Atomic and Molecular Masses

Chemistry SOME BASIC CONCEPTS OF CHEMISTRY ATOMIC AND MOLECULAR MASSES  ATOMIC AND MOLECULAR MASS One of the most important concepts derived from Dalton's atomic theory is that of atomic mass, i.e.,” each element has a characteristic atomic mass. As atoms are very tiny particles, their absolute masses are difficult to measure. However, it is possible to determine the relative masses of different atoms if a small unit of mass is taken as a standard. For this purpose, mass of one atom of hydrogen was assumed as unity and was accepted as standard. The be atomic mass of an element can be defined as the be number wbich indicates how many times the be mass of one atom of the element is heavier in comparison to the mass of one atom: of hydrogen. A = Atomic mass of an element = Mass of an element Mass of one atom of hydrogen In 1858, oxygen atom was adopted as a standard on account of the following reasons: (i) It is much easier to obtain compounds of elements with oxygen than with hydrogen as oxygen is more reactive than hydrogen. (ii) The atomic masses of most of the elements. Become approximately whole numbers but with hydrogen as standard the atomic masses of most of the elements are fractional. The mass of one atom of natural oxygen was taken to be 16.0. Thus, atomic mass of an element = = Mass of one atom of the element 1 th part of the mass of one atom of oxygen 16 Mas of one atom of the element mass of one atom of oxygen By accepting oxygen as a standard, the atomic mass of hydro 6gen comes as 1.008, sodium 22.991 and sulphur 32.066. In 1961, the International Union of Chemists selected a new unit for expressing the atomic masses. They accepted the stable isotope of carbon (12C) with mass number of 12 as the standard. Atomic mass of an element can be defined as the number which indicates how many times the 1 Chemistry mass of one atom of the element is heavier in comparison to 1/12 the part of the mass of one atom of carbon-l2 (12C). A= Atomic mass of an element = = Mass of one atom of the element 1 th part of the mass of one atom of carbon−12 12 Mass of one atom of the element Mass of one atom of carbon−12 × 12 [The quantity' A' was formerly known as atomic weight. However, this term is no longer used as the word 'weight' means gravitational force.] Atomic mass unit: The quantity ~ mass of an atom of 12 carbon-12 (12 C) is known as the atotinc mass unit and is abbreviated as amu. The actual mass of one atom of carbon-l2 is 1.9924 x 10-23 g or 1.99.24 x 10-26 kg. Thus, 1 amu = 1.9924 ×10−23 12 = 1.66 ×10−24 g or 1.66 × 10−27 kg A= atomic mass of an element = Mass of one atom of the element 1 amu The atomic masses of some elements on the basis ofcarbon-l2 are given below: Hydrogen 1.008 amu Iron 55.847 amu Oxygen 16.00 amu Sodium 22.989 amu Chlorine 35.453 amu Zinc 65.38 Magnesium 24.305 amu Silver 107.868 amu Copper 63.546 amu amu The actual mass of an atom of an element the atomic mass of an element in amu x 1.66 x 10-24 g So, the actual mass of hydrogen atom 1.008 x 1.66 x 10-24 = 1.6736 X 10-24 g Similarly, the actual mass of oxygen atom 16 x 1.66 x 10-24 = 2.656 X 10-23 g It is clear from the above list of atomic masses that atomic masses of a number of elements are 2 Chemistry not nearly whole numbers. Actually, the above values are average relative masses. Most of the elements occur in nature as a mixture of isotopes. (Isotopes-the atoms. of the same element having different atomic masses). With very few exceptions, however, elements have constant mixtures of isotopes. Chlorine is found in nature as a mixture containing two isotopes CI-35 (34.969 amu) and CI-37 (36.966amu). These are found in the ratio of 75.53% (CI-35) and 24.47% (CI-37). Therefore, the average relative mass of chlorine is calculated as: (34.969 x 0.7553) + (3'6.966 x 0.2447) = 35.46 amu Based on the average mass, the atomic mass of chlorine is 35.46 or 35.5 amu but it is never possible to have-an atom having a relative mass 35.5 amu. It can have relative mass of about 35.0 or 37.0 amu depending on the particular isotope. Thus, average relative mass of any naturally occurring sample of chlorine is 35.46 or 35.5 amu as it is a mixture of two isotopes present in definite proportion. The same reasoning applies to all other elements. The average atomic masses of various elements are det~ed by multiplying the atomic mass of each is. tope by its fractional abundance and adding the values thus obtained. The fractional abundance is determined by· dividing percentage abundance by hundred. Example 11. Boron has two isotopes boron-1O and boron-II whose percentage abundances are 19.6% and 80.4% respectively. What is the average atomic mass of boron? Solution: Contribution of boron-1O 10.0 X 0.196 = 1.96amu Contribution of boron-II =ll. Ox 0.804 = 8.844amu Adding both =1.96+8.844=10.804amu Thus, the average atomic mass of boron is 10.804 amu. Gram-atomic Mass or Gram Atom When numerical value of atomic mass of an element is expressed in grams, the value becomes gram-atomic mass or gram atom. The atomic mass of oxygen is 16 while gram-atomic mass or gram atom of oxygen is 16 g. Similarly, the gram-atomic masses of hydrogen, chlorine and nitrogen are 1.008 g, 35.5 g and 14.0 g respectively; Gram atomic. mass or gram. Atom of every element consists of same number of atoms. This number is called Avogadro's number. The value of Avogadro's number is 6.02 x 1023. Absolute mass of one oxygen atom = 16amu =16x 1.66 x 10-24 g Therefore, the mass of 6.02 x 1023 atoms of oxygen will be = 16x 1.66 x 10-24 x 6.02 X 1023 3 Chemistry 16g (gram-: atomic mass) Thus, gram-atomic mass can be defined as the absolute mass in grams of 6.02 x 1023 atoms of any element. Number of gram atoms of any element can be calculated with the help of the following formula: Mass of the element in grams No. of gram atoms = Atomiv mass of the element in grams Molecular Mass: Like an atom, a molecule of substance is also a very small particle possessing a mass of the order of lO-24 to 10-22 g. Similar to atomic mass, molecular mass is also expressed as a relative mass with respect to the mass of the standard substance which is an atom of hydrogen or an atom of oxygen or an atom of carbon-12. The molecular mass of a substance may be defined as the mass of a molecule of a substance relative to the mass of an atom of hydrogen as 1.008 or of oxygen taken as 16.00 or the mass of one atom of carbon taken as 12. Molecular mass is a number which indicates how many times one molecule of a substance is heavier in comparison to 1/16th of the mass of oxygen atom or 1/12th of the mass of one atom of carbon-12. M = Molecular mass Mass of one molecule of the substance = 1 th mass of one atom of carbon−12 12 The mass of a molecule is equal to sum of the masses of the atoms present in a molecule. One molecule of water consists of 2 atoms of hydrogen and one atom of oxygen. Thus, molecular. mass of water (2 x 1.008) + 16.06 18.016amu. One molecule of H2 S04 (sulphuric acid) consists of 2 atoms of hydrogen, one atom of sulphur and four atoms of oxygen. Thus, the molecular mass of sulphuric acid is = (2x 1.008) + 32.00 + (4 x 16.00) = 98.0160r 98.016amu Gram-molecular Mass or Gram Molecule A quantity. of substance whose. mass. in grams is numerically equal to its molecular mass' is called gram molecular mass. In other words; molecular mass of a substance expressed in grams is called gram-molecular mass to gram molecule. For example, the molecular mass of chlorine is 71 and, therefore, its gram-molecular mass or gram molecule is 71 g. Similarly, molecular mass of oxygen (02) is 32, i. e., 2x 16= 32amu. 4 Chemistry Gram-molecular mass of oxygen 32g Molecular mass of nitric acid (HN03) is 63, i. e., = 1+ 14 + 3 x 16 = 63 amu Gram-molecular mass of nitric acid = 63 g Gram-molecular mass should not be confused with the mass of one molecule of the substance in grams. The mass of one molecule of a substance is known as its actual mass. For example, the actual mass of one molecule of oxygen is equal to. 32x 1.66 x 10-24 g, i.e., 5.32 x 10-23 g. The number of gram molecules of a substance present in a given mass of a substance can be determined by the application of following formula: No. of gram molecules = Mass of single molecule = Mass of a Substance in grams Molecular mass of the substance in grams Molar mass in grams 6.023 × 1023 = Molar mass in amu × 1.66×10−24 grams Calculate the mass of 2.5-gram atoms of oxygen. Solution: We know that, No. of gram atoms = Mass of the element in grams Atomic mass of the element in grams So, Mass of oxygen = 2.5 x 32 80.0g Calculate the mass of 1.5-gram molecule of sulphuric acid. Solution: Molecular mass of H 2S04 =2x 1+ 32+ 4 x 16= 98.0amu ram-molecular mass of H2S04 =98.0g Mass of 1.5-gram molecule of H2S04=98.0x 1.5=147.0g 5