple proportions from atomic theory was important in convincing chemists of the validity of the theory.

(Part 4th )

What is an Atom?

As you have just seen in the previous section that an atom is the smallest particle of an element that retains its (elements) chemical properties. An atom of one element is different in size and mass from the atoms of the other elements. These atoms were considered ‘indivisible’ by Indian and Greek ‘Philosophers’ in the beginning and the name ‘atom’ was given as mentioned earlier. Today, we know that atoms are not indivisible. They can be broken down into still smaller particles although they lose their chemical identity in this process. But inspite of all these developments atom still remains a building block of matter.


A molecule is an aggregate of at least two atoms in a definite arrangement held together by chemical forces (also called chemical bonds). It is smallest particle of matter, an element or a compound, which can exist independently. A molecule may contain atoms of the same element or atoms of two or more elements joined in a fixed ratio, in accordance with the law of definite proportions stated. Thus, a molecule is not necessarily a compound, which, by definition, is made up of two or more elements. Hydrogen gas, for example, is a pure element, but it consists of molecules made up of two H atoms each. Water, on the other hand, is a molecular compound that contains hydrogen and oxygen in a ratio of two H atoms and one O atom. Like atoms, molecules are electrically neutral.

The hydrogen molecule, symbolized as H2, is called a diatomic molecule because it contains only two atoms. Other elements that normally exist as diatomic molecules are nitrogen (N2) and oxygen (O2), as well as the Group 17 elements-fluorine (F2), chlorine (Cl2), bromine (Br2), and iodine (I2). Of course, a diatomic molecule can contain atoms of different elements. Examples are hydrogen chloride (HCl) and carbon monoxide (CO).

The vast majority of molecules contain more than two atoms. They can be atoms of the same element, as in ozone (O3), which is made up of three atoms of oxygen, or they can be combinations of two or more different elements. Molecules containing more than two atoms are called polyatomic molecules. Like ozone, water (H2O) and ammonia (NH3) are polyatomic molecules.


Substances can be either elements or compounds. An element is a substance that cannot be separated into simpler substances by chemical means. To date, 118 elements have been positively identified. Eighty-three of them occur naturally on Earth. The others have been created by scientists via nuclear processes.

(Part 5th )


Measurement is needed in every walk of life. As you know that for every measurement a ‘unit’ or a ‘reference standard’ is required. In different countries, different systems of units gradually developed. This created difficulties whenever people of one country had to deal with those of another country. Since scientists had to often use each other’s data, they faced a lot of difficulties. For a practical use, data had to be first converted into local units and then only it could be used.

For measuring very large or very small quantities, multiples or sub-multiples of these units are used. Each one of them is denoted by a symbol which is prefixed to the symbol of the unit. For example, to measure long distances we use the unit kilometre which is a multiple of metre, the base unit of length. Here kilo is the prefix used for the multiple 103. Its symbol is k which is prefixed to the symbol of metre, m . Thus the symbol of kilometre is km and

1 km = 1.0 × 103 m = 1000 m


(Part 6th)

Suppose you want to purchase 500 screws. How, do you think, the shopkeeper would give you the desired quantity? By counting the screws individually? No, he would give the screws by weight because it will take a lot of time to count them. If each screw weighs 0.8 g, he would weigh 400 g screws because it is the mass of 500 screws (0.8 × 500 = 400 g). You will be surprised to note that the Reserve Bank of India gives the desired number of coins by weight and not by counting.This process of counting by weighing becomes more and more labour saving as the number of items to be counted becomes large. We can carry out the reverse process also. Suppose we take 5000 very tiny springs (used in watches) and weigh them. If the mass of these springs is found to be 1.5 g, we can conclude that mass of each spring is 1.5 ÷ 5000 = 3 × 10 4 g.


Mass of an atom or a molecule is an important property. However, while discussing the quantitative aspects of a chemical reaction, the number of reacting atoms or molecules is more significant than their masses.

A mole is the amount of a substance that contains as many elementary entities (atoms, molecules or other particles) as there are atoms in exactly 0.012 kg or 12 g of the carbon-12 isotope.

The term mole has been derived from the Latin word ‘moles’ which means a ‘heap’ or a ‘pile’. It was first used by the famous chemist Wilhelm Ostwald more than a hundred years ago.


In the previous section we have learned that a mole of a substance is that amount which contains as many elementary entities as there are atoms in exactly 0.012 kilogram or 12 gram of the carbon-12 isotope. This definition gives us a method by which we can find out the amount of a substance (in moles) if we know the number of elementary entities present in it or vice versa. Now the question arises

how many atoms are there in exactly 12 g of carbon-12. This number is determined experimentally and its currently accepted value is 6.022045 × 1023 . Thus 1 mol = 6.022045 × 10 23entities or particles, or atoms or molecules.

For all practical purposes this number is . rounded off to 6.022 × 1023 .

The basic idea of such a number was first conceived by an Italian scientist Amedeo Avogadro. But, he never determined this number. It was determinned later and is known as Avogadro’s constant in his honour.

Significance of Avogadro’s Constant

You know that 0.012 kg or 12 g of carbon –12 contains its one mole of carbon atoms. A mole may be defined as the amount of a substance that contains 6.022 × 1023 elementary entities like atoms, molecules or other particles. When we say one mole of carbon –12, we mean 6.022 × 1023 atoms of carbon –12 whose mass is exactly 12 g. This mass is called the molar mass of carbon-12. The molar mass is defined as the mass ( in grams) of 1 mole of a substance. Similarly, a mole of any substance would contain 6.022 × 1023 particles or elementary entities. The nature of elementary entity, however,depends upon the nature of the substance as given below :

Formula unit of a compound contains as many atoms or ions of different types as is given by its chemical formula. The concept is applicable to all types of compounds. The following examples would clarify the concept.


You know that 1 mol = 6.022 × 1023  elementary entities

and                        Molar mass = Mass of 1 mole of substance

                                                        = Mass of 6.022 × 1023  elementary entities.

As discussed earlier the elementary entity can be an atom, a molecule, an ion or a formula unit. As far as mole – number relationship is concerned it is clear that one mole of any substance would contain 6.022 × 1023 particles (elementary entities). For obtaining the molar mass, i.e., mole-mass relationship we have to use atomic mass scale.

Atomic Mass Unit.

By inernational agreement, a unit of mass to specify the atomic and molecular masses has been defined. This unit is called atomic mass unit and its symbol is ‘amu’. The mass of one C-12 atom, is taken as exactly 12 amu. Thus, C-12 atom serves as the standard. The Atomic mass unit is defined as a mass exactly equal to the 1/12th of the mass of one carbon-12 atom.

Atomic mass unit is also called unified atomic mass unit whose symbol is ‘u’. Another name of atomic mass unit is dalton (symbol Da). The latter is mainly used in biological sciences.

Relative Atomic and Molecular Masses

You are aware that atomic mass scale is a relative scale with C-12 atom (also written as 12 C) chosen as the standard. Its mass is taken as exactly 12. Relative masses of atoms and molecules are the number of times each atom or molecules.

is heavier than 1/12 th  of the mass of one C-12 atom. Often, we deal with elements and compounds containing isotopes of different elements. Therefore, we prefer to use average masses of atoms and molecules. Thus

Experiments show that one O-16 atom is 1.333 times as heavy as one C-12 atom. Thus

Relative atomic mass of O-16 = 1.333 × 12 = 15.996 ~ 16.0

Atomic, Molecular and Formula Masses

From the definition of atomic mass unit, we can calculate the atomic masses. Let us again take the example of oxygen-16 whose relative atomic mass is 16. By definition:

Mass of one O-16 atom = 16 amu

Or                     Atomic mass of O-16 = 16 amu.

From this example we can see that numerical value of the relative atomic mass and atomic mass is the same. Only, the former has no unit while the latter has the unit amu.

Molecular and formula masses can be obtained by adding the atomic or ionic masses of all the constituent atoms or ions of the molecule or formula unit respectively. Let us understand these calculations with the help of following examples.

Molar Masses

We know that molar mass is the mass of 1 mol of the substance. Also, 1 mol of any substance is the collection of its 6.022 × 1023  elementary entities. Thus

                                   Molar mass = Mass of 6.022 × 1023  elementary entities.

(i) Molar mass of an element

You know that the relative atomic mass of carbon–12 is 12. A 12g sample of it would contain 6.022 × 1023  atoms. Hence the molar mass of C-12 is 12 g mol– 1. For getting the molar masses of other elements we can use their relative atomic masses.

Since the relative atomic mass of oxygen -16 is 16, a 16 g sample of it would contain 6.022 × 1023oxygen atoms and would constitute its one mole. Thus, the molar mass of O–16 is 16 g mol–1. Relative atomic masses of some common elements have been listed in Table 1.4

(ii) Molar mass of a molecular substance

The elementary entity in case of a molecular substance is the molecule. Hence, molar mass of such a substance would be the mass of its 6.022 × 1023 molecules, which can be obtained from its relative molecular mass or by multiplying the molar mass of each element by the number of its moles present in one mole of the substance and then adding them.

Let us take the example of water, H2O. Its relative molecular mass is 18. Therefore, 18 g of it would contain 6.022 × 1023 molecules. Hence, its molar mass is 18 g mol–1 . Alternately we can calculate it as :

Molar mass of water, H2O = (2 × molar mass of H) + (molar mass of O)

                                     = (2 × 1 g mol–1) + (16 g mol–1)

                                                    = 18 g mol–1

(iii) Molar masses of ionic compounds

Molar mass of an ionic compound is the mass of its 6.022 × 1023 formula units. It can be obtained by adding the molar masses of ions present in the formula unit of the substance. In case of NaCl it is calculated as

Molar mass of NaCl = molar mass of Na+ + molar mass of Cl–

                                 = (23 g mol–1) + (35.5 g mol–1)

                                                 = 58.5 g mol–1

Let us take some more examples of ionic compounds and calculate their molar masses.


( Part 7th)

Mass, molar mass and number of moles of a substance are inter-related quantities. We know that :

                                        Molar mass (M) = Mass of one mole of the substance.

Molar mass of water is 18 g mol-1 . If we have 18 g of water, we have 1mol of it. Suppose we have 36 g water (18 × 2), we have 2 mol of it. In general in a sample of water of mass (n × 18) g, the number of moles of water would be n. We may generalize the relation as

These relations are useful in calculations involving moles of substances.


Molar volume is the volume of one mole of a substance. It depends upon temperature and pressure. It is related to the density, by the relation.

In case of gases, we use their volumes at standard temperature and pressure (STP). For this purpose 0 0C or 273 K temperature is taken as the standard temperature and 1bar pressure is taken as the standard pressure. At STP, the molar volume of an ideal gas is 22.7 litre*. You will study that gases do not behave ideally and therefore their molar volume is not exactly 22.7 L. However, it is very close to 22.7 L and for all practical purposes we take the molar volume of all gases at STP as 22.7 L mol-1.


In your previous classes, you have studied how to write chemical formula of a sustance. For example, water is represented by H2 O, carbon dioxide is represented

by CO2 , methane is represented by CH4, dinitrogen penta oxide is represented by N2 O5 , and so on. You are aware, formula for a molecule uses a symbol and subscript number to indicate the number of each kind of atoms present in the molcule (subscript 1 is always omitted). Such a formula is called molecular formula as it represents a molecule of a substance. A molecule of water consists of two hydrogen atoms and one oxygen atom. So its molecular formula is written as H2 O. Thus a molecular formula shows the actual number of atoms of different elements in a molecule of a compound.


You have studied that a reaction can be represented in the form of a chemical equation. A balanced chemical equation carries a wealth of information qualitative as well as quantitative. Let us consider the following equation and learn what all information it carries

4Fe(s) + 3O2 (g) → 2Fe2 O3 (s)

(1) Qualitative Information

Qualitatively the equation (2.1) tells that iron reacts with oxygen to form iron oxide.

2. Quantitative Information Quantitatively a balanced chemical equation specifies numerical relationship among the quantities of its reactants and products. These relationships can be expressed in terms of :

(i) Microscopic quantities, namely, atoms, molecules and formula units.

(ii) Macroscopic quantities, namely, moles, masses and volumes (in case of gaseous substances) of reactants and products.

Now let us again take the reaction (1.1) given earlier and get the quantitative information out of it.

Jan Feb Examination Question paper Solution

(part 8th )
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