CHAPTER 1 STOICHIOMETRY Introduction Chemistry A Molecular Science CAMS the rst half of this two course sequence stressed bonding structure and reactivity The material was qualitative and stressed several types of reactions and the factors that a ected their relative extents of reaction However as the title of this text suggests chemistry is also a quantitative science Chemists must not only predict the products of a reaction they must also predict the amount of product that can be expected and the amount of waste that must be removed They also need to know how much energy is required or how much heat is generated by a reaction They must also understand how the reaction occurs so that they can optimize the reaction conditions These are the types of problems addressed in this text We begin our study of the quantitative aspects of chemistry with stoichiometry the science that deals with the quantitative relationships between the elements in a compound substance stoichiometry and between the substances in a chemical reaction reaction stoichiometry It is the topic of this rst chapter because a thorough knowledge of stoichiometry is vital to an understanding of the material presented in this course Understanding how quantitative data and results are presented is also important so you should review Appendix A Reporting Quantitative Measurements and Results for a treatment of precision signi cant gures and rounding errors Finally we will set up many problems using the factor label method so please review Appendix B The Factor Label Method for a discussion of this procedure 1 1 Mass and Moles Introduction Chemists use chemical equations to design possible routes to desired molecules and to discuss chemical processes However the individual molecules represented in the equations are far too small to be seen so chemists must use a very large number of molecules in their reactions in order that the reactants and products can be observed Indeed the number of molecules required to make a visible sample is staggering Consider that 1 L of water about 1 50th of a drop contains about 100 000 000 000 000 000 or 1017 molecules and a typical reaction in the laboratory involves thousands of times that number Such large numbers are cumbersome so scientists use a more convenient unit when discussing numbers of molecules The unit is the mole the topic of this section Convert between numbers of moles and numbers of particles with Avogadro s number Convert between mass and moles with molar mass Convert between the pressure volume and temperature of a gas and the number of moles with the ideal gas Objectives law 1 1 1 Avogadro s Number Avogadro s number which is given below is simply the number of items in a mole so it also de nes the mole which is simply Avogadro s number of items NA 6 0221 1023mol 1 Avogadro s Number A mole is used to indicate a number of items just as a dozen is used to indicate a number of eggs Since Avodagro s number is so large the mole is used only for the number of atoms or molecules but it can be used for any item For example it is estimated that there are about 1023 1024 stars in the universe which is 1 10 moles Converting from moles to atoms or molecules is done in the same way as converting dozens to items 1 5 doz 1 5 doz 12 items doz 18 items and 1 5 mol 1 5 mol 6 0 1023 atoms mol 9 0 1023 atoms The mole is used simply because it is much easier to discuss the number of atoms in moles than it is as individual items 0 10 mol H2O is a much more convenient expression than 6 0 1022 H2O molecules c cid 13 2014 Advanced Instructional Systems Inc and NC State College of Sciences Foundation 1 1 1 2 Molar Mass Mm Chemists need to be able to readily prepare mixtures of reactants that have the correct atom or molecule ratios for reaction but they certainly cannot count such large numbers Instead they use other more easily determined properties that are related to the numbers of atoms and or molecules The rst such method we examine is mass Mass can be used to count atoms and molecules because a mole is the number of atoms present in one gram atomic weight the atomic weight expressed in grams of any atom or in one gram molecular weight of any molecule Thus the mass of a mole of any substance which is known as its molar mass Mm equals its atomic or molecular weight expressed in grams For example the atomic weight of Mg is 24 3 so its molar mass 24 3 g mol and the molecular weight of CO2 is 44 0 so its molar mass is 44 0 g mol Thus molar mass allows us to quickly convert a mass into a number of moles or a number of moles into a mass Chemists use this fact to quickly count the number of moles of substance by simply weighing it Mole mass conversions are most easily done with the factor label method It uses the units of the given quantity and those of the conversion factors to assure the proper operations are performed To use this method arrange the factors so that the denominator of each factor cancels the numerator of the previous quantity until the units of the answer are obtained See The Factor Label Method 1 1 3 Determining Molar Mass Exercise Determine the molar masses of the following Express all answers to the nearest whole number Ca3 PO4 2 Atomic weight of Ca Atomic weight of P g mol Atomic weight of O Molar mass of Ca3 PO4 2 g mol EXERCISE 1 1 N2F4 Atomic weight of N Atomic weight of F Molar mass of N2F4 1 1 4 Mass Mole Conversion Exercises EXERCISE 1 2 What is the mass of 3 24 mol N2O5 Molar mass Mm g mol Mass m g How many moles of N2O5 are in 12 7 g Moles n mol 2 c cid 13 2014 Advanced Instructional Systems Inc and NC State College of Sciences Foundation 1 1 5 Moles Items Exercise EXERCISE 1 3 How many Al atoms are present in 0 065 g Al Moles of atoms n Individual atoms N mol atoms 1 1 6 Ideal Gas Law The number of moles of molecules in a gas can also be determined with the ideal gas law P V nRT Ideal Gas Law 1 1 P is the pressure of the gas in atmospheres 1 atm 760 torr V is its volume in liters R 0 08206 L atm K 1 mol 1 is the ideal gas law constant T is the temperature on the Kelvin scale K C 273 15 n is the number of moles of gas 1 1 7 Gas Law Exercise EXERCISE 1 4 How many moles of H2 are in a 3 06 L container at 22 C if its pressure is 742 torr P atm V R 0 08206 L atm K 1 mol 1 L T …
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