Atoms & Molecules  

ATOMS & MOLECULES The laws of chemical combination played a significant role in the development of Dalton’s atomic theory of matter. There are two important laws of chemical combination. (A) Law of conservation of mass  Ex. John Dalton calledthese particles by the name of atom. Theword ‘atom’ means ‘indivisible’ somethingwhich cannot be divided further. The particlesof matter (atoms or parmanu) normally existin a combined form. This combined form of atoms is now called ‘molecules’. All matter is made up of small particles called atoms and molecules. Different kinds of atoms and molecules have different properties due to which different kinds of matter also show different properties. Sol. Law of conservation of mass was given by Lavoisier in 1774. According to the law of conservation of mass : Matter is neither created nor destroyed in a chemical reaction. The substances which combine together in a chemical reaction are known as ‘reactants’ whereas the new substances formed as a result of chemical reaction are called ‘products’. The law of conservation of mass means that in a chemical reaction, the total mass of products is equal to the total mass of reactants. There is no change in mass during a chemical reaction. Lavoisier showed that when mercuric oxide was heated, it produced free mercury and oxygen. The sum of masses of mercury and oxygen was found to be equal to the mass of mercuric oxide Mercuric oxide  Mercury + Oxygen 100 g 92.6 g 7.4 g Mass of the reactant = 100 g Mass of the products = 92.6 + 7.4 g = 100.0 g = 100 g Since the total mass of the products formed is equal to the total mass of the reactants undergoing reaction, so the data is in agreement with low of conservation of mass. (B) Law of constant proportions This law was discovered by the french chemists, A. Lavoisier and Joseph Proust. A pure chemical compound always contains same elements combined together in same proportion by mass Ex. Pure water obtained from different sources such as river, well, spring, sea, etc., always contains hydrogen and oxygen combined together in the ratio 1 : 8 by mass. Limiting reagent : - In a reaction having more than one reactant we must identify the limiting reagent “Reagent which is finished early is known as limiting reagent ”. Example : - In Haber’s process to manufacture NH3, N2 + 3H2  2NH3 If we take 2 moles of N2 (56 grams) along with 3 moles of H2 (6 grams) we can see that only 1 moles of N2 (28 grams) is sufficient to react with 3 moles of H2. It means 1 mole N2 (28 grams) is in excess & H2 will be finished when reaction will be completed or H2 is limiting reagent.  Drawbacks of Dalton’s atomic theory     On the basis of laws of chemical combination John Dalton, an English school teacher in Manchester, proposed that behaviour of matter could be explained using an atomic theory. He published his work about atomic theory in 1808. The main points of Dalton’s atomic theory are:  All the matter is made up of very small particles called “atoms”.  Atoms cannot be divided.  Atoms can neither be created nor destroyed.  Atoms are of various kinds. There are as many kinds of atoms as are elements  All the atoms of a given element are identical in every respect, having the same mass, size and chemical properties.  Atoms of different elements differ in mass, size and chemical properties.  Chemical combination between two (or more) elements consists in the joining together of atoms of these elements to form molecules of compounds.  The “number” and “kind” of atoms in a given compound is fixed.  During chemical combination, atoms of different elements combine in small whole numbers to form compounds. Atoms of the same elements can combine in more than one ratio to form more than one compounds.      Some of the drawbacks of the Dalton’s atomic theory of matter are given below : One of the major drawbacks of Dalton’s atomic theory of matter is that atoms were thought to be indivisible (which cannot be divided). We now know that under special circumstances, atoms can be further divided into still smaller particles called electrons, protons and neutrons. So, atoms are themselves made up of three particles : electrons, protons and neutrons. Dalton’s atomic theory says that all the atoms of an element have exactly the same mass. it is, however, now known that atoms of the same element can have slightly different masses. Dalton’s atomic theory said that atoms of different elements have different masses. it is, however, now known that even atoms of different elements can have the same mass. It failed to explain how atoms of different elements differ from each other, i.e., it did not tell anything about internal structure of the atom. It could not explain how and why atoms of different elements combine with each other to form compound atoms or molecules. It failed to explain the nature of forces that hold together different atoms in a molecule. It did not make any distinction between ultimate particle of an element that takes part in reactions (atom) and ultimate particle that has independent existence (molecule). All the matter is made up of atoms. An atom is the smallest particle of an element that can take part in a chemical reaction. Atoms of most of the elements are very reactive and do not exist in the free state. They exist in combination with the atoms of the same element of another element. Atoms are very, very small in size. The size of an atom is indicated by its radius which is called ‘atomic radius’. Atomic radius is measured in ‘nanometres’. The symbol of a nanometre is nm. 1 1 nanometre = 9 metre 10 1 or 1 nm = m 109 or 1 nm = 10–9 m Hydrogen atom is the smallest atom of all. They cannot be viewed by simple optical microscopes. However, through modern techniques such as scanning tunneling microscope it is possible to produce magnified images of surfaces of elements showing atoms. In order to represent the elements, instead of using full lengthy names, scientists use abbreviated names. These abbreviated names of the elements are known as symbols. Thus, symbol may be defined as the abbreviation used for the name of an elements.  Dalton’s symbols of elements Dalton was the first scientist to use the symbols to represent elements in a short way. Element Dalton’s symbol Hydrogen letters or the first and the third letters of the name of the elements. The symbols of the following elements are the first letter of the name of that elements. Element Symbol Hydrogen Carbon H C Nitrogen Oxygen N O Fluorine F Phosphorus Sulphur P S Iodine I Some symbols derived from the first two letters of the names of the elements. Element Symbol Aluminium Barium Ba Lithium Li Beryllium Be Neon Ne Silicon Si Argon Iron Ar Calcium Ca Copper Nickel Ni Carbon Oxygen Phosphorus Sulphur Platinum Al Silver Gold Lead Mercury Dalton’s symbols for elements were difficult to draw and inconvenient to use. So, Dalton’s symbols are only of historical importance. They are not used at all.  Modern symbols of elements IUPAC (International Union of Pure and Applied Chemistry) approves names of elements. The symbols of elements are generally either the first letter or the first two Some symbols derived from the first and the third letters of the names of the elements Element Symbol Arsenic As Magnesium Mg Chlorine Cl Chromium Cr Manganese Mn Zinc Zn Rubidium Rb Some symbols derived from the latin names of the elements are given below Element Iron Gold Copper Potassium Sodium Silver Mercury Tin Lead Antimony Latin name Symbol Ferrum Aurum Cuprum Kalium Natrium Argentum Hydragyrum Stannum Plumbum Stibium Fe Au Cu K Na Ag Hg Sn Pb Sb  Atomic Mass = Atomic Mass of Some Elements Element 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Symbol for aluminum is Al and not AL Symbol for lead is Pb and not PB  Significance of the symbol of an element  Symbol represents name of the element.  Symbol represents one atom of the element.  Symbol also represents one mole of atoms of the element. That is, symbol also represents 6.022 × 1023 atoms of the elements  Symbol represents a definite mass of the element (equal to atomic mass expressed in grams)  Atoms are extremely small ; the heaviest atoms have masses of about 10–22 g. Even an ultramicrobalance cannot measure the mass of a single atom. However, relative masses of atoms of different elements can be determined. At first, the mass of the lightest atom, hydrogen.  In 1961, International Union of chemists selected the most stable isotope of carbon (C - 12 isotope) as standard for comparison the atomic masses of various elements. Atomic mass of an element tells us the number of times an atom of the element is heavier than of the mass of an atom of carbon - 12. Mass of 1 atom of the element 1 of the mass of an atom of carbon  12 12 The atomic mass of magnesium is 24 u which indicates that one atom of magnesium is 24 1 times heavier than of a carbon 12 atom. 12 Ex. It is important to note that the first letter of every chemical symbol is capital letter but, if the symbol consists of two letters, the second letter is not capital letter. Ex. Atomic mass of an element may be defined as the average relative mass of an atom of the element as compared with mass of an atom of carbon (C - 12 isotope) taken as 12 amu. Symbol Hydrogen Carbon Nitrogen Oxygen Sodium Magnesium Aluminium Phosphorus Sulphur Chlorine Potassium Calcium Iron Copper H C N O Na Mg Al P S Cl K Ca Fe Cu Atomic mass 1u 12 u 14 u 16 u 23 u 24 u 27 u 31 u 32 u 35.5 u 39 u 40 u 56 u 63.5 u  Gram atomic mass Gram atomic mass of an element is defined as that much quantity of the element whose mass expressed in grams is numerically equal to its atomic mass. To find gram atomic mass we keep the numerical value the some as the atomic mass, but simply change the units from u to g. for example, atomic mass of aluminium is 27 u. Its gram atomic mass is 27 g.  Gram atomic mass of Isotopes : M1X1  M 2 X 2 X1  X 2 M1 & M2 are relative masses of isotopes and X1 & X2 are relative % content Chlorine contains two types of atoms having relative masses 35 and 37 and their relative abundance is 3 : 1. In such cases the atomic mass of the element is the average of relative masses of different isotopes of the element. 35  3  37  1 Atomic mass of chlorine = = 35.5 4 Atoms usually exist in two ways. (i) Molecules (ii) Ions Ex.  A combination of atoms is called a molecule. The forces which hold the atoms together in a molecule are called covalent bonds.  A molecule is the smallest particle of a substance which has the properties of that substance and can exist in the free state.  Atomicity The number of atoms present in one molecule of an element is called its atomicity. Ex. Noble gases (helium, neon, argon, krypton, etc.) have one atom each in their molecules such as He, Ne, Ar and Kr. So, the atomicity of noble gases is 1. Ex. Hydrogen (H2), nitrogen (N2), oxygen (O2), chlorine (Cl2), bromine (Br2), and iodine (I2), all have 2 atoms each in their molecules. So, the atomicity of hydrogen, nitrogen, oxygen, chlorine, bromine and iodine is 2 each. Atomicity of some common elements. There are two types of molecules.  Molecules of elements 2 The molecule of an element contains two (or more) similar atoms chemically combined together. Ex. 2 2 2 A molecule of hydrogen element contains 2 hydrogen atoms combined together, and it is written as H2. 4 8  Molecules of compounds The molecule of a compound contains two (or more) different types of atoms chemically combined together Ex. Hydrogen chloride is a compound. The molecule of hydrogen chloride (HCl) contains two different types of atom. Hydrogen(H) and chlorine atom (Cl) An ion is a positively or negatively charged atom (or group of atoms). An ion is formed by the loss or gain of electrons by an atom, so it contains an unequal number of electrons and protons. Molecules of some compounds Compound Combining Formula Ratio by elements mass Water Hydrogen H2 O 1:8 and oxygen Ammonia Nitrogen 14:3 NH3 and Hydrogen Carbon Carbon 3:8 CO2 dioxide and Oxygen Sodium ion Na+, magnesium ion Mg2+, chloride ion Cl–, and oxide ion O2–. Ex.  There are two types of ions : cations and anions.  Cation A positively charged ion is known as cation. A cation is formed by the loss of one or more electrons by an atom. Ex. Sodium atom loses 1 electron to form a sodium ion, Na+, which is cation : Na  Na  1 electron     Sodium ion Sodium (A cation ) The ions of all the metal elements are cations. –1 electron    Anion A negatively charged ion is known as anion. An anion is formed by the gain of one or more electrons by an atom. Ex. A chlorine atom gains 1 electron to form a chloride ion, Cl–, which is an anion. Cl 1 electron    Chlorine atom  Ionic compounds The compounds which are made up of ions are known as ionic compounds. In an ionic compound, the positively charged ions (cations) and negatively charged ions (anions) are held together by the strong electrostatic forces of attraction. The forces which hold the ions together in an ionic compound are known as ionic bonds or electrovalent bonds. Since an ionic compound consists of an equal number of positive ions and negative ions, so the overall charge on an ionic compound is zero. Ex. Sodium chloride (NaCl) is an ionic compound which is made up of equal number of positively charged sodium ions (Na+) and negatively charged chloride ions (Cl–). Some ionic compound Cl – Chlorine ion ( An Anion ) An anion contains more electrons than a normal atom. A normal atom (or a neutral atom) contains an equal number of protons and electrons. Now, since an anion is formed by the addition of one or more electrons to an atom, therefore, an anion contains more electrons than protons. The ions of all the non metal elements are anions 1 electron    Simple ions Those ions which are formed from single atoms are called simple ions. Ex. Sodium ion, Na+, is a simple ion because it is formed from a single sodium atom, Na.  Compound ions Those ions which are formed from groups of joined atoms are called compound ions Ex. Ammonium ion NH4+, is a compound ion which is made up of two types of atoms joined together, nitrogen and hydrogen. The combining capacity of an element is known as its valency. Formulae and valencies of common ions  Formulae of elements  Variable valency  There are certain elements that exhibit more than one valencies in their ions (or compounds). Iron can exist as Fe2+ or Fe3+ in its compounds. In such cases the name of the ion with lower valency ends with a suffix ‘ous’ while that with higher valency ends with a suffix ‘ic’. Ex. The chemical formula of an element is a statement of the composition of its molecule in which symbol tells us the element and the subscript tells us how many atoms are present in one molecule. One molecule of hydrogen element contains two atoms of hydrogen, therefore, the formula of hydrogen is H2. The formula H2 indicates that one molecule of hydrogen element contains 2 atoms of hydrogen. 2 H represents 2 separate atoms of hydrogen; H2 represents 1 molecule of hydrogen and 2H2 represents 2 molecules of hydrogen. Ex. Some basic ions exhibiting variable valency  Formulae of compounds  Ex. The chemical formula of a compound is a statement of its composition in which the chemical symbols tell us which elements are present and the subscripts tell us how many atoms of each element are present in one molecule of the compound. Water is a compound whose molecule contains 2 atoms of hydrogen and 1 atom of oxygen. So, the formula of water is H2O.  Rules for writing a chemical formula    Ex.  A compound is represented in the abbreviated form by chemical formula.  The chemical formula of a compound represents the composition of a molecule of the compound in terms of the symbols of the elements present in it. Water is a compound made up of 2 atoms of hydrogen element and 1 atom of oxygen element, so the formula of water is written as H2O. In the formula H2O, the subscript 2 indicates 2 atoms of hydrogen. In the formula of water, oxygen O is written without a subscript and it indicates 1 atoms of oxygen. We first write the symbols of the elements which form the compound Below the symbol of each element, we write down its valency. Finally, we cross-over the valencies of the combining atoms. That is, with first atom we write the valency of second atom (as a subscript); and with the second atom we write the valency of first atom (as subscript). Ex. Ex. Element H Valency 1 Formula HCl C l 1 Step-4 : Not applicable, because ratio is already simple Ex. Element H O Valency 1 2 Step-5 : Formula H2O Ex. Element H S Valency 1 2 Thus, the formula of barium nitrate is Ba(NO3)2  Significance of the formula of a substance Formula H2S Ex. Element N H Valency 3 1  Formula represents the name of the substance  Formula represents one molecule of the substance  Formula also represents one mole of molecules of the substance. That is, formula also represents 6.022 × 1023 molecules of the substance.  Formula gives the name of all the elements present in the molecule.  Formula gives the number of atoms of each element present in one molecule.  Formula represents a definite mass of the substance Formula NH3  Writing the formula of a compound Step-1 : Write the symbols of formulae of the ions of the compound side by side with positive ion on the left hand side and negative ion on right hand side. Step-2 : Enclose the polyatomic ion in a bracket. Molecular mass expresses as to how many times a molecule of a substance is heavier 1 than th of the mass of an atom of carbon 12 (carbon-12). Thus, Molecular mass = Step-3 : Write the valency of each ion below its symbol Mass of a molecule 1 th mass of a carbon atom (carbon  12) 12 Step-4 : Reduce the valency numerals to a simple ratio by dividing with a common factor, if any. Step-5 : Ex. Cross the valencies. Do not write the charges positive or negative of the ions. Ex. Molecular mass = 2 × vapour density Formula of barium nitrate. Step-1 : Writing the formula of the ions : Ba2+ 2+ NO3– – Step-2 : Ba (NO3) Step-3 : Ba2+ (NO3)– 2 1 A molecule of water is 18 times heavier than 1 th of the mass of carbon atom. Therefore, 12 the molecular mass of water is 18 u.  Calculation of molecular mass from atomic masses The molecules are made up of two or more atoms of different elements. Therefore, the molecular mass may be calculated as the sum of the atomic masses of all the atoms in a molecule of that substance. Ex. Ammonia has the formula, NH3. it consists of one atom of N and three atoms of H. The atomic mass of N and H are 14.0 and 1 respectively. Therefore, the molecular mass of NH3 is No. of moles = n Given mass = m Molar mass = M Given number of particles = N Avogadro number of particles = N0 These relations can be interchanged as Mass of element, m = n × M or No. of particles of element, N = n × N0 Similarly, 1 Mole of molecules = 6.022 × 1023 molecules = Gram molecular mass of Molar mass Molecular mass of NH3 = At. mass of N + 3 × At. mass of H = 14 + 3 × 1 = 17 u Sulphuric acid has the formula H2SO4. It consists of two H, one S and four O atoms. The atomic masses of H, S and O are 1,32 and 16 respectively. Therefore, the molecular mass of H2SO4 is Molecular mass of H2SO4 = (2 × at. m. of H) + (1 × at. m. of S) + (4 × at. m. of O) = (2 × 1) + (1 × 32) + (4 × 16) = 98 u  Gram molecular mass The molecular mass of a substance expressed in gram is called its gram molecular mass. Ex. Molecular mass of oxygen, O2 = 32 u So, gram molecular mass of oxygen, O2 = 32 grams. Ex. Ex. Atoms and molecules are so small in size that they cannot be counted individually. The chemists use the unit mole for counting atoms, molecules or ions. It is represented by n. A mole represents 6.022 × 1023 particles. 1 mole of atoms = 6.022 × 1023 atoms. 1 mole of molecules = 6.022 × 1023 molecules The number of particles present in 1 mole of any substance is fixed i.e. 6.022 × 1023. This number is called Avogadro constant or Avogadro number. it is represented by No. 1 mole of atoms = 6.022 × 1023 atoms = Gram atomic mass or Molar mass of element Number of moles = Mass of element Molar mass n= m M Number of moles = Given number of atoms Avogadro number n= N N0 Number of moles = Mass of substance Molar mass m M Number of moles Given number of molecules = Avogadro number n= n= N N0 or m = n × M and N = n × N0  Relationship between mole, number of particles and mass and interconversion of one into the other. Molarity (M) : - Moles of solute is one litre of solution is known as molarity . M = Number of moles of solute Volume of solution in litre Ex. Sol. An ornament of silver contains 20 g of silver. Calculate the moles of silver present (atomic mass of silver = 180 u) Moles of silver, m n= M Mass of silver, m = 20 g, Molar mass of silver, M = 108 g 20  n= = 0.185 mol. 108 Ex. Sol. Ex. How many moles of CO2 are present in 51.2 g of it ? Molecular mass of CO2 = 12 + 2 + 16 = 44 u Molar mass of CO2 (M) = 44 g Mass of CO2 (m) = 51.2 g Moles of CO2, m 51.2  = 1.16 mol. n= N 44 Calculate the mass of (i) 0.5 moles of N2 gas (ii) 0.5 moles of N atoms Sol. (i) 0.5 moles of N2 gas Mass = Molar mass × Number of moles m=M×n M = 28 g, n = 0.5  m = 28 × 0.5 = 14 g (ii) Mass = Molar mass × Number of moles m=M×n n = 0.5 mole, M = 14 g m = 14 × 0.5 = 7 g  Mass percentage of an element from molecular formula : The molecular formula of a compound may be defined as the formula which specifies the number of atoms of various elements in the molecule of the compound. Ex. The molecular formula of glucose is C 6H12O6. This indicates that a molecule of glucose contains six atoms of carbon, twelve atoms of hydrogen and six atoms of oxygen. The mass percentage of each element is then calculated by the following formula : Mass percentage of element X = Mass of X in one mole × 100. Gram molecular mass Ex. Calculate the percentage composition (by mass) of formaldehyde (CH2O). Sol. Molecular mass of formaldehyde, Percentage of carbon = 12g × 100 = 40.0% 30g Percentage of hydrogen = Percentage of oxygen = 2g × 100 = 6.7% 30g 16g × 100 = 53.3% 30g  Empirical formula The empirical formula of a compound may be defined as the formula which gives the simplest whole number ratio of atoms of the various elements present in the molecule of the compound. Ex. The empirical formula of the compound glucose (C6H12O6), is CH2O which shows that C, H, and O are present in the simplest ratio of 1 : 2 : 1.  Rules for writing the empirical formula The empirical formula is determined by the following steps :  Divide the percentage of each elements by its atomic mass. This gives the relative number of moles of various elements present in the compound.  Divide the quotients obtained in the above step by the smallest of them so as to get a simple ratio of moles of various elements.  Multiply the figures, so obtained by a suitable integer, if necessary, in order to obtain whole number ratio.  Finally write down the symbols of the various elements side by side and put the above numbers as the subscripts to the lower right hand corner of each symbol. This will represent the empirical formula of the compound. Ex. A substance, on analysis, gave the following composition : Na = 43.4%, C = 11.3%, O = 45.3%. Calculate its empirical formula [Atomic masses = Na = 23, C = 12, O = 16] Sol. CH2O = 12 × 1 + 1 × 2 + 16 × 1 = 30 Mass of one mole of formaldehyde = 30 g 1 Mole of CH2O contains 1 mole (12 g) of carbon. 2 moles of hydrogen (2 g) and 1 mole of oxygen (16 g) Therefore, the empirical formula is Na2CO3  Determination molecular formula : * Interesting by we can apply Conversation of mass or wt. of CaO Molecular formula = Empirical formula × n n= = wt. of CaCO3 taken – wt. of CO2 produced Molecular formula Empirical formula = 0.5 – 0.22 = 0.28 gm What is the simplest formula of the compound which has the following percentage composition : Carbon 80%, Hydrogen 20%, If the molecular mass is 30, calculate its molecular formula. Calculation of empirical formula : Ex. Sol. Ex. If all iron present in 1.6 gm Fe2O3 is converted in form of FeSO4. (NH4)2SO4.6H2O after series of reaction. Calculate mass of product obtained. Sol. If all iron will be converted then no. of mole atoms of Fe in reactant & product will be same. 1.6 1 = 160 100 1 1 mole atoms of Fe = 2 × = 100 50 mole of FeSO4. (NH4)2SO4.6H2O will be same as mole atoms of Fe because one atom of Fe is present in one molecule.  Mole of Fe2O3 =   Empirical formula is CH3. Calculation of molecular formula :  Mole of FeSO4.(NH4)2.SO4.6H2O = Empirical formula mass = 12 × 1 + 1 × 3 = 15 Molecular mass 30 n= = =2 Empirical formula mass 15 1 × Molecule wt. 50 1 = × 342 = 7.84 gm. 50 Mass = Molecular formula = Empirical formula × 2 = CH3 × 2 = C2H6. Ex. On heating a sample of CaCO3, volume of CO2 evolved at NTP is 112 cc. Calculate Ex. (i) Weight of CO2 produced Sol. (ii) Weight of CaCO3 taken (iii) Weight of CaO remaining Sol. 112 1 (i) Mole of CO2 produced = mole 22400 200 1 mass of CO2 = × 44 = 0.22 gm 200 (ii) CaCO3  CaO + CO2 (1/200 mole) mole of CaCO3 = mass of CaCO3 = 1 mole 200 1 × 100 = 0.5 gm 200 (iii) mole of CaO produced = mass of CaO = 1 mole 200 1 × 56 = 0.28 gm 200 1 50 Calculate mass of hydrazine N2H4 obtained when 1.12 litre of N2 taken at NTP reacts with H2 according to N2 + 2H2  N2H4. 1.12 1 Moles of N2 taken = = 22.4 20 N2 + (1/20 mole) 2H2  N2H4 (1/20 mole) mass of N2H4 = 1 × 32 = 1.6 gm 20 Ex. Calculate mass of Na2SO4 obtained when 100 ml of 0.2 M H2SO4 is completely neutralised by NaOH. Sol. Mole of H2SO4 taken = 100 Molarity × Vol. (lit) = 0.2 × = 0.02 1000 H2SO4 + 2NaOH  Na2SO4 + 2H2O 0.02 mole 0.02 mole Mole of Na2SO4 obtained = 0.02 mass of Na2SO4 = 0.02 × 142 = 2.84 gm