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35 MOLES AND MOLE CALCULATIONS INTRODUCTION The purpose of this section is to present some methods for calculating both how much of each reactant is used in a chemical reaction, and how much of each product is formed. In this section theoretical details are kept to the minimum necessary for a mastery of calculation methods to be achieved. It is desirable, however, that at some stage students learn of the historical development of the ideas applied here, and of the underlying theory. It is assumed that students have a good mastery of basic arithmetic and algebra, especially of calculations involving ratios and proportions. It is assumed also that students are able to both read and write chemical formulae and equations, accurately and with fair confidence. Until such knowledge and skills have been acquired, it is difficult to achieve success with mole calculations. SCOPE OF CALCULATIONS COVERED IN THIS SECTION There are three basic requirements to be mastered in this section: 1) to calculate masses of reactants that will be consumed in a reaction, and the masses of products likely to be formed from a given mass of reactants. 2) to calculate what volume of gas may be either consumed or produced in a reaction . 3) to calculate what volumes and concentrations of solutions of reactants should be mixed to produce predicted concentrations of products in the solution. DEFINITION OF A MOLE AND OF MOLAR MASS Atoms of different elements have different masses. It is possible both to measure the mass of individual atoms, and to measure the relative masses of different kinds of atoms. Actual masses of atoms are very small (an atom of carbon has mass = 2 x 10-23 g approx), so the masses are given in atomic mass units (amu). The mass of an atom of carbon has been selected as a standard for comparing the masses of atoms: an atom of carbon has been assigned a mass of 12.00 amu.1 The relative atomic mass of an atom of any other element is given in proportion to the mass of an atom of carbon. For example, the relative atomic mass of an oxygen atom is given as 16.00 amu, which indicates that an atom of oxygen is times more massive than an atom of carbon. The relative atomic mass of hydrogen = 1.00 amu; an atom of hydrogen has of the mass of an atom of carbon. 1 The definitions given here do not allow for the existence of different isotopes of elements. This omission does not affect the validity of the methods described. Detailed treatment of this topic should consider the presence of isotopes. 36 The relative atomic masses (ram) of some common elements are listed below: Element ram Element ram Element ram Aluminium 27.0 Gold 197.0 Oxygen 16.0 Barium 137.3 Hydrogen 1.0 Phosphorus 31.0 Bromine 79.9 Iodine 126.9 Potassium 39.1 Calcium 40.1 Iron 55.8 Silicon 28.1 Carbon 12.0 Lead 207.2 Silver 107.9 Chlorine 35.5 Magnesium 24.3 Sodium 23.0 Chromium 52.0 Manganese 54.9 Sulfur 32.1 Cobalt 58.9 Mercury 200.6 Tin 118.7 Copper 63.5 Nickel 58.7 Titanium 47.9 Fluorine 19.0 Nitrogen 14.0 Zinc 65.4 The mass of one mole of an element is the relative atomic mass of an element, stated in grams. A mole is defined as the number of atoms in 12.00 g of pure carbon. The value of this number is 6.023 x 10 23. It is called the Avogadro Number, symbol NA. One mole of any element also contains 6.023 x 1023, or NA, atoms. WHAT ABOUT COMPOUNDS? The mass of one mole of any compound can be calculated by adding the relative atomic masses of all atoms in the formula, and stating the total in grams. Examples: Compound Formula Sum of masses of atoms in Mass of formula one mole Water H2O (1.0 x 2) + 16.0 18.0 g Carbon dioxide CO2 12.0 + (16.0 x 2) 44.0 g Sodium chloride NaCl 23.0 + 35.5 58.5 g Calcium sulfate CaSO4 40.1 + 32.1 + (16.0 x 4) 136.2 g Lead nitrate Pb(NO3)2 207.2 + 2(14.0 + 16.0 x 3) 331.2 g Ammonium phosphate (NH4)3PO4 3(14.0 + 1.0 x 4) + 31.0 + (16.0 x 149.0 g 4) 37 The

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