The mass of the formula unit is called the formula mass Formula masses are calculated the same way as molecular masses

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1 Chapter 4: The Mole Atomic mass provides a means to count atoms by measuring the mass of a sample The periodic table on the inside cover of the text gives atomic masses of the elements The mass of an atom is called its atomic mass When using atomic masses, retain a sufficient number of significant figures so the atomic mass data contributes only slightly to the uncertainty of the result The molecular mass allows counting of molecules by mass The molecular mass is the sum of atomic masses of the atoms in the compounds formula For example the molar mass of water, H, is twice the mass of hydrogen (1.008) plus the mass of oxygen (15.999) = Strictly speaking, ionic compounds do not have a molecular mass because they don t contain molecules The mass of the formula unit is called the formula mass Formula masses are calculated the same way as molecular masses For example the formula mass of calcium oxide, Ca, is the mass of calcium (40.08) plus the mass of oxygen (15.999) = ne mole of a substance contains the same number of formula units as the number of atoms in exactly 1 g of carbon-1 ne mole of a substance has a mass in grams numerically equal to its formula mass The mass of one mole of a substance is also called its molar mass ne mole of any substance contains the same number of formula units This number is called Avogadro s number or constant 1 mol formula units = 6.0 x 10 formula units Counting formula units by moles is no different than counting eggs by the dozen (1 eggs) or pens by the gross (144 pens) Avogadro s number is huge because atoms and molecules are so small: a huge number of them are needed to make a lab-sized sample Avogadro s number links moles and atoms, or moles and molecules and provides an easy way to link mass and atoms or molecules Using water (molar mass ) as an example: 1 mole H 6.0 x 10 molecules H 1 mole H g H g H 6.0 x 10 molecules H Within chemical compounds, moles of atoms always combine in the same ratio as the individual atoms themselves so: 1 mole H mole H 1 mole H 1 mole 1

2 Stoichiometry is the study of the mass relationships in chemical compounds and reactions A common use for stoichiometry is to relate the masses of reactants needed to make a compound These calculations can be solved using the factor-label method and equivalence relations relating molecular masses and/or formula masses Example: How many grams of iron are in a 15.0 g sample of iron(iii) oxide? AALYSIS: 15.0 g Fe? g Fe LIKS: 1 mol Fe mol Fe 1 mol Fe g Fe 1 mol Fe g Fe 15.0 g Fe 1mol Fe mol Fe g Fe 1mol Fe g Fe 1mol Fe = 10.5 g Fe The usual form for describing the relative masses of the elements in a compound is a list of percentages by mass This is called the percentage composition or percentage composition by mass The percentage by mass is the number of grams of the element in 100 g of the compound and can be calculated using: mass of element element = 100% % mass of whole sample Example: A sample was analyzed and found to contain g nitrogen and g oxygen. What is the percentage composition of this compound? AALYSIS: Find sample mass and calculate % LIKS: whole sample = g % = % = g g sample g g sample 100% = 5.94 % 100% = % Hydrogen peroxide consists of molecules with the formula H This is called the molecular formula The simplest formula for hydrogen peroxide is H and is called the empirical formula It is possible to calculate the empirical formula for a compound from mass data The goal is to produce the simplest whole number mole ratio between atoms Example: A.01 g sample of a compound contains 0.5 g of nitrogen and g of oxygen. Calculate its empirical formula AALYSIS: We need the simplest whole number mole ratio between nitrogen and oxygen 1 mol 0.5 g = 0.07 mol g g 1 mol g = mol

3 Empirical formulas may also be calculated indirectly When a compound made only from carbon, hydrogen, and oxygen burns completely in pure oxygen only carbon dioxide and water are produced This is called combustion Empirical formulas may be calculated from the analysis of combustion information Example: The combustion of a 5.17 g sample of a compound of C, H, and gave g C and 4.51 g of H. Calculate the empirical formula of the compound. AALYSIS: This is a multi-step problem. The mass of oxygen is obtained by difference: g = 5.17 g sample ( g C + g H ) The masses of the elements may then by used to calculate the empirical formula of the compound g C 1.011g C g C =.0 g C.0158 g H 4.51 g H = g H g H total mass of C and H =.47 g mass = 5.17 g -.57g =.690 g 1 mol C C :.0 g C 1.011g C = mol C 1mol H H : g H = mol H g H 1mol :.690 g = mol g C H = C H = CH The formula for ionic compounds is the same as the empirical formula For molecules, the molecular formula and empirical are usually different If the experimental molecular mass is available, the empirical formula can be converted into the molecular The molecular formula will be a common multiplier times all the coefficients in the empirical formula Example: The empirical formula of hydrazine is H, and its molecular mass is.0. What is its molecular formula? AALYSIS: The molecular mass (.0) is some simple multiple of the mass calculated from the empirical formula (16.0) multiplier 1.00 H = The correct formula is then =.00 H 4 The coefficients of a balanced chemical equation provide the mole-to-mole ratios for the substances involved in the reaction Whenever a problem asks you to convert between different substances, the calculation usually involves a mole-to-mole relationship How to detect unbalanced equations will be covered shortly

4 Example: If mole of C is produced by the combustion of propane, C H 8, how many moles of oxygen are consumed? The balanced equation is: C H C + 4 H AALYSIS: Relating two compounds usually requires a mole-to-mole ratio In many problems you will also need to perform one or more mole-to-mass conversions These types of stoichiometry problems are summarized with the flowchart: mol C 5 mol H8 1 mol C H =.88 mol 8 Example: How many grams of Al are produced when 41.5 g Al react? Al(s) + Fe (s) Al (s) + Fe(l) AALYSIS: 41.5 g Al? g Al grams Al moles Al moles Al grams Al 41.5 g Al 1mol Al 6.98 g Al 1mol Al 10.0 g Al mol Al 1 mol Al = g Al Chemical equations provide quantitative descriptions of chemical reactions Conservation of mass is the basis for balancing equations To balance an equation: 1) Write the unbalanced equation ) Adjust the coefficients to get equal numbers of each kind of atom on both sides of the arrow Guidelines for Balancing Equations: 1) Balance elements other than H and first ) Balance as a group any polyatomic ions that appears unchanged on both sides of the arrow ) Balance separately those elements that appear somewhere by themselves As a general rule you should use the smallest whole-number coefficients when writing balanced chemical equations All reactions eventually use up a reactant and stop The reactant that is consumed first is called the limiting reactant because it limits the amount of product that can form Any reagent that is not completely consumed during the reactions is said to be in excess and is called an excess reactant The computed amount of product is always based on the limiting reagent 4

5 Example: How many grams of can form when 0.0 g H and 40.0 g react according to: 4 H H AALYSIS: This is a limiting reactant problem 0.0 g H 40.0g 1mol H 17.0g H 1mol.00 g 4 mol 4 mol H 4 mol 5 mol 0.01g 1mol 0.01g 1mol = 5.9 g = 0.01g is the limitingreagent and 0.01g form The amount of product isolated from a chemical reactions is almost always less than the calculated, or maximum, amount The actual yield is the amount of the desired product isolated The theoretical yield is the amount that would be recovered if no loss occurred (the calculated, maximum amount) The percentage yield is the actual yield as a percentage of the theoretical yield percentage yield = actual yield theoretical yield 100% When working with percentage yield: Remember they involve a measured (actual yield) and calculated (theoretical yield) quantity The calculation may be done in either grams or moles The result can never be a number larger than 100% 5

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