Packet'5b:'The'Mathematics'of'Formulas'and'Equations! 1!

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1 Packet'5b:'The'Mathematics'of'Formulas'and'Equations 1 Moles THE MOLE: Bridge between the visible and invisible world A represents a quantity: particles Just like a is 12 Just as you can have a dozen eggs or a dozen doughnuts, you can have a mole of atoms or ions or molecules. Because atoms, ions, and molecules are so small, they must be grouped into a larger set to measure significant mass. This number is known a, in honor of the famous Italian chemist, Amadeo Avogadro, who formulated the mole concept One mole of sodium has 6.02 x atoms One mole of water has 6.02 x molecules CALCULATING GRAM FORMULA MASS Gram Formula Mass is also known as molar mass molecular mass gram atomic mass (for single atoms) the formula mass of a substance will be equal to its gram formula mass One mole is equal to the of any substance Therefore, the mass of one mole of any substance can be found by determining its gram formula mass Ex: the gram formula mass of sodium (Na) is equal to its formula mass in grams. Na = 23 amu (mass on periodic table) = 23 g 1 mole of Na = g What is the gram formula mass of the following elements? F = N = Ag =

2 2' Packet'5b:'The'Mathematics'of'Formulas'and'Equations Ex: the gram formula mass of sodium chloride (NaCl) is equal to its formula mass in grams. Na: 23 amu Cl: 35 amu 58 amu = 58 g 1 mole NaCl = g To find the gram formula mass of a compound or molecule: Look at how many atoms of each element are present Multiply the number of atoms for each element by its atomic mass (round to nearest whole number) Add Ex: What is the molecular mass of H 2 O? H: O: Ex: What is the molar mass of Na 2 CO 3? Na: C: O: Ex : What is the gram formula mass of Fe 2 (SO 4 ) 3? Fe: S: O: What is the gram formula mass of the following compounds? BaSO 4 Ca(NO 3 ) 2

3 Packet'5b:'The'Mathematics'of'Formulas'and'Equations 3 MOLE CONVERSIONS Grams to Moles TABLE T: Mole Calculations Number of moles = given mass (g) gram-formula mass Ex: What is the number of moles in 51 grams of ammonia (NH 3 )? 1. Find the gram formula mass (GFM) of NH 3 N = 14 H = 3(1) = 3 GFM = 17 grams 2. Use the conversion formula (Table T) Number of moles = 51 grams (given) 17 grams (GFM) mol (mol is the abbreviation for moles) How many moles are in each of the following substances? 212 grams of Na 2 CO 3

4 4' Packet'5b:'The'Mathematics'of'Formulas'and'Equations 1.7 grams of AgNO 3 49 grams of H 2 SO 4 90 grams of C 2 H 6 Mole to grams: just rearrange the formula or use the triangle Moles = grams gram formula mass grams = moles X gram formula mass How many grams in 2.5 moles of HF? 1. Find the gram formula mass of HF H = 1 F = 19 GFM = 20 grams 2. Use the conversion formula: Number of grams = 20 g (GFM) x 2.5 moles = How many grams are in each of the following substances? 0.50 moles of HgO

5 Packet'5b:'The'Mathematics'of'Formulas'and'Equations moles of Fe 2 O moles of Mg 3 (PO 4 ) 2 Purple Book p (top and bottom sections) Molar Volume of a Gas STP means STP is At STP: 1 mole of ANY GAS (6.02 X ) occupies 22.4 liters Avogadro s Hypothesis: Equal volumes of ALL gases contain the same number of. Ex: At STP, 1 liter of O 2 has the same number of particles as 1 liter of H 2 ( even though a particle of oxygen is 16 times heavier than a particle of hydrogen) Practice Questions 1. At STP, 1 liter of CH 4 (g) and 1 liter of O 2 (g) has the same A) density B)mass C) number of molecules D) number of atoms 2. Which rigid cylinder has the same number of molecules at STP as 2.0 liter rigid cylinder containing H 2 (g) at STP? A) 1.0 L cylinder of O 2 (g) (C) 2.0 cylinder of CH 4 (g) B) 1.5 cylinder of NH 3 (g) (D) 4.0 cylinder of He (g) Purple Book p If asked to convert between moles, particles or liters, set up proportions knowing your conversion factors. Going through the mole you can

6 6' Packet'5b:'The'Mathematics'of'Formulas'and'Equations Percent Composition Tells the percentage of the of each element in a compound Table T Percent Composition % composition by mass = mass of part X 100 mass of whole ( mass of whole is equal to the GFM) Ex: What is the percent composition of oxygen in KCLO 3? Ex: What is the percent by mass of nitrogen in (NH 4 ) 2 CO 3? Percent of Water in a Hydrate A hydrated crystal is a salt that contains definite amounts of water as part of their crystal structure. Therefore, is part of the empirical formula. Crystals that contain water are called, while those that do not contain water are called The percent of water in a hydrate can be calculated using the percent composition formula from Table T. The formula for a hydrate will always be written like this: Cu SO 4 5H 2 O This means that there are 5 water molecules per unit of copper sulfate. Ex: What is the percent by mass of water in Na 2 CO 3 10H 2 O?

7 Packet'5b:'The'Mathematics'of'Formulas'and'Equations 7 Percent of water in a hydrate using lab data: What happened here? By taking masses before and after heating, you can calculate the percent of water in the hydrate. The difference in the masses is equal to the water lost. Ex: A 3.0 g sample of Na 2 CO 3 10H 2 O is heated to a mass of 2.4g. Calculate the percent of water in the hydrate Ex: A student obtained the following data: Mass of empty crucible + cover 11.7g Mass of crucible, cover and hydrated salt 14.9g Mass of crucible, cover and anhydrous salt AFTER heating 14.3g What is the percent of water in the hydrated salt? MOLECULAR FORMULA FROM EMPIRICAL FORMULA The molecular formula of a compound can be determined from the empirical formula, if it is known. The molecular formula is a whole-number multiple of the empirical formula Ex: The empirical formula is CH and the molecular mass is 26. What is the molecular formula?

8 8' Packet'5b:'The'Mathematics'of'Formulas'and'Equations Step 1: Find formula/molecular mass of empirical formula Step 2: Divide molecular mass of compound by mass of empirical formula (result is an integer- if not you did something wrong) Step 3: Multiply the subscripts by this number to get the molecular formula. Ex: A compound has a molecular mass of 180 amu and an empirical formula of CH 2 O. What is its molecular formula? Interpreting Chemical Equations: Chemical equations can be interpreted either in terms of number of or number of Can be read 2 ways: 1. 1 molecule of nitrogen combines with 3 molecules in one molecule of ammonia there are 3 atoms of hydrogen. or 2. 1 mole of nitrogen combines with 3 moles...in 1 mole of ammonia there are 3 moles of hydrogen Ex: What is the total number of atoms of hydrogen to form one molecule of C 3 H 5 (OH) 3? Ex: What is the total number of moles of oxygen atoms present in 1 mole of Mg(ClO 3 ) 2? Problems Involving Chemical Equations Mole-Mole Problems Coefficients in a chemical equations give the ratios of moles of each substance

9 Packet'5b:'The'Mathematics'of'Formulas'and'Equations 9 What is the ratio of moles of N 2 consumed to moles of NH 3 produced? Using these ratios, the number of moles can be determined for any substance in the reaction by setting up a proportion. Ex: If 4.8 moles of H 2 react with N 2, how many moles of NH 3 will be produced? To solve: Identify problem (mole-mole) Put a box around the formulas in problem Take inventory along the bottom Fill in the known Use a proportion to solve for the unknown Ex: How many moles of HCl are needed to react with 2.3 moles of Zn? 2HCl + Zn ZnCl 2 + H 2 Purple Book p. 62 #1-5