Laws of Chemical Combinations XI

The combination of elements to form compounds is governed by the following five basic laws.
Laws of conservation of mass states that matter can neither be created nor destroyed.
This law was put forth by Antoin Lavoisier in 1789. He performed careful experimental studies for combustion reactions for reaching to the above conclusion. This law formed the basis for several later developments in chemistry. In fact, this was the result of exact measurement of masses of reactants and products, and carefully planned experiments performed by Lavoisier.
Lavoisier stated that “during any physical or chemical change the total mass of the products remains equal to the total mass of the reactants”. He showed that when mercuric oxide was heated the total mass of mercury and oxygen produced was equal to the total mass of mercuric oxide.
Can you think of any exception to this law?
Illustration 1: When 20 g of NaH2CO3 is heated, 12.62 g of Na2CO3 and 5.24g of CO2 is produced. How many grammes of is produced?
Solution: Total mass of heated = 20 gms
Total mass Na2CO3 produced = 12.62 gms
Total mass of CO2 produced = 5.24 gms
Mass of H2O produced = 20 – 12.62 –5.24 = 2.14 gms
Law of the definite proportion of was given by, a French chemist, Joseph Proust. He stated that a given compound always contains exactly the same proportion of elements by weight.
Irrespective of the source, a given compound always contains same elements in the same proportion. The validity of this law has been confirmed by various experiments. It is sometimes also referred to as Law of definite composition.
This law implies that irrespective of how a compound is prepared or from where the compound originates, it is always made up of the same elements combined in the same proportion by the weight.
For example, if water is taken from difference sources, such as rivers, oceans, wells etc. they all contain hydrogen and oxygen combined in the same proportion by weight.
Illustration 2: When 50 g of ammonia is heated it gives 41.18 g of Nitrogen. When 10 g. of Nitrogen is combined with the required amount of hydrogen it produces 12.14 g show that the given data follows the law of constant compositions.

This law which was proposed by Gay-Lussac states that the volumes of gaseous reactants reacted and the volumes of gaseous products formed, all measured at the same temperature and pressure bear a simple ratio.
For eg in the reaction involved in Haber’s Process (Nitrogen and hydrogen gases react to form ammonia)

It is observed that the ratio the Volumes of and reacted and volume of produced is equal to 1: 3: 2 which is a simple ratio.
This law is applicable only for gaseous reactions and should not be used for non-gaseous reactants and products.
Analysis of water shows that it contains 88.89% oxygen and 11.19% of hydrogen by mass. Thus the ratio of masses of hydrogen and oxygen in water is 11.19: 88.89 or 1: 8. Moreover, the ratio of number of hydrogen and oxygen atoms in water molecule can be shown to be 1: 2
Therefore oxygen is 16 times heavier than hydrogen. Therefore relative atomic mass of oxygen is 16 units if we take the mass of hydrogen atom as 1 unit.
In 1961 International Union of Pure and Applied Chemists (IUPAC) selected the most stable isotope of carbon, C-12 as the standard for comparison of atomic masses of elements. The mass of C-12 is taken as 12 atomic mass unit.
The scale in which the relative atomic masses of different elements is expressed is called atomic mass unit or amu.
Stanislao Cannizzaro (1826-1910), the pioneer in this field, adopted the hydrogen atom as a standard of mass and set its atomic weight at 2. Others accepted the idea of using a specific atom as a standard of mass but preferred a more massive standard in order to reduce experimental error.
As early as 1850, chemists used a unit of atomic weight based on saying the atomic weight of oxygen was 16. Oxygen was chosen because it forms chemical compounds with many other elements, simplifying the determination of their atomic weight.
Sixteen was chosen because it was a lowest whole number that could be assigned to oxygen and still have an atomic weight of hydrogen that was not less than 1.
The 0 =16 scale was formalised when a committee appointed by the Deutsche Chemische Gesellschaft called, in March 1899, for the formation of an international commission on atomic weights. A commission of 57 members was formed. Since the commission carried on its business by correspondence, the size proved unwieldy, and the Gesellschaft suggested a smaller committee be elected. A 3-member International Committee of Atomic Weights was duly elected, and in 1903 issued its first report, using the 0 =16 scale.

Gram molecular mass
Molecular mass expressed in grams is termed as Gram
Molecular Mass. We shall observe later that this is the mass of one mole of the molecules.
For example, One gram molecule of water will have a weight equal to 18 grams which are its gram molecular mass.
Formula mass: For substances which are ionic the formula does not represent a molecule (molecules are formed only with covalent bond) the mass based on the formula would be called as formula mass and not molecular mass.
For example, The formula mass of NaCl is 23+35.5=58.5
One mole is an amount of substance containing Avogadro’s number of particles. Avogadro’s number is equal to 602,214,199,000,000,000,000,000 or more simply, 6.02214199 × 1023.
Some people think that Amedeo Avogadro (1776-1856) determined the number of particles in a mole and that is why the quantity is known as Avogadro number. In reality, Avogadro built a theoretical foundation for determining accurate atomic and molecular masses. The concept of a mole did not even exist in Avogadro’s time.
Much of Avogadro’s work was based on that of Joseph-Louis Gay-Lussac (1778-1850).Gay-Lussac developed the law of combining volumes that states: “In any chemical reaction involving gaseous substances the volumes of the various gases reacting or produced are in the ratios of small whole numbers”. (Masterton and Slowinski, 1977) Avogadro reinterpreted Gay-Lussac’s findings and proposed in 1811 that (1) some molecules were diatomic and (2) “equal volumes of all gases at the same temperature contain the same number of molecules”. The second proposal is what we refer to as Avogadro’s hypothesis.
The hypothesis provided a simple method of determining relative molecular weights because equal volumes of two different gases at the same temperature and pressure contained the same number of particles, so the ratio of the masses of the gas samples must also be that of their particle masses. Unfortunately, Avogadro’s hypothesis was largely ignored until Stanislao Cannizzaro (1826-1910) advocated using it to calculate relative atomic masses or atomic weights. Soon after the International Chemical Congress Karlsruhe in 1860, Cannizzaro’s proposal was accepted and a scale of atomic weights was established.
To understand how Avogadro’s hypothesis can be used to determine relative atomic and molecular masses, visualize two identical boxes with oranges in one and grapes in the other. The exact number of fruit in each box is not known, but you believe that there are equal numbers of fruit in each box (Avogadro’s hypothesis). After subtracting the masses of the boxes, you have the masses of each fruit sample and can determine the mass ratio between the oranges and the grapes. By assuming that there are equal numbers of fruits in each box, you then know the average mass ratio between a grape and an orange, so in effect, you have calculated their relative masses (atomic masses). If you chose either the grape or orange as a standard, you could eventually determine a scale of relative masses for all fruit.

So far, we were dealing with the number of entities present in a given sample. But many a time the information regarding the percentage of a particular element present in a compound is required. Suppose an unknown or new compound is given to you, the first question you would ask is: what is its formula or what are its constituents and in what ratio are they present in the given compound? For known compounds also, such information provides a check whether the given sample contains the same percentage of elements as is present in a pure sample. In other words, one can check the purity of a given sample by analysing this data.
Let us understand it by taking the example of water (H2O). Since water contains hydrogen and oxygen, the percentage composition of both these elements can be calculated as follows:





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Multiple Choice Questions

Solution: If 50g of gives 41.18g of, then the percentage of in ammonia is




If 10g of gives 12.41 gms. of Ammonia then the percentage of in ammonia is = 80.6% 82.36%.




This law of multiple proportions was proposed by Dalton in 1803. According to this law, if two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element, are in the ratio of small whole numbers.
For example, carbon and oxygen combine to form CO and CO2. In CO, 12 parts by mass of carbon combine with 16 parts by mass of oxygen while CO2 12 parts by mass of carbon combined with 32 parts by mass of oxygen. Therefore the ratio of the masses of oxygen that combines with a fixed mass of carbon is 16: 32 that is 1: 2.
Illustration 3: Sodium and oxygen combine to form two compounds of which one is Na2O. The percentage of sodium in the other compound is 59%. Find the formula of this compound.

Solution: Percentage of sodium in Na2O is =74.2% and percentage of oxygen is 25.8%. Percentage of sodium in other compound is 59% while that of oxygen is 41%. This means that in the first compound (Na2O) if we take 100 gm then 25.5 gm of oxygen will be present therefore the mass of sodium combining with 1g of oxygen would be

74.2/25.8= 2.87g.
Similarly, in the second compound, the mass of sodium combining with one gm of oxygen is 59/41 = 1.44g.The ratio of masses of sodium combining with the fixed mass of oxygen is
2.87 : 1.44 = 2 : 1. Therefore formula of the other compound is Na2O2.

This law of reciprocal proportions which was proposed by Ritcher (1792) states that “when two elements combine separately with fixed mass of the third element then the ratio of their masses in which they do so is either the same or some whole number multiple of the ratio in which they combine with each other”.
For example Carbon, Sulphur and Oxygen form, and. In 12 parts by mass of carbon combine with 32 parts by mass of oxygen while in 32 parts by mass of Sulphur combined with 32 parts by mass of oxygen. The ratio of masses of carbon and sulphur which combine with fixed mass of oxygen is 12: 32 or 3: 8.
In 12 parts by mass of carbon combines with 64 parts by mass of sulphur therefore 12: 64 i.e. 3: 16.
Therefore, the ratios are 3/8:3/16 or 2: 1
All the above laws about the relative weights of elements that are necessary to form compounds are valid only for compounds which have a definite formula. while most of the molecules have a fixed formula, not all will have a definite formula. Such compounds are termed as non-stoichiometric compounds which have varying composition depending upon the condition of preparation for eg. to.
Can you guess whether the physical & Chemical properties of & would be different or same?

Taking isotopes into account
The discovery of isotopes complicated the picture, In nature, pure oxygen is composed of a mixture of isotopes: some oxygen atoms are more massive than others.
This was no problem for the chemists, calculations as long as the relative abundance of the isotopes in their reagents remained constant, though it confirmed that oxygen’s atomic weight was the only one that in principle would be a whole number (hydrogen’s, for example, was 1.000 8).
Physicists, however, dealing with atoms and not reagents, required a unit that distinguished between isotopes. At least as early as 1927, physicists were using an atomic mass unit defined as equal to one-sixteenth of the mass of the oxygen-16 atom (the isotope of oxygen-containing a total of 16 protons and neutrons).
In 1919, isotopes of oxygen with mass 17 and 18 were discovered. Thus the two Amu's clearly diverged: one based on one-sixteenth of the average mass of the oxygen atoms in the chemist’s laboratory and the other based on one-sixteenth of the mass of an atom of a particular isotope of oxygen.
In 1956, Alfred Nier (at the bar in the Hotel Krsna Polski in Amsterdam) and independently A. Olander, both members of the Commission on Atomic Masses of the IUPAC, suggested to Josef Mattauch that the atomic weight scale is based on carbon-12. That would be okay with physicists since carbon-12 was already used as a standard in mass spectroscopy. The chemists resisted making the amu one-sixteenth the mass of an oxygen-16 atom; it would change their atomic weights by about 275 parts per million. Making the amu-twelfth the mass of a carbon-12 nucleus, however, would lead to only a 42 parts per million change, which seemed within reason.
Mattauch set to work enthusiastically proselytising the physicists, while E. Wichers lobbied the chemists. In the years 1959-1961 the chemists and physicists resolved to use the isotope carbon-12 as the standard, setting its atomic mass at 12.
Atomic mass Unit (AMU) = 1/12 the mass of a carbon – 12 atoms(in gm) =1.660539×10-24

Atomic mass of elements




Molecular mass is the sum of atomic masses of the elements present in a molecule. It is obtained by multiplying the atomic mass of each element by the number of its atoms and adding them together. For example, the molecular mass of methane which contains one carbon atom and four hydrogen atoms can be obtained as follows:
Molecular mass of methane,



Similarly, molecular mass H2O= 2 × atomic mass of hydrogen + 1 × atomic mass of oxygen = 2 (1.008) + 16.00 = 18.02 grams atomic mass
Atomic mass expressed in grammes is termed as Gram Atomic Mass. We shall observe later that this is the mass of one mole of the atoms. Gram atomic mass is the weight of 1 gram atom of the element.
For example, Atomic mass sodium is 23 am, therefore, 1 gram atom of sodium weighs 23g. Its gram atomic mass is 23 grams.
Mass of 1 atom of sodium is, grams =gms. Do not confuse it with gram atomic mass.

How big is a Mole?
One mole of marbles would cover the entire Earth (oceans included) for a depth of three miles.
One mole of $100 bills stacked one on top of another would reach from the Sun to Pluto and back 7.5 million times.
It would take light 9500 years to travel from the bottom to the top of a stack of 1 mole of $ 1 bills.
A mole (symbol mol) is defined as the amount of substance that contains as may atoms, molecules, ions, electrons or any other elementary entities as three are carbon atoms in exactly 12 gm of 12C. The number of atoms in 12 gm12Cis called Avogadro’s number (NA).





Methods of Calculations of Mole










If volume of gas is given along with its temperature (T) & pressure (P) then n =PV/RT where R = .0821 lit-atm/mol K & P is in atmosphere & T in Kelvin.
Do not use the expression for solids/liquids for eg. H2O at 100.
STP or NTP conditions Standard conditions means that temperature is C or 273K and pressure is one atmosphere or 760mm of Hg.
1 gm -atom is same as 1 mole of an atom & hence will have weight. equal to atomic weight. expressed in gms.
1 gm-molecule is same as 1 mole of the atom & hence will have weight. equal to molecule weight. expressed in gms.
1 gm- I on is same as 1 mole of an ion & hence will have weight. equal to ionic weight.
Now, can you differentiate b/w 1 gm - atom oxygen & 1gm-molecule oxygen.
Remember 1 gm of atom & 1 gm-atom are two different phases. Former is mentioning weight (equal to 1 gm) & latter is mentioning moles. (indirectly weight is equal to atomic weight in gms).
(1) “x g atom of nitrogen” = x moles of N atom = number of N atoms.
(2) “x g molecular of nitrogen” = x moles of N2 molecules

number of N atom


(3) “x g moles of nitrogen is an ambiguous statement “ It will be completed as x g moles of nitrogen atom or, x g moles of nitrogen molecule.