On this scale, 1 H = amu, 16 O = amu the mass of an atom in atomic mass units (amu). Atomic mass unit is defined as the mass exactly equal to one-twelfth of the mass of carbon-12 atom. 3.1 Atomic mass: Chapter 3 Mass Relationships in Chemical Reactions By definition: 1 atom 12 C “weighs” 12 amu Average atomic mass- average mass of naturally occurring mixture of isotopes. Natural lithium is: 7.42% 6 Li (6.015 amu) 92.58% 7 Li (7.016 amu) Average atomic mass of lithium: 7.42 x x = amu Listed on the Periodic Table Avogadro’s Number and the Molar Mass of an Element In SI system, the mole (mol) is the amount of a substance that contains as many elementary entities as there are atoms in exactly grams of 12 C. Avogadro’s number (N A )1 mol = N A = x Molar mass is the mass of 1 mole of atoms / molecules in grams 1 mole 12 C atoms = x atoms = g 1 mole lithium atoms = g of Li For any element atomic mass (amu) = molar mass (grams) Atomic mass of Na is 22.99amu and it’s molar mass is gram. Molecular mass (or molecular weight) is the sum of the atomic masses (in amu) in a molecule. 1S32.07 amu 2O + 2 x amu SO amu 1 molecule SO 2 = amu 1 mole SO 2 = g SO 2

Formula mass is the sum of the atomic masses (in amu) in a formula unit of an ionic compound amu amu 1 mole NaCl = g NaCl 3.2 1Na NaCl 1Cl amu For any ionic compound, formula mass (amu) = molar mass (grams) What is the formula mass of Ca 3 (PO 4 ) 2 ? Ca3 x P2 x O+ 8 x Relationship between amu and grams 1 g = x amuN A = Avogadro’s number How many atoms are in g of potassium (K) ? 1 mol K = g K 1 mol K = x atoms K g Kx 1 mol K g K x atoms K 1 mol K x= 8.49 x atoms K

Do You Understand Molor Mass? How many H atoms are in 72.5 g of C 3 H 8 O ? mol C 3 H 8 O = (3 x 12) + (8 x 1) + 16 = 60 g C 3 H 8 O 1 mol H = x atoms H 5.82 x atoms H 1 mol C 3 H 8 O molecules = 8 mol H atoms 72.5 g C 3 H 8 O 1 mol C 3 H 8 O 60 g C 3 H 8 O x 8 mol H atoms 1 mol C 3 H 8 O x x H atoms 1 mol H atoms x =

Percent composition by mass is the percent of each element in a compound. Percent composition of compounds 3.5

Percent composition of an element in a compound = n x molar mass of element molar mass of compound x 100% n is the number of moles of the element in 1 mole of the compound C2H6OC2H6O %C = 2 x (12.01 g) g x 100% = 52.14%H = 6 x (1.008 g) g x 100% = 13.13%O = 1 x (16.00 g) g x 100% = 34.73% 52.14% % % = 100.0% 3.5

Percent Composition and Empirical Formulas

3.5 Percent Composition and Empirical Formulas K : ~ ~ Mn : = 1.0 O : ~ ~ KMnO 4 Determine the empirical formula of a compound that has the following percent composition by mass: K 24.75, Mn 34.77, O percent. n K = g K x = mol K 1 mol K g K n Mn = g Mn x = mol Mn 1 mol Mn g Mn n O = g O x = mol O 1 mol O g O

3.7 3 ways of representing the reaction of H 2 with O 2 to form H 2 O A process in which one or more substances is changed into one or more new substances is a chemical reaction A chemical equation uses chemical symbols to show what happens during a chemical reaction reactantsproducts Chemical Reactions and Chemical Equations

How to “Read” Chemical Equations 2 Mg + O 2 2 MgO 2 atoms Mg + 1 molecule O 2 makes 2 formula units MgO 2 moles Mg + 1 mole O 2 makes 2 moles MgO 48.6 grams Mg grams O 2 makes 80.6 g MgO IS NOT 2 grams Mg + 1 gram O 2 makes 2 g MgO Mg(s) + O 2 (g) 2 MgO(s) 2 HgO(s) O 2 (g) + 2Hg(l) Indicate physical state

Balancing Chemical Equations 1.Write the correct formula(s) for the reactants on the left side and the correct formula(s) for the product(s) on the right side of the equation. Ethane reacts with oxygen to form carbon dioxide and water C 2 H 6 + O 2 CO 2 + H 2 O 2.Change the numbers in front of the formulas (coefficients) to make the number of atoms of each element the same on both sides of the equation. Do not change the subscripts C 2 H 6 NOT C 4 H 12

Balancing Chemical Equations 3.Start by balancing those elements that appear only once on each side of the equation and balance them. C 2 H 6 + O 2 CO 2 + H 2 O 3.7 start with C or H but not O 2 carbon on left 1 carbon on right multiply CO 2 by 2 C 2 H 6 + O 2 2CO 2 + H 2 O 6 hydrogen on left 2 hydrogen on right multiply H 2 O by 3 C 2 H 6 + O 2 2CO 2 + 3H 2 O

Balancing Chemical Equations 4.Balance those elements that appear in two or more reactants or products oxygen on left 4 oxygen (2x2) C 2 H 6 + O 2 2CO 2 + 3H 2 O + 3 oxygen (3x1) multiply O 2 by 7 2 = 7 oxygen on right C 2 H 6 + O 2 2CO 2 + 3H 2 O 7 2 remove fraction multiply both sides by 2 2C 2 H 6 + 7O 2 4CO 2 + 6H 2 O

Balancing Chemical Equations 5.Check to make sure that you have the same number of each type of atom on both sides of the equation C 2 H 6 + 7O 2 4CO 2 + 6H 2 O ReactantsProducts 4 C 12 H 14 O 4 C 12 H 14 O 4 C (2 x 2)4 C 12 H (2 x 6)12 H (6 x 2) 14 O (7 x 2)14 O (4 x 2 + 6)

1.Write balanced chemical equation 2.Convert quantities of known substances into moles 3.Use coefficients in balanced equation to calculate the number of moles of the sought quantity 4.Convert moles of sought quantity into desired units Amounts of Reactants and Products 3.8

Methanol burns in air according to the equation 2CH 3 OH + 3O 2 2CO 2 + 4H 2 O If 209 g of methanol are used up in the combustion, what mass of water is produced? grams CH 3 OHmoles CH 3 OHmoles H 2 Ograms H 2 O molar mass CH 3 OH coefficients chemical equation molar mass H 2 O 209 g CH 3 OH 1 mol CH 3 OH 32.0 g CH 3 OH x 4 mol H 2 O 2 mol CH 3 OH x 18.0 g H 2 O 1 mol H 2 O x = 235 g H 2 O 3.8

Limiting Reagents The reactant used up first in a reaction is called limiting reagent NO + O 2 2NO 2 7 mole NO and 8 mole O 2 NO is the limiting reagent O 2 is the excess reagent The maximum amount of products formed depends on the amount of the limiting reagent.

Do You Understand Limiting Reagents? In one process, 124 g of Al are reacted with 601 g of Fe 2 O 3 2Al + Fe 2 O 3 Al 2 O 3 + 2Fe Calculate the mass of Al 2 O 3 formed. g Almol Almol Fe 2 O 3 neededg Fe 2 O 3 needed OR g Fe 2 O 3 mol Fe 2 O 3 mol Al neededg Al needed 124 g Al 1 mol Al 27.0 g Al x 1 mol Fe 2 O 3 2 mol Al x 160. g Fe 2 O 3 1 mol Fe 2 O 3 x = 367 g Fe 2 O 3 Start with 124 g Alneed 367 g Fe 2 O 3 Have more Fe 2 O 3 (601 g) so Al is limiting reagent 3.9

Use limiting reagent (Al) to calculate amount of product that can be formed. g Almol Almol Al 2 O 3 g Al 2 O g Al 1 mol Al 27.0 g Al x 1 mol Al 2 O 3 2 mol Al x 102. g Al 2 O 3 1 mol Al 2 O 3 x = 234 g Al 2 O 3 2Al + Fe 2 O 3 Al 2 O 3 + 2Fe 3.9

The amount of the limiting reagent determines the theoretical yield of the reaction, that is the amount of product that would result if all the limiting reagent reacted. Actual Yield is the amount of product actually obtained from a reaction. % Yield = Actual Yield Theoretical Yield x Reaction Yield

Worked Example 3.16a

Worked Example 3.16b